An ecological and economical assessment

of the Falkland Islands inshore crab, Paralomis granulosa

by

Daniel David Hoggarth

A thesis submitted for the degree of Doctor of Philosophy and the Diploma of Imperial College in the Faculty of Science of the University of London.

1991

Renewable Resources Assessment Group Centre for Environmental Technology Imperial College of Science, Technology and Medicine 8 Princes Gardens London SW7 INA

1 Abstract

This thesis examines the potential of Falkland Island stocks of the lithodid crab Paralomis granulosa to support a commercial fishery.

From continuous observation of the 11-month period of commercial fishing on this stock, a model is developed for the standardisation of catch rates for variation in selectivity and effort. Local crab abundance, estimated from the corrected time series of catch and effort, is shown to be considerably less than previously thought.

A final 6-week period of purely experimental fishing and sampling, during the 1988 moulting and mating season, completed the field work. From the combined data base, the sizes at maturity are estimated and the life history strategy is described, following an analysis of the temporal and spatial organisation of the moulting and mating cycles. These cycles are shown to be biennial in most adults of both sexes, suggesting relatively low growth and mortality rates in this stock. Further (unsuccessful) attempts to quantify growth rates are described and the effects of parasitism by the rhizocephalan Briarosaccus callosus are investigated.

In a comparative examination of the lithodid crabs, P. granulosa is found to be the smallest and least productive member of the family. The potential of the Falkland Islands stock is shown to be particularly limited by the relatively small area of suitable inshore habitat.

The likely sustainable yields are estimated under various assumptions. The considerable logistical difficulties of exploiting the resource are discussed and the commercial viability of two possible fishing scenarios is assessed. At current price levels, it is shown that the small potential yields from this stock could not support a permanent industry located in the Falkland Islands. A single, self- contained vessel could fish economically, but only by fishing in infrequent pulses to maintain catch rates. Potential licence revenues and other management implications are discussed.

2 Acknowledgements

This research has been primarily supported by a grant from Stanley Fisheries Ltd., the commercial arm of the Falkland Islands Development Corporation. Generous financial support has also been provided by Witte Boyd Holdings Ltd, particulary during the final, important phase of research. I am grateful to the directors of the latter company, Mr. Thomas Boyd and Mr. Alan Johnson, both for this and for allowing me full access to their vessel, the ’Laura Jay’, during all its commercial operations in the Falkland Islands.

I would also like to thank the four skippers and the crewmen of the ’Laura Jay’ for their patience and cooperation in often difficult circumstances and the many Falkland Islanders whose kind and generous hospitality so assisted our work.

Finally, I give my thanks to all the staff and the other students of the Renewable Resources Assessment Group who have helped me during the last three years. For their ideas and discussions, I am particularly indebted to my supervisor, Dr. John Beddington, and to Mr. Mark Bravington and Dr. Andrew Rosenberg.

3 Table of Contents

4 Table of Contents

Page

Abstract 2

Acknowledgements 3

Table of contents 5

List of tables 11

List of figures 14

Chapters:

1. Introduction 18

1.1. Background to the exploitation of Falkland Island crabs 18

1.1.1. King crab fisheries 18 1.1.2. The Taiyo survey 19 1.1.3. The Fortoser study 19 1.1.4. Evaluation of the fishery proposals by ERL 21 1.1.5. Commercial exploitation - the SWB joint venture 22

1.2. Aims of the project 24

1.3. Observation of the fishery and data collection 26

1.3.1. The five phases of fishing and research 26 1.3.2. Data collection and the project database 28

1.4. Outline and structure of the thesis 36

2. Standardisation of CPUE and Estimation of Abundance 39

2.1. Introduction 39

2.2. Modelling of Selectivity: Prediction of Composition Corrected CPUE 44

2.2.1. Factors affecting the Size Composition of the catch 44

5 2.2.2. The Dependent Variable: Selectivity 46 2.2.3. The Independent Variables 51 2.2.4. Modelling Techniques 55 2.2.5. Data used in the analysis 56 2.2.6. Results of Modelling 56 2.2.7. The Selectivity Model 58 2.2.8. Application of the Selectivity Model 62

2.3. Modelling of Catch Size: Prediction of Effort Corrected CPUE 65

2.3.1. The Components of Fishing Effort 65 2.3.2. Data Used in the Analysis 66 2.3.3. Modelling of Composition Corrected CPUE on Soaktime 66 2.3.4. The Catch Rate Model 67

2.4. The Examination of CPUEadj and Estimation of Abundance 71

2.4.1. Examination of the raw data 71 2.4.2. The Leslie Catch-Effort method of Abundance Estimation 77 2.4.3. Results and Discussion 83

2.5. Estimation of the commercial biomass of Choiseul Sound for 1987 89

3. Biology of Paralomis granulosa in the Falkland Islands 94

3.1. Size at Maturity 94

3.1.1. Introduction 94 3.1.2. Definitions of maturity and patterns of growth 94 3.1.3. Estimation of the size at morphological maturity of males 98 3.1.4. Estimation of the size at functional maturity of females 105 3.1.5. Summary 111

3.2. Life History 112

3.2.1. Introduction 112 3.2.2. The effect of depth / habitat on the size distribution of crabs 112 3.2.3. Temporal organisation of the moulting and mating cycles 117 3.2.4. The effect of size on moult frequency 133 3.2.5. Spatial organisation of the moulting and mating cycles 140 3.2.6. Summary and Conclusions 152

3.3. Growth Rates 156

3.3.1. Methods of estimating growth rates of crustaceans 156

6 3.3.2. Estimation of growth rates by tagging methods 159 3.3.3. Examination of available length frequency data 160 3.3.4. Summary and conclusions 169

3.4. The effect of parasitism by B. callosus 171

4. Comparative biology of Paralomis granulosa 174

4.1. Introduction 174

4.2. Comparison of P. granulosa from Choiseul Sound and Adventure Sound 176

4.2.1. Introduction 176 4.2.2. Physical Environment 178 4.2.3. Relative Abundance 181 4.2.4. Size Distributions 181 4.2.5. Moult Stages 185 4.2.6. Weight at Length 185 4.2.7. Female Maturity 187 4.2.8. Prevalence of the parasite B. callosus 191 4.2.9. Summary and Conclusions 191

4.3. A qualitative examination of the commercial potential of P. granulosa in comparison with other lithodid crabs 194

4.3.1. Introduction 194 4.3.2. The relative commercial importance of the exploited lithodid crabs 196 4.3.3. Relative production from the individual growth of male crabs 205 4.3.4. Relative production from the reproductive rates of female crabs 213 4.3.5. Summary and conclusions 219

5. Bioeconomic Analysis 222

5.1. Introduction 222

5.2. Estimation of the sustainable yield 224

5.2.1. Estimation of the biomass of exploitable stocks 224 5.2.2. Assumptions about growth and mortality 225 5.2.3. Estimation of the equilibrium annual yield 228

7 5.2.4. Available yield and the pattern of exploitation 233

5.3. Logistic and financial aspects of development 236

5.3.1. Introduction 236 5.3.2. Relative distribution of stock and onshore facilities 236 5.3.3. Local weather conditions 240 5.3.4. Processing, marketing and product value 241 5.3.5. Labour availability 245 5.3.6. Fishery management regulations 246

5.4. Exploitation of the resource 249

5.4.1. Previous exploitation 249 5.4.2. Scenario 1. Continuous fishing with shore-based processing 251 5.4.3. Scenario 2. Pulse fishing with at-sea processing 255

5.5. Summary and conclusions 271

6. Discussion 274

6.1. The commercial potential of the stock 274

6.2. Management of the fishery 278

Appendices:

A l. Derivation of a simple linear equation for steady-state numbers at length and its potential use for the simultaneous estimation of Z/K and L m 284

A l.l. Estimation of Z from age-based data 284 A1.2. Estimation of Z/K from length-based data 284 A1.3. Simultaneous estimation of L and Z/K 288 A1.4. Discussion 290

A2. An age structured model for the prediction of future yields under variable fishing effort 293

A2.1. Basic structure of the model 293

8 A2.2. Decomposition of starting biomass into contribution of each age class 296 A2.3. Estimation of recruitment 298 A 2A . Estimation of future biomasses conditional on fishing mortality 298 A2.5. Use of fishing effort data 299 A2.6. Summation of biomasses and estimation of annual yields 300

References 302

Annex:

Hoggarth, D.D., 1990, The effects of parasitism by the rhizocephalan, Briarosaccus callosus on the lithodid crab, Paralomis granulosa in the Falkland Islands. Crustaceana 59: 156-170

9 List of tables

10 List of tables

Chapter 1 Page

Table 1. The duration of the five phases of fishing and research. 27

Table 2. The four main levels of the project database. 31

Table 3. Sampling effort in each of the five research phases. 34

Chapter 2

Table 1. The parameters of the 580 selectivity model for the prediction of composition corrected catch rates during phases 1-4. 60

Table 2. The parameters of the P80 selectivity model for the prediction of composition corrected catch rates during phase 5. 61

Table 3. The parameters of the Catch Rate model for the prediction of effort corrected CPUE. 69

Table 4. Monthly catch and effort statistics. 76

Table 5. Leslie method regression statistics for the estimation of stock size at four levels of natural maturity. 87

Table 6. The estimated total numbers and weights of male crabs in Choiseul Sound at the start of December 1987. 92

Chapter 3

Table 1. The percentages of adult male crabs in Choiseul Sound in each moult stage and reproductive condition in each month. 130

Table 2. The characteristics of the seven communities identified by the cluster analysis. 149

Chapter 4

Table 1. A comparison of the biological characteristics of crabs sampled from Choiseul Sound and Adventure Sound during July, 1988. 180

11 Table 2. The relative commercial importance of different stocks of lithodid crabs. 204

Table 3. Relative sizes of male lithodid crabs. 211

Table 4. Approximate relative growth rates of male lithodid crabs. 212

Table 5. Factors affecting the reproductive potential of female lithodid crabs. 217

Table 6. Publications referred to in tables 2-5. 218

Chapter 5

Table 1. The areas inhabited by P, granulosa (from Fortoser, 1986(b)) and the estimated available biomasses of crabs. 224

Table 2. Potential annual yields expressed as fractions of the unexploited recruited biomasses for the likely range of M and K and c = 0.7. 232

Table 3. Potential annual yields from the Falkland Islands for the likely range of M and K and c = 0.7. 232

Table 4. Estimated costs and values for scenario 1 (continuous fishing). 253

Table 5. Estimated costs and values for scenario 2 (pulse fishing). 267

Table 6. The short-term viability of the pulse fishing scenario for the likely range of fishing effort and natural mortality. 268

Table 7. The long-term viability of the pulse fishing scenario for the likely range of natural mortality and discount rate. 268

12 List of figures

13 List of figures

An illustration of the effect of variable selectivity on CPUE. 40

Size compositions of two real catches from periods of extreme selectivities. 41

A length converted Log catch curve of the landed catch samples indicating full selection of crabs over 80mm CL. 50

The original 237 Selectivity (580) data points, plotted against time, for phases 1-5 of commercial exploitation. 53

A plot of the 58 0crew data points and the fitted function, used to represent crew selectivity. 64

The catch rate model: /(Composition Corrected CPUE) vs. Log Soaktime, with the fitted equation superimposed. 70

The catch rate model plotted with back-transformed variables: Composition Corrected CPUE vs. Soaktime. 70

The raw CPUE data plotted against time and the CPUEadj data after correction for catch composition and fishing effort. 75

Monthly variation in the corrected (CPUEadj) catch rates. 76

The monthly CPUEadj plotted against cumulative catch, with the fitted line from the weighted Leslie estimate of total abundance with M = 0. 87

Confidence intervals (% probability) for the true initial population size, N q, for the December and January data sets, at two levels of natural mortality. 88

The number and the estimated weight of male crabs sampled from Choiseul Sound in each 1mm class of carapace length. 91

Chelae length plotted against carapace length on logarithmic scales indicating the estimated size at male maturity.

14 The proportion of female P. granulosa in ovigerous condition in 1mm classes of carapace length indicating the estimated size at female maturity. 110

Length frequencies of male crabs from four habitat types. 115

Length frequencies of female crabs from four habitat types. 116

The monthly percentages of adult male crabs in Choiseul Sound in each moult stage and the average surface sea temperature (°C) in each month. 131

The monthly percentages of adult female crabs in Choiseul Sound in each category of moult stage and reproductive condition. 132

The size-specific proportions of male crabs in recently moulted condition during the 1988 moult season in Choiseul Sound. 138

The size-specific proportions of female crabs in recently moulted condition during the 1988 moult season in Choiseul Sound. 139

The spatial distribution of clusters (communities) during the non-moulting or ’off season, between January and August, in Choiseul Sound. 150

The spatial distribution of clusters (communities) during the moulting season, between September and December, in Choiseul Sound. 151

Monthly length frequencies of male crabs sampled from small meshed CR pots in all regions of Choiseul Sound during 1987 and 1988. 166

Monthly length frequencies of female crabs sampled from small meshed CR pots in all regions of Choiseul Sound during 1987 and 1988. 167

The monthly mean carapace lengths of male and female crabs and the monthly mean surface sea temperature (°C). 168

15 Chapter 4

Figure 1. The size compositions of female and male crabs sampled from Choiseul Sound and Adventure Sound from two pot types during July, 1988. 184

Figure 2. The proportions of female P. granulosa in ovigerous condition in 1mm classes of carapace length in Choiseul Sound and Adventure Sound indicating the estimated sizes at female maturity. 190

Chapter 5

Figure 1. The distribution of P. granulosa in the Falkland Islands (redrawn from Fortoser, 1986(b)). 239

Figure 2. An illustration of the scenario 2 (pulse fishing) model showing the future harvesting of the fishery at the minimum interpulse periods for two levels of fishing effort. 269

Figure 3. The influence of Interpulse Period on the Net Present Value of the fishery at two levels of the discount rate. 270

Appendix 2

Figure 1. An illustration of the matrix format of the age-structured model for prediction of future yields under variable fishing mortality. 295

16 Chapter 1

17 1.1. Background

1. Introduction

1.1. Background to the exploitation of Falkland Island crabs

1.1.1. King crab fisheries

This thesis is about the ecology and the commercial potential of the false king crab, Paralomis granulosa , of the Falkland Islands. King crabs (Crustacea,

Decapoda, Anomura, Lithodidae) are found over a wide range of depths in all the oceans of the world and support some of the most important of all the crab fisheries. At its peak in 1980, the largest of these fisheries, for the red king crab, Paralithodes camtschatica , in the South-Eastern Bering Sea, produced a massive yield of almost 59,000 tonnes (Otto, 1986). The subject of this study, P. granulosa , is a relatively small species found in the inshore waters of both the

Falkland Islands and around much of the southern tip of South America, from

42°S on the Pacific side to 24°S in the Atlantic (Campodonico et al , 1983).

While not of the same importance as the red king crab, P. granulosa (in addition to the larger Lithodes antarctica) has supported a significant local fishery in the

Straits of Magellan since 1977, producing a maximum recorded yield of 952 tonnes in 1979 (CORFO, 1981; Fortoser, 1986(a)). The fishery has been described in a number of papers, summarised in Campodonico et al , 1983. The life history and population dynamics of the stock, however, remain poorly understood and the fishery is simply managed, using such measures as minimum legal sizes and gear restrictions (CORFO, 1981).

The commercial viability of the Falkland Island crab population has been a subject of interest and speculation for some time. Prior to this research, two resource surveys had already been made, but without drawing firm conclusions.

The following sections give the relevant historical background and the main results of these previous investigations.

18 1.1. Background

1.1.2. The Taivo Survey

The first documented researches on the inshore waters of the Falkland Islands were made by the Taiyo Fishery Company, Ltd. of Tokyo in 1976 with the support of the Falkland Islands Company (Taiyo, 1976). Three short research cruises were made on a small, locally chartered vessel and crabs were sampled by strings of pots from about a dozen different locations around the islands. In certain places, good numbers of crabs were caught, but the individual crabs were mostly "too small in size to assure profitable commercial operations". The marketability of the crab and the facilities for cold storage and transport in this undeveloped location were also questioned. The larger species, L . a n ta r c tic a was captured in one location in the Falkland Islands and was felt to offer greater potential if higher concentrations could be found. Apparently, the survey was not followed up and no further inshore fishing activity took place until eight years later.

1.1.3. The Fortoser Study

Since the ’Falklands conflict’ of 1982, interest in the islands and their resources has increased. In 1984, the Falkland Islands Development Corporation (FIDC) contracted Fortoser Ltd. of Grimsby to undertake a more detailed survey of the inshore resources of these waters. Particular attention was to be placed on species suitable for exportation, with low bulk and potentially high commercial value. Suitable methods of fish capture, handling, processing, marketing and distribution were all to be investigated and recommendations made for the development of a new inshore fishing industry (Fortoser, 1986(c)).

An 18m inshore fishing vessel, the ’Coastal Pioneer’, was delivered to the islands for this purpose, arriving in November 1984. After trying a number of fishing methods and taking limited catches of roundfish, skate, squat lobsters, queen scallops, squid and octopus, it was soon decided that the two crab species

19 1.1. Background offered the best prospects for an inshore fishery. Both P. granulosa and L. antarcticus were found, but only the former in commercially viable quantities.

Early samples of P. granulosa sent to J. Van Smirren Ltd., a shellfish and fish processing company from Boston, Lincolnshire, found that the meat quality was excellent, identical to that of king crab, and capable of fetching the premium market prices. All further effort was directed to quantifying the crab resources and assessing suitable industry practices.

Over the next year, Fortoser sampled much of the inshore waters of the

Falkland Islands using both pots and a small beam trawl in an intensive grid survey. The highest concentrations of crabs were found to occur in the region known as Lafonia, in the southern half of East Falkland (Fortoser, 1986(b)).

Other concentrations in western and northern waters were small by comparison, of low density and remote from the main centres of population. It became evident that any future industry would need to be primarily based in the Lafonia area.

In 1986, Fortoser started a pilot fishing industry with the creation of the locally- registered company, Falkland Seafoods Ltd. A factoiy unit was prepared in the main population centre of Stanley in East Falkland, near to the main stocks, and the ’Coastal Pioneer’ started fishing on a full commercial scale in Choiseul

Sound, one of several large bays in Lafonia. Catches were landed either at

Mare Harbour (the only suitable port in Lafonia) and transported by road to the factory, or else carried directly by the ’Coastal Pioneer’ on her weekly visits for re-fuelling and supplies. At the factory, the crabs were boiled and the meat extracted manually by local labourers before blast freezing and cold storage.

Only the larger crabs were found to be suitable for this type of hand processing and the catches were restricted to those animals in excess of 75mm carapace length. The females, being virtually all smaller than this size, were excluded from the landings and returned alive to the sea. Using only these larger males, a meat yield of approximately 20% was achieved at commercial rates of production. In five months, over the austral winter of 1986, the ’Coastal

20 1.1. Background

Pioneer’ hauled 8309 pots and landed over 19 tonnes of crabs from Choiseul Sound. Considering only the ’legal-sized’ crabs over 75mm, the average catch rate in this virgin fishery was 2.1kg per pot hauled.

During the same period, Fortoser’s marine biologist estimated the potential annual yield of the Lafonia stocks at between 168 and 252 tonnes using the well- known formula, Yield = 0.5 M B0 of Gulland (1970) (Fortoser, 1986(b)). The biomass estimate used in this calculation was derived by raising a single density estimate (obtained by mark-recapture methods) to the total abundance of the region using the grid-survey results. The uncertainties of these methods were acknowledged by Fortoser (op cit) and the estimate was recognised as neither reliable, nor conservative. In addition, the size at maturity of male crabs was roughly estimated at well below 75mm and it was concluded that the reproductive potential of the stock should not be affected by harvesting those crabs above the commercially viable size limit.

The final conclusions of Fortoser (1986(c)) suggested that, with a sustainable yield of 250 tonnes per annum and factory processing of the catches in Stanley, a two-boat inshore fishing industry could be successful. Markets were investigated and the tariff-free entry of Falkland Island products into EEC markets made this the most likely destination. At the expected retail value of £9/kg for the processed crab meat, an annual turnover of £0.5 million was felt to be "not unreasonable". Detailed financial proposals for the expansion of the industry were submitted by Fortoser Ltd. to FIDC in November 1986.

1.1.4. Evaluation of the fishery proposals by Environmental Resources Ltd.

For an unbiased comment on the Fortoser survey, and that company's future proposals, FIDC approached the consultants Environmental Resources Ltd. (ERL) for their assessment of the available material. ERLs principal conclusions were as follows. Although the estimate of potential yield was felt to be "well

21 1.1. Background based on the relatively limited data available", the financial success of the venture was shown to be critically dependent on the attainable yield being close to the upper end of the range given. In view of the assumptions made and the methods used, this was seen as "somewhat speculative". Still further concern was expressed about the apparent lack of consideration given by Fortoser to the logistical constraints of the location and the difficulties of achieving a satisfactory distribution of effort. In all, the viability of the project was felt to be unproven.

1.1.5. Commercial exploitation - the SWB joint venture

Full commercial exploitation of the Falkland Islands’ inshore crab stocks finally began in September 1987. In full awareness of the recent survey results, Stanley Fisheries Ltd. (SFL), the commercial arm of FIDC, entered into a joint venture arrangement with Witte Boyd Holdings Ltd. of Hull, creating a further company SWB Fisheries Ltd. Falkland Seafoods Ltd. was purchased as the trading branch of this joint venture, along with the Stanley processing factory and all its machinery. The ’Coastal Pioneer’ returned to the UK and a much smaller (11m), GRP-built Devon crabber, the ’Laura Jay’ was purchased and delivered to the Falkland Islands, along with an experienced UK crew and around 300 purpose made pots.

The ’Laura Jay’ started fishing in Choiseul Sound on 1 September 1987, using the same mode of operation as the ’Coastal Pioneer’, delivering catches by road, usually twice a week, to the Stanley factory. The more efficient fishing practices and the greater resulting effort of the ’Laura Jay’ soon showed that localised catches declined far more rapidly after their initial exploitation than had been suggested by Fortoser. The density (and hence the overall abundance) estimates of Fortoser were quickly disputed, when the location of the tagging exercise yielded only one fifteenth of its reputedly available stock before catch rates declined. Both the catch rates and the overall level of optimism were briefly improved after the sudden recruitment and growth associated with the male

2 2 1.1. Background moult season in October and November of 1987. Similar improvements were noted with the congregation of crabs in shallower feeding grounds over the austral summer. Exploitation continued into 1988, but on the whole, catches in Choiseul Sound were disappointing and gradually declined to uneconomic levels. In the austral winter of 1988, two extended visits were made to Adventure Sound, in the south of Lafonia and yet further from the factory in Stanley. Catches there were indeed better than in the depleted Choiseul Sound, but the inclement weather, the small size of the ’Laura Jay’ and the lack of shore-based facilities made such excursions logistically difficult. A later report by one of the skippers of the ’Laura Jay’ (Whitehead, 1987) suggests that SWB may have been under the impression that the Choiseul Sound fishery alone would be capable of supporting "at least two boats", although this was never implied in the written documentation of Fortoser. Commercial operations finally ceased, with significant financial losses, at the end of July 1988 after a total catch of only 39 tonnes from this brief 11-months of exploitation. At the time of writing (December 1990), no further exploitation has occurred since that time.

23 1.2. Aims of the project

1.2. Aims of the project

The research detailed in this thesis began on 1 August 1987, after the Fortoser study, in the early, optimistic days of the SWB joint venture and the first commercial catches of the ’Laura Jay’. The research has been financed by a grant from Stanley Fisheries Ltd., the commercial subsidiary of FIDC and the majority (51%) shareholder of the joint venture company. At the beginning, the greatest potential of the Falkland Islands’ inshore waters and the subject of the new fishery had already been identified as the false king crab, P. granulosa. The distribution of the stock had been well described and suitable commercial practices identified. Still very little, however, was known about the ecology and the population dynamics of the species. The broad aims of this research were thus to continue the studies of Fortoser, to provide a greater understanding of the biology of the stock and to refine the previously wide-ranging and uncertain estimates of the potential yield.

Surprisingly, no official terms of reference were ever provided by SFL. Given both the commercial and developmental interests of the sponsors, it was felt that the research should concentrate mainly on better quantifying the potential yield of the stock, but also on providing a suitable management strategy for the new industry. On the commercial side, considerable attention has been paid to the practicalities, the logistics and the financial realities of actually harvesting the available yield from this very undeveloped location. On the stock management side, the approach taken has been necessarily somewhat simpler. Over the past ten years or so, the management of crustaceans, indeed all those invertebrate and tropical animals for which age determination is difficult, has become increasingly sophisticated. Both length-based methods of assessment and moult- based growth models are now well established (for example applications, see Bannister, 1986 and Campbell, 1986 respectively). Furthermore, the most valuable crustacean stocks are actively managed (though not always successfully), to promote both biological and economic stability by the careful use of catch quotas and effort limitation (eg. Otto, 1986). From the outset, however, it was

24 1.2. Aims of the project realised that the potential yield of the Falkland Islands’ inshore zone was likely to be small, perhaps supporting only a two-boat fishery as suggested by Fortoser (1986(c)). As with many other small crustacean stocks (Jamieson, 1986), Falkland Islands P. granulosa will probably never justify the cost or the effort required for the more active management strategies. Such small and often low density and widely scattered resources are better managed with simple and easily enforceable measures such as minimum legal sizes and closed seasons. These methods are intended both to protect the reproductive potential of the stock and to prevent wasteful fishing activities, thereby maximising the yield available from whatever level of recruitment naturally occurs (Jamieson & Caddy, 1986).

Given these stated intentions, and little more than a simple distribution map of the stock from the previous researches, much of this thesis is devoted to the estimation of the basic stock parameters needed for such aims. These include the abundance of the Falkland Islands’ stock and the life history, maturation and growth rates of the animals. In the absence of officially-defined research objectives, considerable attention has also been given to the interesting comparative ecology of this largely unstudied species.

25 1.3. Data collection

1.3. Observation of the fishery and data collection

1.3.1. The five phases of fishing and research

The practical work of this research occurred during five distinct periods, corresponding to separate periods of activity of the ’Laura Jay’ and referred to in this thesis as phases 1 to 5 (table 1). The 11-month commercial exploitation of the SWB joint venture (section 1.1.5.) took place during the first four of these phases; the final phase 5 was a special period, devoted purely to research with all the catches being returned to the sea immediately after sampling and measurement.

The duration of each of the phases was the result of SWB’s policy of hiring expatriate labour for the project for single 100-day contracts. Phases 1 and 2 in late 1987 (table 1) thus, in fact, relate to one single contract period, divided into two halves on the discovery of the male moult season during late October, when the majority of crabs were too soft to process. Phases 3 and 4 formed the second and the final phases of commercial activity. Different skippers and crews were employed for each separate contract. The author of this thesis worked in the Falkland Islands for the duration of these four phases as a scientific observer of the fishery. Permission was granted by SWB for the observer to work on board the ’Laura Jay’ with full access to the catches for sampling purposes, both before and after sorting. More than half the fishing activities of the ’Laura Jay’ were ’observed’ and sampled during this time (table 1): during the remaining days, the processed data were entered into a computer database for safe storage. Given the main commercial objectives of the ’Laura Jay’, such scientific presence at this time was purely observational. The daily activities and the fishing pattern of the boat remained the complete responsibility of the skipper.

A s s h o w n in table 1 and discussed in section 1.1.5., the ’Laura Jay’ operated almost exclusively and continuously in the Choiseul Sound area during these

26 1.3. Data collection commercial phases. Both catch-effort and biological time series have thus been recorded from this location for almost the full annual cycle and both the local abundance and the cyclic nature of the life history strategy have subsequently been analysed using these data. A number of other fishing grounds on the Lafonia coastline have also been briefly visited and the limited data from these have been used to verify the relevance of statistics estimated from the Choiseul Sound data to the Falkland Islands stock as a whole.

Table 1. The duration of the five phases of fishing and research. (CS = Choiseul Sound, AS = Adventure Sound, BS = Berkeley Sound)

Days Fishing Days Duration Observed of phase Area: CS AS BS Total Phase

1 31 2 2 35 22 9 Sep 87 to 3 Nov 87 2 17 17 4 23 Nov 87 to 15 Dec 87 3 72 72 44 6 Jan 88 to 4 Apr 88 4 58 6 64 40 30 Apr 88 to 1 Aug 88 5 25 25 25 28 Oct 88 to 5 Dec 88

Totals 203 8 2 213 135

Month: J F M A M J J A S O N D Year

1987 1 1 1 1 2

1988 i 3 1 1 4 1 1 5 1

The commercial fishery closed at the end of phase 4 in August 1988 (section 1.1.5.). While much useful information had been successfully recorded, it was

27 1.3. Data collection realised that the available data probably would not be sufficient to assess the growth and mortality rates needed for subsequent estimation of potential yield. In addition, for a variety of reasons, the 1987 moulting and mating seasons had been veiy poorly sampled, so that much of the life history and behaviour of the stock still remained largely unknown. A further short phase of fishing activity was thus proposed, devoted entirely to answering these important questions and timed to coincide with the 1988 moulting and mating seasons. At this time, considerable uncertainty surrounded not just the future of the inshore crab fishery but the future funding of all the FIDC joint venture companies. It was thus several weeks before the research proposal was finally accepted and, in the end, phase 5 was generously sponsored by the fishing company Witte Boyd Holdings Ltd. Yet another new skipper and crew were recruited and a five week period of fishing and sampling began under wholly scientific direction. Resulting from this, the life history and migratory behaviour of the stock has been greatly clarified and though the delay in starting proved too great to estimate complete growth rates by the intended tagging procedures, the insights gained about moult frequency have considerably refined the previous estimates of the fishery’s potential. Due to financial restraints and decreasing optimism about the fishery, it is thought that any proposals for further fieldwork on this subject would not have been supported.

1.3.2. Data collection and the project database

The usual fishery data have been recorded, including catch and effort statistics and length frequencies of both the unsorted and the landed catches. Crabs have been caught from strings of between 25 and 60 pots. Catch-effort data have been noted for every such string hauled: on those days not ’observed’, the minimal catch-effort data have been subsequently extracted from the skipper’s logbooks.

The length frequency and other biological data have been sampled and

28 1.3. Data collection processed only by the scientific observer on those days spent at sea, thus ensuring both reliability and accuracy. For the unsorted catches, the individual pots have been used as ’sampling units’. Depending on the time available and on the fullness of the pots, between zero and eight such ’pot samples’ have been taken from each string observed. The usual practice has been to select a number of pots and measure the whole contents of each one. Sampling has, however, been slightly biased towards male crabs due to their greater commercial importance and wider size range. For some particularly full pots, then, only the males have actually been measured, especially when sufficient females had already been sampled from other pots from the same string. A number of different pot types have been used in the fishery varying both in shape and mesh size: the majority of samples have been taken from the pot type with the smallest mesh so as to obtain the maximum information on the widest size range of animals.

The raw data have been entered into a computerised, custom-designed project database. The database is primarily composed of four main tables, containing separate data for (1) each day of fishing, (2) each string hauled, (3) each pot sample taken and (4) each crab sampled. A ’relational’ database has been used, whereby a number of ’key variables’ allow the data from one table to be related to those in any other table. Such a structure allows great flexibility in later analyses, so that catch and length data for example can be summarised over any variable of interest: time period, area, pot type or whatever. The main structure of the database, including the relational key variables, is illustrated in table 2. The following sub-sections describe the most important variables measured or sampled at each of these main database levels. Further details are given in the methodological sections of certain chapters.

In addition to this main structure, a number of subsidiary tables have also been constructed using data collected for special purposes. Most importantly, the size composition of the landed catches has also been monitored to examine the effect of variable selectivity on the fishery. In this case each string has been taken as

29 1.3. Data collection a sampling unit, so that the whole retained catch of those strings observed has usually been measured. Further key variables have allowed these data also to be related to the time of sampling, or the pot type or the soaktime etc. producing the observed catch.

30 1.3. Data collection

Table 2. The four main levels of the project database.

Table: Daily String Pot sample Crab

Key variables: Date Date (hauled) String no. String no. String no. Pot sample no. Pot sample no.

Other variables: Weather Location Morphology

Wind direction Latitude Carapace length (mm) Wind strength Longitude Sex Sea temp. (°C) Depth (m) Chelae length (mm) Bottom type Female maturity stage Live weight (g) Moult stage Parasitised? Effort Effort

Pot type Sample pot type Number of pots Date set Time set Time hauled Soaktime

Landed catch Pot catch

Number retained Number caught Boxes Number sampled Weight (kg)

Comments Comments Comments

Observer

31 1.3. Data collection

Database level 1: Daily data

Only the raw data on weather conditions and any ’comments’ applying to the whole days fishing have been recorded in this table, although, as noted before, much of the data from the lower tables can easily be summarised on a daily basis. The surface sea temperature (°C) and the wind strength (Beaufort scale) and direction have been recorded before leaving harbour, at the start of each fishing day, usually in the early mornings.

Database level 2: String data

The data recorded for each string may be divided into three sections: the location of the string, the ’effort’ applied and the resulting catch (table 2). String locations have been noted at sea during shooting with the help of the variable range marker and direction finder of the boat’s radar. The distance and direction of each end of the string has been recorded in relation to the nearest useful landmarks. The two resulting coordinates for each string have later been plotted on a chart and the latitude and longitude of the mid-point of the string estimated and recorded on the log-sheet and in the database. The approximate depth of the ground fished and a three category ’bottom type’ classification have been taken from the pattern and the colour of the echo-sounder trace.

The fishing effort of each string has initially been recorded as the number and type of pots used and the soaktime (in hours and minutes from the start of shooting to the start of hauling, some days later). Pot type has been recorded in the database as a mnemonic code. Three basic varieties of English style pots have been regularly used in the fishery, two inkwell designs (FIW and DIWE) and one creel (CR). Various alterations involving escape holes (CRE and CRE2), a brief trial with large Chilean inkwell pots (CIW) and the use of a particularly small meshed pot (JAP) for research sampling have meant that, in all, seven different pot types have been used. All the commercial pot types had

32 1.3. Data collection single, plastic, top-mounted funnels, the main differences being due, not to any structural factors, but to the sizes of the original meshes and any escape holes fitted. With further variability in soaktimes, from only one day to almost a month, the real fishing effort of different strings has been far from constant and it has been necessary to standardise the apparent catch rates using the landed catch length frequency data in a model described in chapter 2. The same bait, locally obtained mutton, has, however, been used in nearly all strings: fish, squid and even local geese have also been tried on occasions but without any obvious differences in attractiveness.

Catches have been recorded at sea as the number of 40kg ’boxes' of crabs retained, to the nearest eighth of a box. The total weight of crabs subsequently landed at the factory at the end of each trip has then been divided between the strings in proportion to the number of boxes taken from each one. Such an approach has been used to avoid the necessity of weighing the individual catches at sea, which proved impossible except on the very infrequent calm days.

Database level 3: Pot Sample data

Relatively few variables are actually contained in this table: it exists primarily to separate samples taken from different pots in a string. Although each string was initially made up of only one single type of pot, to allow safe stacking during hauling, one or two of the small meshed research pots have also occasionally been included for sampling purposes. More than one pot type has then sometimes been sampled from a single string. The pot type records in this table thus enable the variability between individual pots to be assessed and the data from different pot types to be processed separately.

As noted in table 1, 135 days of fishing activity have been observed in detail at sea. The actual numbers of strings hauled and observed in each phase and the number and sizes of samples taken are presented in table 3. With total sample

33 1.3. Data collection

sizes of over 50,000 crabs from the unsorted pot samples and over 30,000 from

the landed catches, the data form a substantial record of both the biology of P. g r a n u lo s a and the entire history of this short-lived fishery.

Table 3. Sampling effort in each of the five research phases

Phase Number of Strings: Unsorted Catch Landed Catch

Hauled Observed Sampled Number Total Number Total o f sample of sample samples size samples size

1 168 117 96 162 5704 0 0 2 58 21 32 46 2404 1 372 3 343 216 193 481 20334 18 3295 4 349 220 91 197 10334 212 23136 5 89 89 74 316 16583 31 5017

Totals 1007 663 486 1202 55369 262 31820

Database level 4: Crab data

This final database level records the biological and morphometrical details of each crab sampled. Every single crab forms an individual record in the database, which is expensive in terms of computer memory, but does allow easy summaries of the biological data to be made against any variable of interest. All crabs have been sexed, according to the shape of the abdomen (broadly straight and pointed in males, rounded and curved in females) and measured for carapace length. The majority of the animals have also been classified according to moult stage, maturity stage (females) and inspected for the presence of the rhizocephalan parasite Briarosaccus callosus. This parasite, uncommon in the Falkland Islands but more prevalent elsewhere, affects the maturity and development of lithodid crabs and such parasitised crabs have been excluded from many of the analyses. The above data have been recorded for those samples processed while at sea. A small number of the samples have been saved until later and worked up more fully in the crab factory in Stanley. Such

34 1.3. Data collection animals have been weighed (difficult at sea) and, in the case of males, measured for chelae length to determine the size at sexual maturity.

35 1.4. Thesis structure

1.4. Outline and structure of the thesis

Following this section, the thesis is subdivided into four main chapters, a brief final discussion, two appendices and one annexed publication.

In chapter 2, a regression model is developed for the standardisation of catch rates allowing for variation in selectivity and fishing effort. The corrected CPUE data are used in the same chapter to estimate the total abundance and biomass of Choiseul Sound by the ’removal’ method and in later chapters to interpret the migration and life history pattern of the stock.

Chapter 3 is devoted to the estimation of the basic biology of the Choiseul Sound stock and is divided into four subsections. Firstly, the sizes at maturity of male and female crabs are estimated. Secondly, the life history is examined, in particular the temporal and spatial organisation of the moulting and mating cycles. In a third section, growth rates are investigated and the final section summarises the relevant effects of the parasite, Briarosaccus callosus. A full report on the latter topic, annexed to the thesis, has recently been published in the journal Crustaceana. Such biological results are used both to determine applicable management regulations and for their implications on the potential yield of the stock.

Chapter 4 concerns two aspects of the comparative biology of P. granulosa. As stated before, the parameters estimated in chapter 3 relate only to those crabs sampled from the Choiseul Sound region. In the first half of this chapter, these results are compared with the limited data taken from the more southerly Adventure Sound as an indication of their applicability to the Falkland Island stock as a whole. In a second comparative study, the likely productivity of the local stock is contrasted with that of other stocks of lithodid crabs around the world.

Chapter 5 involves two main aspects of the bioeconomics of the fishery. First,

36 1.4. Thesis structure

the maximum potential equilibrium yield is calculated, conditional on the estimated biomass and likely levels of growth and natural mortality. After discussing the logistic and financial restraints of this special fishery, this potential equilibrium harvest is shown to be uneconomical. A more realistic and potentially profitable pulse fishing approach is then examined using a dynamic yield model to investigate optimal harvest strategies and long-term revenues.

Most sections include their own summaries and discussions. The main conclusions and their implications, both for industry and management are also briefly discussed together in the concluding chapter 6.

37 Chapter 2

38 2.1. CPUE Introduction

2. Standardisation of CPUE and Estimation of Abundance

2.1. Introduction

The investigation of changes in relative abundance is basic to the assessment of any developing fishery. Such changes, with additional information on the biology and distribution of the stock, can lead to an understanding of the migrational behaviour and life history of the animal. Further, in relation to the pattern of exploitation, they can also be used to estimate total abundance by Leslie / DeLury type methods (Seber, 1982).

An index of relative abundance can be obtained by the use of data on catch per unit effort (CPUE). This index is generally taken to be directly proportional to abundance, but for this to be true, a number of conditions must first be satisfied (Cooke & Beddington, 1984). The nominal CPUE from the Falkland Islands inshore crab fishery has been recorded for all commercial operations in terms of kg per pot hauled (Gulland, 1983). In this basic form, the index fails to satisfy the following two conditions. Firstly, the catch part of CPUE should have a constant size composition; secondly, the index of effort should adequately describe the amount of fishing. The latter factor has been well studied in many trap fisheries, particularly the effect that variations in soaktime have on effort and catches. The former, related to the size selectivity of both the gear and the fishermen, has been less commonly studied in this context. As will be seen, however, the effect of such variable selectivity is far from unimportant (see also Smith & Jamieson, 1989). The basic reasons for these inadequacies of the nominal CPUE are discussed in the remainder of this introduction. Their detailed solutions leading to the final ’CPUEadj’, in a form thought to be proportional to abundance, are the subjects of sections 2.2. and 2.3..

In a normal fishing situation the aim of individual fishermen will generally be to

39 2.1. CPUE Introduction maximise their catch and profits. The conflicting interests of the fishermen to land the largest catch, and the processing industry to buy only the larger animals, will tend to lead to an early stabilisation of the mean size at selection, which will then remain constant with time. However, due to the constant wage policy of the fishermen employed in the Falklands fishery, it has not always been their aim to land the maximum catch. Factors such as the ease of handling of the gear, as well as the persuasions of the processors have also been dominant at certain times. As a result selectivity has not stabilised and the composition of catches has varied both with time and between different gear types.

As an illustration of the effect of selectivity on CPUE, consider figure 1 below, where curve A represents the size composition of the target species on the fishing ground at any one time.

Two hauls made on that ground, on the same day, could produce the catches represented by curves labelled B and C; catch C simply having, for one reason or another, a higher selectivity pattern than catch B. Although both hauls came from the same ground, of constant abundance, the nominal CPUE (kg/pot) of catch B would be greater than that of catch C.

A correct CPUE could only be obtained by calculating the catch rate above some chosen size limit (e.g. SL in figure 1) where all sizes in the catch would be fully selected. This corrected CPUE would then be equal for the two catches, as was the underlying abundance.

Figure 1.

An illustration of the effect of variable Frequency selectivity on CPUE.

The nominal catch B would be greater than catch C, while the composition corrected catches, above size limit SL, Length would be equal. (See text.)

40 2.1. CPUE Introduction

Note that the two catches need not come from the same ground on the same day. The example simply illustrates the fact that selectivity must be taken into account when expressing CPUEs.

To produce such a correction exactly, the size composition of each haul must be known. For this fishery, however, the majority of commercial catches have only been recorded as total weight, with no knowledge of the size composition of those catches. Given sufficient data from the more closely observed hauls, though, the dependent variable, selectivity can be modelled on its various causal factors. Using this model, the ’composition corrected CPUE’ can then be predicted for all the nominally observed strings.

This selectivity model takes the form of a multiple linear regression, the details of which are given in the first and major part of this section. The importance of the correction must not be underestimated for this fishery. As only a small proportion of the larger animals are actually suitable for processing, even a small change in size at selection has a great effect on the nominal catch rate. Figure

2 shows two real length frequencies of catches from periods with extreme selectivities. Note that the catches of larger crabs (over an imaginary length equivalent to SL) are approximately equal. If the same level of effort had been used for the two catches, then the underlying abundances must also have been the same. However, the uncorrected, nominal CPUE for the ’larger’ catch is over treble that of the ’smaller’ catch, in terms of numbers, and still more than double when expressed as kg/pot. This great difference is due only to a change in selectivity of less than 1cm.

Figure 2.

Size compositions of two real catches from periods of extreme selectivities.

A decrease in size at selection of less than 1 cm more than doubles the nominal catch rate. 2.1. CPUE Introduction

Secondly, the effect of incorrect definition of effort must be considered. In many trap fisheries, a longer soaktime, within a certain range, usually results in a greater catch/pot. Such a catch, however, does not rise in proportion to soaktime, so that the catch/pot/day decreases with soaktime (Skud, 1979; Boutillier, 1986). Thus, in a pot fishery with variable soaktimes, neither of these catch rates gives a valid index of abundance.

The majority of strings in this fishery have been hauled between one and four days after shooting. The shortest soaktime recorded is 14.2 hours, and for various operational reasons, some strings have not been hauled for over two weeks. Such wide variation in soaktimes and hence in fishing effort must be standardised. This is achieved in section 2.3. by modelling the non-linear relationship between nominal catch rate (after correction for selectivity) and soaktime. The actual model is fitted by a simple linear regression of the variables after suitable transformations have been made. The eventual unit of effort produced by this model, as used in many trap fisheries, is a single pot fished for a standard soaktime of 24 hours (Austin, 1977; Skud, 1979; Rothschild e t a l, 1970 in Blau, 1986).

With corrections thus made, both to catch and effort, CPUE is finally presented in a form, as far as possible, proportional to abundance. The corrected time series of data is examined in detail in section 2.4. and is used to estimate the total abundance of crabs in Choiseul Sound and in a number of later analyses.

At this stage, it is assumed that a linear relationship does exist between CPUE and abundance. Considering the possibility of variation in catchability and gear saturation, particularly for the small-meshed pot types, this assumption may be invalid (Miller, 1979; Gulland, 1983; Cooke & Beddington, 1984). Catch rates in the Falkland Islands, however, are low compared to those of most other lithodid fisheries (see section 4.3.2.) and the high abundances associated with non­ proportional CPUEs are probably uncommon. The assumption of linearity is

42 2.1. CPUE Introduction therefore likely to be acceptable in this case, at least over the main part of the range of abundances observed.

43 2.2. Selectivity model

2.2. M o d e l l i n g o f Selectivity: Prediction o f Co m p o s i t i o n C o r r e c t e d C P U E

2.2.1. Factors Affecting the Size Composition of the Catch

Size at Crew Selection

Catches of P. granulosa in the Falkland Islands have been processed by hand picking, assisted by the use of compressed air and mangles. A higher meat yield is thus obtained per unit processing time, as the size of crabs in the landed catch increases. For this reason, the factory has always encouraged the fishermen only to keep crabs above a certain size limit. Below this size it becomes uneconomic to process the catch by hand.

The pots used in this fishery catch many crabs too small to keep and process. The selection of crabs for processing has been done by the fisherman, as the pots are hauled, without the aid of any measuring device. The minimum size at which crabs have been selected has not remained constant with time but has varied by a few mm. in terms of carapace length. In general, when catches have been good, the size at selection has been high, but as catches have been reduced, so has the size of crabs landed. Large fluctuations in catch have thus been avoided, both to assist the running of the factory and to maintain the morale of the crew. As will be seen, this variability in crew behaviour has been the single greatest source of error in the nominal CPUE.

Pot Type

Three basic designs of pot have been used in this fishery each with a different mesh size. The two varieties of small meshed pots have had escape holes incorporated part way through the fishing operation to avoid the necessity of sorting through excessive numbers of small crabs. Unfortunately, these escape holes were initially made too large and many of the smaller, but still retainable,

4 4 2.2. Selectivity model

crabs were able to escape. The size composition of the catch therefore also varies with pot type, in line with the relative dimensions of mesh and escape hole sizes.

Soaktime

The number of crabs in a pot at any one time is a balance between those entering and those escaping. As the bait is exhausted those crabs capable of escape, due to the large size of the escape holes, will go, while the larger crabs will remain, trapped. As soaktime increases, the size composition of the catch is progressively dominated by larger animals.

Ground

It has been observed, at sea, that the catches from certain central grounds in Choiseul Sound contain an increased proportion of large male crabs, accompanied by the highest abundances of females. These grounds have also been identified in a separate analysis (see section 3.2.5.) as the central mating arena of the Choiseul Sound stock. The landed catches from this area contain a greater proportion of crabs over the size limit, and this difference in composition must also be accounted for in the modelling.

Due to variation in the size composition of the catches caused by the above factors, the CPUE must be expressed as either a weight or number greater than a chosen size limit. The composition corrected CPUE will therefore be at its greatest, in relation to the nominal CPUE, for catches from times of large size at (crew) selection; for pots with oversized escape holes; for strings with long soaktimes and strings fished in the central ’large crab’ ground.

45 2.2. Selectivity model

2.2.2. The Dependent Variable: Selectivity

As previously noted, a nominal CPUE in terms of kg/pot is available for all strings hauled in this fishery. The objective is now to convert this nominal CPUE into a catch of crabs greater than or equal to a certain size limit to take account of variation in the size composition of the catches.

This composition corrected CPUE can be expressed either as a number or a weight of crabs; the actual choice is immaterial so long as the size compositions are consistent after correction. For the purpose of total abundance estimation, however, it is more generally acceptable to express CPUE in terms of numbers. A secondary aim of the exercise is thus to make this conversion from weight to numbers of crabs.

To model selectivity and make the above conversion, some parameter must be used to summarise the variation in size composition. Such variation is mainly caused by changes in the position of the overall selection curve applicable to each catch (ie. the position along the abscissa of lines B and C of figure 1). Such positions are commonly summarised by a point known as the size at 50% selection (Gulland, 1983), at which half the animals are retained and half are released. This parameter, however, can not accurately be estimated for small samples. At least over the range experienced, though, the size at 50% selection is approximately related to such functions as the mean size in the catch or the percentage above a constant size limit. The development of the actual function used for this purpose is now described.

Awareness that the selectivity of the crew was, in fact, variable only occurred part of the way through phase 2 of this exploitation. Since that time, length composition samples have been taken from the landed catches on a regular basis. From the earliest ’Landed catch Length Frequency’ (LLF) samples, it soon became apparent that other factors such as pot type and soaktime were also important in determining the size composition of the catch. In order to

46 2.2. Selectivity model understand these relationships, LLF samples have been taken from the catches of all scientist observed strings hauled during phase 4.

For each of these LLF samples, a parameter, here called S(SL ) to represent selectivity over the size limit, has been calculated as:

S(SL) = Number of crabs > SL in catch

Total weight of catch (kg)

where S L = a specified size limit. The total weights of these LLF sample catches has been calculated from a weight for length relationship of adult male crabs in Choiseul Sound, obtained during the routine sampling programme. This weight should be more accurate than the apportioned bin fraction estimate available for other strings.

The parameter, S(SL ), adequately describes the variation in size composition between catches. It has been chosen in preference to, say, mean size in the catch (which it closely resembles), as it serves the purposes of modelling size composition, and converting the catch from weight to numbers, simultaneously.

Thus, by modelling S(SL) on the four ’selection factors’, composition corrected CPUEs can then be predicted as a number of crabs over the size limit, for the unmeasured catches, by the formula:

Number > SL per pot = Weight per pot * S(SL).

The question now arises of which size limit to use. It has been previously noted that this size should be chosen to result in complete selection of all crabs over and above the limit (e.g. SL in figure 1). Ideally, the size at which the probability of selection first becomes unity should be used, ie. at the upper end of the maximum combined crew/mesh selection curve.

47 2.2. Selectivity model

Note that the crew selection curve varies over time, and that the mesh selectivity varies with pot type, or mesh size. The overall selection ogive of each string depends not only on the combination of current crew behaviour and pot type, but is also influenced by soaktime. If soaktime is short, the pots are still full and selection is mainly due to the crew. If soaktime is long, overall selectivity, is, at least potentially, due to the gear, (conditional on the current crew selectivity being higher than the mesh selectivity of the pot type.)

With the unplanned observer data available, it is not possible to separate the overall or resultant selection pattern into the components of crew behaviour and gear. Fortunately, this step is not necessary: it is still possible to discover the point at which all crabs are fully selected (at all times and by all pot types), simply by looking for the point of deviation from linearity in length converted log catch curves.

In appendix 1., an equation for such a length converted catch curve is derived. The expected numbers at each length are predicted as a function of the growth and mortality parameters of the stock. It is assumed that the instantaneous coefficient of total mortality has been constant with time and that individual growth has followed the von Bertalanffy pattern, also with constant parameters.

The model has a linear form, obtained by plotting InAfy against h^L^ / (L^ - /)), where is the number of animals in length class / and L*, is the asymptotic length of the von Bertalanffy growth function (see appendixAl., equation (9)). Now, conditional on the above assumptions, those length classes which assume a straight line on such a plot may be taken to represent sizes which are fully selected at all times. Furthermore, the point at which such a curve deviates from linearity may be equated with the desired point at the upper end of the combined crew/mesh selection curve.

Figure 3 shows the whole combined LLF catches taken from Choiseul Sound, from all pot types, with the scales plotted according to the above equation. From the secondary scale of carapace lengths prior to transformation, it can be

48 2.2. Selectivity model seen that a linear portion exists for those size classes above around 80mm. The departure from linearity below this size is assumed to be due to a progressive decrease in selectivity operating on crabs below this size. The dashed line represents the proposed maximum level attained by the overall selectivity ogive, being a gradual decrease from the upper limit of 80mm. Note that the log- transformed scales reduce the apparent difference between this curve and the lowest selection curve given by the unbroken line (cf. figure 2).

The size limit to be used in modelling has therefore been set to 80 mm, and

S(SL) renamed as 580.

49 2.2. Selectivity model

Carapace Length, 1 (nn)

Figure 3. A length converted Log catch curve of the combined landed catch samples taken from Choiseul Sound during phases 1- 5 from all commercial pot types. Full selectivity is indicated for crabs over 80mm by the linearity of the catch curve above this size (see text and appendix 1). The dotted line represents the assumed maximum resultant selectivity ogive with an upper limit of approximately 80mm.

50 2.2. Selectivity model

2.2.3. The Independent Variables

Size at Crew Selection

It has not been possible to apply a direct value to size at crew selection because the behaviour of the crew did not follow a measurable quantitative pattern. Only the actual effect is measurable, by observing the catches and the resulting LLF samples and 580s.

Although the size at crew selection generally remained constant within any one day, it is also not possible to use the average of the day’s 580s to represent crew selection. This is because the gear hauled on each day does not comprise a random mixture of pot types, grounds and soaktimes. For example, if, on one day, only large meshed pots are hauled after a long soaktime, the use of a daily mean of 580 to represent size at crew selection, will incorrectly assign variation actually caused by pot type and soaktime to the behaviour of the crew.

However, the examination of plots of 580 vs date of hauling, has revealed that, for a large number of the LLF samples, during part of Phase 4, the variation in 580 has followed a pattern which can be reasonably described as a quadratic function of time (see figure 4). Since the other predictor variables have not followed any such trend, this variation can only be attributed to the effect of crew selectivity. The broad reasons for this pattern are as follows. At the beginning of the period, catches were good and only the larger crabs were retained by the crew. As catches gradually declined, this high level of crew selectivity was, possibly unwittingly, decreased in order to maintain deliveries to the factory. Eventually, the average size of the crabs sank to such a low level that the processing manager was forced to complain: from this time onwards crew selectivity rose back towards the original high level. The use of such a function as a predictor variable presents the behaviour of the crew as a smooth trend through the data. While a stepped function may be more realistic, it would be difficult to fit for the reasons given in the previous paragraph. The

51 2.2. Selectivity model

use of this quadratic function at least allows the independence and investigation of the other predictor variables.

Two new variables have therefore been created: NDATE = the number of days from 1 Sept. 1987 (being the approximate start of commercial crab fishing in the Falkland Islands, although any date could equally well be chosen for this purpose) to the hauling of the string; and NDATE2 = NDATE squared. These two variables have been entered simultaneously into the model to produce a quadratic function representing the size at crew selection. As a result of this choice, the model, in its basic form, has necessarily been limited to observations within the period of the quadratic fit, between 10 May and 23 July 1988. The model is, however, extended in a later section (2.2.8.) to permit correction of all five phases of exploitation.

52 2.2. Selectivity model

Expanded detail of quadratic l i t

Time CNunier of days since 1 Sept 1987)

Figure 4. The original 237 Selectivity (580) data points, plotted against time, for phases 1-5 of commercial exploitation. The quadratic function of date, representing crew selectivity (see text) has been fitted to the period marked, during phase 4. The hatched areas represent periods with no fishing activity, between the five commercial / sampling phases.

53 2.2. Selectivity model

Soaktime

Soaktimes have been recorded, in hours to the nearest minute, from the beginning of shooting the string to the start of hauling, some time later. During normal operation of the gear, soaktime would vary between 1 and 4 days depending on logistics and regular delay factors such as weather. On occasions, extreme soaktimes would result after visits to remote areas or breakdown and repair of the vessel etc. The distribution of soaktime as an independent variable is thus positively skewed. To normalise the distribution and reduce the influence of the few observations at very long soaktimes, a transformation to natural logarithms has been made on this variable.

Pot Type

During phase 4, four pot types have been in operation. Pot types coded CRE and DIWE had had escape holes incorporated previous to the start of this period to allow the release of small crabs. The largest, and definitely ’oversized’, escape holes were those fitted during phase 3 to create the CRE pot type. CRE2 pots are a modification of the CRE pots with the escape holes reduced in size to improve the retention of the smaller ’keepers’. Strings of CRE pots were gradually converted to CRE2 during phase 4.

Both CRE2 and the remaining FIW pots are thought to have mesh selection curves at or below the minimum crew selection curve. The original CR pot type, fished during phases 1 and 2 without escape holes, effectively had a very small mesh, retaining all crabs to well below the smallest processable size.

The effect of pot type has been modelled by the use of three dummy variables (for the four pot types) with codes set at either 0 or 1 (see Draper and Smith, 1981, page 241.) With this structure, each dummy variable isolates a single comparison between two categories of pot type, conditional on the full

54 2.2. Selectivity model formulation of the model. The regression coefficient then gives the difference, in units of the predicted variable (580), between the two pot categories; while the significance test (HQ: B = 0) effectively becomes a test of this difference between the two pot types.

Ground

During previous analyses, Choiseul Sound has been subdivided into 36 small fishing ’grounds’ of variable size, delimited partly by geographic features such as islands and shallow reefs and partly by concentrations of fishing effort both in space and time. However, there are insufficient LLF data to analyse all these grounds separately. The location of each string has, therefore, been reclassified into one of two geographical ’major’ grounds, depending on broad observations of the appropriate catches. Three adjacent minor grounds to the east of Centre Island have been allocated to the central major ground, while the rest have been put in the outer ground. In a later analysis (section 3.2.5.), this central area is found to comprise the major breeding site of this stock of crabs, explaining the domination of large males in this location.

The difference between the size compositions of crabs on these 2 major grounds has also been modelled by the use of dummy variables, this time set at 0 for the outer ground, and 1 for the central region. As for the pot type arrangement, a significant coefficient for this variable is thus additive to the predicted 580 for strings fished in the central area. The best allocation of minor grounds to the central breeding ground has been checked during the fitting procedure by finding that division producing the highest R2.

2.2.4. Modelling Techniques

Least squares regression analysis has been used to model selectivity. The four

55 2.2. Selectivity model independent predictor variables have been entered simultaneously into the model. Interaction between the discrete variables pot type and ground has been analysed by ANOVA, with the continuous variables soaktime and size at crew selection entered as covariates. The model has been simplified where possible on both statistical and biological or intuitive grounds. Both regression and ANOVA methods have been weighted by the sample sizes which produced each 580 observation, corrected so that the sum of weights equals the number of samples.

2.2.5. Data used in the analysis.

From 262 LLF samples measured during phases 2-5, 1987-88, the first 35 resulting 580 observations have been removed from the data set as they were sampled previous to the fit of the quadratic function for date. The 31 observations taken during phase 5 have been removed for the same reason, and 25 LLFs taken from a separate location, Adventure Sound, have also been excluded from the initial modelling. Finally, 12 more points have been rejected, during the modelling, as outliers (with justification found for removal), or as isolated observations with excessive influence on the result.

The remaining data set comprised 159 580 observations, obtained from the measurement of 19,042 crabs, all from Choiseul Sound, during the fit of the quadratic function for crew selectivity. LLF sample size varied from n = 4 to n = 330 crabs.

2.2.6. Results of Modelling

For the first estimation of the selectivity model, 580 has simultaneously been regressed upon LogSoaktime, NDATE, NDATE2 and the dummy variables representing the 4 pot types and 2 major grounds.

56 2.2. Selectivity model

The coefficients for LogSoaktime and crew selectivity (NDATE and NDATE2) were all significant at P < 0.00005, and have been accepted as predictors without any further modifications.

Comparing the differences between pot types, by the arrangement of dummy variables, it has been found that the CRE2 and FIW pot types are not significantly different (P = 0.3621). These represent the smallest meshed pots with the fullest selectivity, and have been joined together as a single class. Remodelling with only 3 classes, the CRE pots proved to be different to the new small-meshed class at P < 0.00005. The DIWE pot type, however, did not differ significantly from either class and has been left as an intermediate group.

Pot type, therefore, has been modelled as a 3-class variable, with the CRE2 and FIW pot types forming the base level as the low selectivity class, DIWE in the middle, and CRE in the highest class. In the terms of the model, two new variables have been formulated, DIWEcode (identical to the dummy variable isolating the DIWEs and the small-meshed pots), and CREcode being the equivalent for CRE pots. The regression coefficients of these variables give the increment made to 580 for strings composed of DIWE and CRE pots. No increment is made to 580 when the string is composed of either of the small-meshed pot types.

The coefficient for the ground dummy variable is significant at P < 0.00005, with no significant interaction with pot type (P = 0.798), thus forming a very satisfactory predictor. However, due to the subjective classification of the ground variable, each of the minor grounds, adjacent to the central area have then been added or removed from the ’large crab’ major ground to check if the model could be further improved and the ground better defined. The original classification with the three grounds to the east of Centre Island assigned to the ’large crab’ major ground gave the maximum R 2. This formulation of the ground variable is hereafter referred to as the GROUNDcode.

57 2.2. Selectivity model

At each stage in the modelling process, the analysis has been tested for violations of the regression method assumptions. The final model is linear with no remaining outliers or excessively influential points. The variance of residuals around the predicted values is constant and follows a normal distribution, and there is no serial correlation in the data set.

However, there is considerable (weighted) correlation between the following independent variables. Even so, the model produced is both reasonable and believable and these violations are assumed to have had little influence on the result.

The dummy variables DIWEcode and GROUNDcode are correlated (r = 0.6996 **) as the DIWE pots were consistently fished in the Centre Island ground during phase 4.

Pot type and date are correlated (r = -0.3830 **, for CREcode with NDATE, and r = -0.3896 ** for CREcode with NDATE2) as the escape holes were gradually removed from CRE pots during the period to produce CRE2 pots.

There is also a small, negative correlation between LogSoaktime and GROUNDcode (r = -0.2161 *), due to the strings in the large crab ground being hauled more regularly for their better catches.

2.2.7. The Selectivity Model

The final version of the 580 selectivity model is described in table 1. The partial determinations (partial R2) given in the table, indicate how the total coefficient of determination ( R2) for the model, can be decomposed into the relative contributions of each factor. Thus, ground explains 19% of the variation in 580, while soaktime accounts for only 5%. Note that the DATE effects must be

58 2.2. Selectivity model considered in combination, since they jointly define the quadratic function describing crew selectivity. Even though this factor is the least explicitly expressed, it is the variability in crew behaviour that is responsible for the majority, 27%, of the variation in 580 or selectivity. The same consideration must be taken of pot type - the two pot codes jointly accounting for 6% of the variability in 580. Note that 42% of the variation remains unexplained.

This decomposition of R2 is derived from the method of ’path analysis’ (Li, 1975.) The partial i?2s are calculated as the product of the correlation coefficient and the standardized regression coefficient (also known as the path coefficient). Simply stated, the partial determination expresses the sum of the direct, independent correlation between the factor and 580, plus any indirect effects via other determinants. The sum of the partial determinations thus equal the total R2; the small difference here being due to rounding error.

During the experimental phase 5, catches have not been landed at the factory and no weights have been obtained. The retained or landed catches have simply been counted at sea instead. The 580 model can not, therefore, be used to predict selectivities for this phase. It has been necessary to reformulate the model in terms of numbers instead of weights, the dependent variable simply becoming the percentage of crabs greater than or equal to 80mm in the catch (or P80).

The equivalent version of the P80 selectivity model is described in table 2. Note that, while the regression coefficients are different to the 580 model, due to the new units, the partial determinations are very similar.

59 2.2. Selectivity model

Table 1. The parameters of the 580 selectivity model for the prediction of composition corrected catch rates during phases 1-4.

M ultiple R 0.76104 R2 0.57919 Adjusted R2 0.56258 Standard Error 0.15503

Analysis of Variance

DF Sum of Squares Mean Square Regression 6 5.02790 0.83798 Residual 152 3.65304 0.02403

F = 34.86784 Significance of F < 0.00005

Dependent variable ... 580 Independent variables...

Variable B SE B T Sig T Partial R2

LogSoaktime 0.10426 0.01836 5.678 0.0000 0.05104 NDATE -0.18098 0.01723 -10.504 0.0000 -0.69613 ^ NDATE2 3.13603E-4 2.96872E-5 10.564 0.0000 0.96970 ^ 021351 GROUNDcode 0.22130 0.04011 5.518 0.0000 0.19316 DIW Ecode 0.08230 0.04978 1.653 0.1003 0.04800 ^ CREcode 0.14289 0.03378 4.230 0.0000 0.01309 ^ °-06109 Constant 26.12642 2.48517 10.513 0.0000

60 2.2. Selectivity model

Table 2. The parameters of the PS0 selectivity model for the prediction of composition corrected catch rates during phase 5.

M ultiple R 0.77304 R2 0.59759 Adjusted R2 0.58171 Standard Error 5.96558

Analysis of Variance

DF Sum of Squares Mean Square Regression 6 8033.10573 1338.85096 Residual 152 5409.39774 35.58814

F = 37.62070 Significance of F < 0.00005

Dependent variable ..... P80 Independent variables...

Variable B SE B T Sig T Partial

LogSoaktime 4.11797 0.70659 5.828 0.0000 0.05285 NDATE -7.51654 0.66306 -11.336 0.0000 -0.83018 NDATE2 0.01302 1.14240E-3 11.396 0.0000 1.14211 •0.31193 GROUNDcode 8.39580 1.54335 5.440 0.0000 0.17878 DIWEcode 3.30590 1.91542 1.726 0.0864 0.04847.\ CREcode 5.34882 1.30002 4.114 0.0001 0.00682' 0.05529 Constant 1081.25052 95.63194 11.306 0.0000

61 2 2 Selectivity model

2.2.8. Application of the Selectivity Model

As the effect of crew behaviour on catches has been modelled as a quadratic function of time, the basic model is only suitable for the correction of catches obtained during this time period. It has not been possible to fit an acceptable ’function’ for size at crew selection to other periods of the year.

However, due to the additive nature of the 580 model, it is possible to use the LLF observations outside the fit of the model to produce a nominal value of 580, attributable only to crew selection, for these times. This parameter, referred to as S8Qcrew, is calculated as:

S80crew = 580 - (0.10426*LogSoaktime) - (0.22130*GROUNDcode) - (0.08230*DIWEcode) - (0.14289*CREcode) so that 58 0crew represents the theoretical selectivity that would have resulted if the string had been fished in the outer ground, with small-meshed pots, at a zero soaktime.

These values of S80crew can then be used as the basis of the model, replacing the constant, NDATE and NDATE2 terms outside the fit of the quadratic function.

It has previously been mentioned that crew selectivity, itself, could not be directly measured, only its effect. The modelling process, by defining and subtracting the effects of the other independent variables, can thus be seen to have quantified crew behaviour, from its effect.

In this way, the 580 model has been modified to produce a formula applicable to the whole fishing period as:

62 2.2. Selectivity model

580 = 580creM, + (0.10426*LogSoaktime) + (0.22130*GROUNDcode)

+ (0.08230*DIWEcode) + (0.14289*CREcode)

where 580^^ has been tabulated for each string hauled on the basis of its proximity to the nearest LLF sample. This tabulation has been plotted in figure

5 where the fitted function basically follows the available 58 0crew data points.

The interpretation of these data has been greatly aided by comments made, by both the skippers and the processors, at the times of any deliberate changes in selectivity. Note that the ordinal scale is arbitrary, due to the subtraction of soaktime: a doubling of 580cmv, for instance, no longer implies a doubling in the amount of adjustment.

Unfortunately, LLF samples were not taken at the beginning of commercial fishing in the Falklands, and some subjectivity has inevitably been introduced into the tabulation of 580crevv. For example, no LLF samples were taken during phase 1, and an average value obtained from samples during phase 3, when size at selection had apparently levelled off at the size requested by the factory, has been used to correct this period. Also, for phase 2, partially on the advice of the fishermen, the single LLF obtained at the end of the phase has been used to predict the 580cmv for the whole of this phase. These early composition corrected CPUEs must therefore be regarded with some caution, but are thought to be the best estimates possible in view of the available data.

The nominal catch rates (kg/pot) have thus been corrected for all strings fished to date, for variation in size composition caused by soaktime, pot type, ground and size at crew selection. Naturally, for those strings where LLF samples have been taken, the actual number over the size limit has been used instead.

63 2.2. Selectivity model

Tine (Nunier of days since 1 Sept 87)

Figure 5. A plot of the S 8 0 crew data points and the fitted function, used to represent crew selectivity. S8Qcrew is the remaining portion of 580, after the effect of soaktime, pot type and ground have been subtracted; ie the portion of 580 attributable only to crew selectivity. The solid line is the ’function’ used to represent crew behaviour in the final, modified version of the selectivity model. Note the lack of data points used in fitting the early part of the function. The hatched areas represent periods with no fishing activity, between the five commercial / sampling phases.

64 2 .3 . Effort model

2.3. Modelling of Catch Size: The Prediction of Effort Corrected CPUE

2.3.1. The Components of Fishing Effort

Having so far considered the catch part of CPUE, it remains to more accurately define the effort applied to each string, as a causal factor of the actual magnitude of the catches. In trap fisheries the basic unit of fishing effort is the number of pots set, thus the nominal CPUE: kg/Pot. In fisheries where all other variables remain constant, the pot unit alone will be sufficient definition of effort. In the present situation, however, those factors, important to catch composition, must now be reconsidered in the context of their influence on effort.

As long as all crabs, over and above the size limit, chosen for correction of composition, are fully selected by all gear types at all times (as in figure 1, above size limit SL ), variations in crew size at selection and differences between pot types should have no effect on fishing effort. In other words, given that catch composition has been correctly accounted for, by a well chosen size limit, these selection factors should have no bearing on effort or catch rate.

Within the ’large crab’ ground, and on certain other grounds at certain times, catch rates much above the average have been achieved. This can be best explained as a function of abundance, though, and no correction is needed for this factor either.

Soaktime, however, affects both the composition and the magnitude of the catch.

As soaktime increases, the effective fishing effort is increased, but less than proportionally. The catch per haul therefore rises with soaktime but the catch per haul-day declines (Austin, 1977; Gulland, 1983). One of the skippers of the

Laura Jay commented that, in his experience in the Falkland Islands, catches were increased by about 25% after a second days fishing but, longer than this,

65 2.3. Effort model

the extra catch was negligible. This relationship must therefore be examined and

catches corrected for variation in effort due to soaktime.

2.3.2. Data used in the analysis

For the prediction of effort corrected CPUE, it is thus necessary only to model the composition corrected CPUE (ie the number of crabs, greater than or equal to 80mm, per pot) on soaktime.

A choice must now be made between two different data sets: the actual numbers over 80mm per pot, obtained from the LLF samples, as used in the 580 model and automatically correct for size composition (n = 159); or the whole years data set with catch rates corrected by the 580 model (n = 950 after exclusion of non-Choiseul Sound data etc.) The first data set has the advantage that all observations are exact, not estimates, and that the data are concentrated in a limited period of time. The second data set has a much larger sample size, but errors may be introduced if the 580 selection model is, in fact, biased in any way. Further sources of potential error also exist in the larger data set, due to the ’bin fraction’ estimation of string weights, and inaccuracies in recording on days when the catches were observed only by the crew.

The resulting models are actually very similar for both data sets, which is encouraging support for the 580 model. The main analysis has, therefore, been restricted to the smaller, more accurate data set.

2.3.3. Modelling of Composition Corrected CPUE on Soaktime

Composition corrected CPUE has been modelled on soaktime, as for the selection model, by the method of least squares regression. Both independent and dependent variables are positively skewed with occasional good catches and

66 2.3. Effort model long soaktimes, but not necessarily in combination. The variance of CPUE also appears to increase with soaktime. The distributions have therefore been normalised, and the variance of CPUE stabilised, by the use of a square root transformation for catch rate, and a natural logarithm transformation for soaktime. The latter transformation is the more extreme of the two, reflecting the fact that the soaktimes are more skewed than the catches. No weighting has been used for this model, as the sample sizes are now the actual catches or raw data.

2.3.4. The Catch Rate Model

The result of modelling CPUE on soaktime is given in table 3 and illustrated in figure 6. Due to the different transformations made to the two variables, this model has a curved fit to the raw data, steep at short soaktimes and levelling off at longer times as shown in figure 7. The model is therefore in accordance with the experiences of the fishermen, and predicts very close to a 25% increase in catch after a second days lie. The catch is not doubled until nine days later.

It may be noted from table 3 that the model only explains 9% of the variation in the raw data ( R 2 « 0.09). This figure could, in fact, be greatly increased by including other variables such as GROUNDcode in the regression. Variation due to the different grounds, however, is a function of the true local abundance, not of effort, which obviously should be investigated rather than ’corrected’.

The model satisfies the previously mentioned regression assumptions with the exception that the Durbin-Watson test for serial correlation is significant. This, however, is to be expected due to the nature of the fishing pattern (ie. the daily correlation of soaktimes).

This model has been used to adjust the catch rates of all strings, hauled in this

67 2.3. Effort model fishery, to the expected catch at 24 hrs of soaktime, by the relationship:

C PU E adjusted for soaktime = C PU E * Predicted C PU E 2 4 hours

Predicted CPUE hours

w here i hours is the soaktime of the string. For CPUE, read composition corrected CPUE. It would, perhaps, be more understandable to apply this adjustment to effort instead. It has actually been made on the catches, because the model has necessarily been formulated as catch, not effort, on soaktime. It would, of course, be possible to calculate a soaktime-corrected effort from the ratio of the catches, before and after correction.

This composition and effort corrected CPUE, hereafter called CPUEadj, is the final representation of CPUE. Assuming that all factors have been accounted for, CPUEadj should be directly related to abundance. The catch is expressed in numbers of male crabs greater than or equal to 80mm in carapace length, while a unit of effort is a single pot adjusted for the duration of fishing time.

68 2.3. Effort model

Table 3. The parameters of the Catch Rate model for the prediction of effort corrected CPUE.

Multiple R 0.29215 R 2 0.08535 Adjusted R2 0.07953 Standard Error 0.30049

Analysis of Variance

DF Sum of Squares Mean Square Regression 1 1.32286 1.32286 Residual 157 14.17616 0.09029

F = 14.65055 Significance of F — 0.0002

Dependent variable.... /(Composition Corrected CPUE) Independent variables...

Variable B SE B T Sig T

LogSoaktime 0.13970 0.03650 3.828 0.0002 Constant 0.29407 0.14957 1.966 0.0511

69 2.3. Effort model

Figure 6. The catch rate model. /(Composition Corrected CPUE) vs. Log Soaktime, with the fitted equation superimposed.

B oattise (hours)

Figure 7. The catch rate model plotted with back-transformed variables: Composition Corrected CPUE vs. Soaktime. Note the curved fit of the model, in accordance with practical experience.

70 2.4. Abundance estimation

2.4. The Examination of CPUEadj and Estimation of Abundance

2.4.1. Examination of the raw data

Figure 8 shows the original uncorrected catch data (a) and the progressive changes to the data set as corrections are made, first for (b) the composition of catches (the £80 model), and then for (c) variable soaktimes (the Catch Rate model) to produce the final CPUEadj. The data cover all the commercial fishing operations of phases 1-5, restricted to within Choiseul Sound only. The variability of catch rates during this period is much more noticeable after correction (figure 8).

These raw data have been aggregated by calendar month (table 4) for further analysis. The monthly CPUEadj given is simply the unweighted mean of all the strings hauled in the month so as to weight the results from long and short strings equally. Catches are the actual number of male crabs over and above the size limit, ie. with correction made for composition, but not for soaktime. Effort is given both as the number of strings hauled and the actual number of pots hauled, and as the real ’effort’ as pots adjusted for soaktime. The ’weighting factor’ is used later in the estimation of abundance (see section 2.4.2.).

The changes in monthly CPUEadj with time are further illustrated in figure 9. Certain features of the observed pattern may be explained as follows.

The best catches taken in December of both 1987 and 1988 reflect the completion of the male moult season around the end of November (section 3.2.). Such a moulting pattern produces a sudden, yearly pulse of recruitment to the fishable stock at this time. The decline in CPUEadj* after this recruitment, during 1988, may be due to various factors including losses from the stock caused by natural and fishing mortality and changes in catchability. It is assumed that the Choiseul Sound stock is a self contained unit without significant emigration or

71 2.4. Abundance estimation

immigration at any time of the year.

Great variations in the catchability coefficient of lobsters and crabs have been illustrated dependent on both temperature and the proportion of animals in moulting condition (Bennett, 1974; Morgan, 1974; Skud, 1979; Krouse, 1989). Food intake generally decreases in animals preparing for a moult (see section 3.2. for female P. granulosa ) and increases immediately after. Such changes may contribute to the November/December rise in CPUEadj.

It is also possible though, that the CPUEadj given for December 1987 is overestimated, as only a single LLF sample was taken at the end of this month in phase 2 (see figure 5). It is quite likely that the S80crew would have increased more gradually during phase 2, and actually been closer to the level of phase 1, at the beginning of the phase. It is probably the large catches at the start of phase 2, (see the uncorrected catches in figure 8a) which prompted the increase in crew size at selection in the first place. Thus, it may be unrealistic to assume the same crew behaviour for the whole of the phase. The fishermen, though, were unable to say when, or even if, a change had occurred. In support of the corrected catch rates of figure 9, the well sampled data for the austral spring of 1988 show a similar increase in CPUEadj to those of the same period in 1987.

The poor catches observed during February are thought to be due to the movement of crabs on to the shallow water feeding grounds during summer, largely unknown to the fishermen until a month later. Effort may therefore have been directed away from the main portions of the stock at this time. Conversely, the aggregation of large male crabs in the Centre Island ’mating ground’ (see section 3.2.5.) was only discovered and exploited effectively from around March 1988 onwards, possibly increasing the ’mean’ CPUEadj of these later months. These observations highlight the fact that the distribution of fishing has not been random but, at least intentionally, directed at the highest densities of crabs at all times. Due to the recent development of the fisheiy, such targeting may often have been far from optimal. In addition, four different

72 2.4. Abundance estimation

skippers have been in charge of the Laura Jay during this short time: both the individuals experience and the collective knowledge of the area will have increased over the year. The catchability coefficient of a unit of gear can thus be expected to increase with time for each skipper and also throughout the whole year.

The rapid decrease in CPUEadj after December 1987 may also be due to a second, related factor. The dispersion of crabs on to the shallow grounds in summer effectively increases the occupied area of Choiseul Sound and decreases the density of crabs at this time. Without accurate definition of the distribution of crabs throughout both times of the year, this variation cannot be corrected for.

During phase 5, effort has deliberately been distributed to cover as much of Choiseul Sound as possible. Catch rates, from this period, should, therefore, not be considered to be the result of commercial targeting as the catchability coefficient for phase 5, overall, is reduced. The still high catch rates obtained in this period presumably reflect the increased knowledge of stock distribution gained since the previous year. The deliberate sampling may thus have covered a similar ratio of densely to sparsely populated areas as did the commercial ’sampling’ of 1987.

Finally, note the relatively small fishing efforts for the months of April, August, October and December 1987 (table 4). Data points for these months may be less accurate than at other times.

In conclusion, the assumption that CPUEadj is linearly related to abundance may be far from true. Variation in the catchability coefficient, the proportion of the stock removed by a single unit of effort, may result both from the activities of the stock and the actions of the fishermen. The relative effect of each of the factors mentioned is largely unknown at present and any conclusions must be made with full awareness of this uncertainty.

73 2.4. Abundance estimation

However, a number of comments may also be made in support of this data set, suggesting that it is still probably better than many. In most fisheries, with many vessels fishing wide areas, catch and effort data are often subsampled at port, with largely unknown levels of bias. In the Falkland Islands, all the catches (and their locations) and the efforts (including gear types and soaktimes) have been accurately recorded. Sixty-six percent of all the strings fished have even been hauled under scientific observation, representing a very high level of scrutiny. Indeed, it is only this close observation and understanding of the fishery which have enabled the various caveats above. A similar number probably exist in most other sets of catch/effort data but cannot even be identified. At least two of the most important sources of error have been well corrected by the models in this section and the resulting CPUEadj is at least felt to be adequate for a preliminary assessment of this undeveloped fishery.

74 2.4. Abundance estimation

a) Uncorrected CPUE (kg / pot)

b) Number of crabs > 80mm per pot

c) CPUEadj

Time (number of days since 1 Sept 1987)

Figure 8. a) The raw CPUE data (kg/pot) plotted against time for phases 1-4 (catches were not weighed in phase 5), b) the same raw data corrected for catch composition by the 580 and N80 models for the whole period and c) the final CPUEad: corrected for both composition and effort after applying the eaten rate model.

75 2.4. Abundance estimation

Table 4. Monthly catch and effort statistics (see text).

---- Number of ---- — CPUEadj- — Weighting Month Strings Pots Potsadj Catch Mean Std Dev Factor

87 9 58 3263 3800 2896 0.76 0.43 314.45 87 10 95 4065 5249 3053 0.53 0.33 859.84 87 11 24 944 1414 2096 1.55 1.13 18.96 87 12 43 1503 2374 3974 1.75 0.95 47.98 88 1 95 3302 4582 4220 1.00 0.79 151.93 88 2 114 3861 5399 3349 0.68 0.39 735.37 88 3 112 3733 5211 4066 0.91 0.56 360.66 88 4 11 389 652 539 0.98 0.66 25.47 88 5 128 4354 5782 3603 0.67 0.51 500.86 88 6 108 3806 5380 2825 0.53 0.33 963.02 88 7 64 2143 3125 1781 0.60 0.44 333.47 88 8 3 82 164 106 0.62 0.38 21.22 88 10 4 193 237 143 0.65 0.19 106.77 88 11 59 1849 2925 4169 1.38 0.80 92.39 88 12 11 321 522 831 1.57 1.15 8.29

2 -r 1.9 - l.B - 1.7 - 1.6 - m 1.5 - CJ 1.4 - CO 1.3 - - P3h 1.2 O 1.1 - 1 - A 0.9 - P i o O.B — i d 0.7 - 0.6 - 0.S - 0.4 - 0.3 - 0.2 - 0.1 - 0 -- i i i i i i i i i i i r- i i r~ Sep Oct lor Dae Jan Tali Bar ipr Hay Jm Jul Aug- O c t Nov Dbc Tine (nonth. 1987-88)

Figure 9. Monthly variation in the corrected (CPUEadj) catch rates.

76 2.4. Abundance estimation

2.4.2. The Leslie Catch-Effort method of Abundance Estimation

The Leslie Catch-Effort method works on the basic assumption that the size of a catch is proportional to the amount of effort put into taking it (Leslie & Davis, 1939; Seber, 1982). Thus, when catch per unit effort (CPUEadj) is plotted against the catch accumulated up to the time of the sample, it follows that, when CPUEadj is reduced to zero the accumulated catch is the total which was available at the start of sampling. The ’line of best fit’ plotted through the available points, therefore intersects the abscissa at the predicted point of stock exhaustion, when everything has been caught.

This and other similar methods involve a number of assumptions, not least that of constant catchability which remains uncertain in this case. The population is also assumed to be closed, except for the removals, implying no migration in or out of the study area and no recruitment to the stock during the sampling period. The distribution of crabs mostly in the centre of Choiseul Sound does suggest a fairly self contained stock. By taking December as the start of the year, recruitment can also reasonably be considered to be negligible for around the ten months or so until the next moult season (section 3.2.3.). In the basic Leslie model, natural mortality is assumed to be zero. With only a limited idea of the true value of ’M several possible values must be tried to assess the effect of mis-specification. The corrections of the 580 and Catch Rate models are assumed to take care of the final assumptions about constant trap efficiency and size composition of the catch.

The abundance of male crabs over 80mm is thus estimated in this section from the stock decline within Choiseul Sound as a whole. In an ideal case, this area could be taken to be a single homogenous ground, with randomly distributed stock and fishing effort. Of course, this has not been the case: crabs have migrated with the seasons, and the fishermen have followed them, to their best ability. As previously mentioned, neither is it possible in this case to assume a consistent level of targeting the highest stock densities. However, the effect of

77 2.4. Abundance estimation these slight infringements is probably small given the many data available.

With the initial assumption of zero natural mortality, the Leslie equation takes the form:

t-1 CPUEadj t = <1N o - q S ■ Ct + et 1=0 where CPUEadj t and are the CPUEadj and the number of crabs captured over 80mm during each (monthly) time period. The regression of CPUEadj- 1 on the accumulated catch from the start of the season to month M, thus gives the estimated catchability coefficient, -q as the slope and the product q N Q as the intercept.

The variance of residuals, ep is not assumed to be constant over time (see figure 8c), but given by:

F(ef) = 1 / Wt where

Wt = number of strings,.

std dev2.

In a normal weighted regression (Draper & Smith, 1981) an analysis is weighted by the inverse of the variance of ’Y at each level of 5X \ In this case however, the data take the form of the mean CPUEadj of each month. The variance of residuals therefore applies to the variance of means about the line, in other words the standard error of the raw data or s^/n. The inverse of this variance is the quantity, Wv given above and tabulated as the ’weighting factor’ in table 4. The use of such a weight takes into account both the variance of observations

78 2.4. Abundance estimation and the highly variable sample size in each month (table 4).

Approximate 100-a per cent confidence limits for the initial population size, N q, have been calculated using a special linear regression model given in Seber, 1982. The method involves solving the roots, dj and d2 of the quadratic equation d2 ( q 2 - {(SEq? Fa;U .2} ) - d (2 U .q) + (U2 - { a 2 Fa;1^_2 / n } ) = 0 where SE^ = the standard error of the estimated slope, q,

Fa .1/t_2 = the a% value from the F distribution with 1 and n-2 df, U = the weighted mean of CPUEadj, a 2 = the estimated variance of residuals around the regression line and n — the number of data points (the sum of the rescaled weights).

The upper and lower confidence limits are found as the sums of the weighted mean of cumulative catch and dj and d2 respectively. Thus, with variable a, the equation explicitly describes the entire distribution of the estimated N 0.

In the presence of natural mortality, M (to a yearly basis), the equation takes the form:

t-1 C P U E adj t = q N 0 e < ‘ + 0 5)M - q r C,- + e t i=0 assuming that the catch occurs in the middle of each interval t to t+ 1 (Rosenberg et al , 1990). The et are assumed to be distributed as before and the same weights are employed. The model may be fitted as a multiple regression with two independent variables, constrained so that the line passes through the origin. Then, there is no constant term and q N Q is given by the first regression

79 2.4. Abundance estimation coefficient instead: q itself is given by the second coefficient of the model.

Unfortunately, the equation in this basic form can not be used to estimate confidence limits in the same way, due to the respecification of the regression model with two variables. By dividing both sides of the equation by the first variable, e'(r+0*5)^, the model can, however, be expressed as a single linear regression for which confidence limits can be obtained as before:

M CPUEadj( = q N 0 - q S Ct e

Now, for any random variable, X and constant, k,

V(kX) = k 2 V(X) ,

(Bain & Engelhardt, 1989), and so:

V{e\) = V(et) / (e‘(f + °-sW )2 .

New weights, W p must therefore be used where

W \ = Wt * (e~(*+ °-5)M)2 — W( * e'^ + '

80 2.4. Abundance estimation

Post Script

During the final editing of this thesis, it has been realised that the main equation used in this section has been slightly mis-specified. The ’Leslie method discounted for Af:

t-1 CPUEadj t = q N0 e<‘ + °'5>M - q S C, e<‘ ' W + et

i= 0 has been used as given mistakenly by Rosenberg et al (1990). The correct formula, as shown below, includes half the catch of the final period in the discounted cumulative catch on the RHS thereby reflecting the averaged nature of the CPUE data on the LHS (cf. Tillman & Breiwick, 1977; Seber, 1982):

t-1 CPUEa(1j ( = q N0 e<‘ + a5)M - q { ( s Ct e<‘ ' W ) + C J2} + et. (=0

A comparative simulation exercise has shown that this small mis-specification does not, in any circumstances, affect the estimate of the Biomass, N0. However, as the earlier catches are large relative to the later ones, the slope of the regression is somewhat flattened in the mis-specified version and hence the catchability coefficient, q is correspondingly underestimated. The simulations have further shown that the amount of bias in q is unaffected by the magnitude iVie fishlruj mod will), of either M or q itself: the parameter is however increasingly underestimated as A F becomes larger. When catches are tabulated by days or weeks (as in the Falkland Island squid assessment of Rosenberg et al, 1990) and F per time interval is small, the error can be fairly negligible. In this assessment, monthly data have been used and the results obtained can be used to show that F has been slightly below 0.1 per month (depending on the assumed magnitude of M). At this level of F, the simulations show that the bias in q is approximately 5%.

81 2.4. Abundance estimation

In view of the small magnitude of this bias and the considerable effort which would have been needed to re-run the whole assessment and modify the various figures and tables involved, this post-scripted comment has been included simply to acknowledge that the presented q s are underestimated by about 5%. These estimates are later used in the pulse fishing section of the bioeconomics chapter to translate fishing effort into fishing mortality and ultimately to obtain estimates of the potential yields. Such later results are therefore also underestimated by around 5% and the pulse fishing scenario on the whole is undervalued by the same small amount. The implications for the profitability of the fishery and the interpulse periods are more complex, and it may be simplest to state that all the results presented could actually have been obtained by using fishing efforts of 5% less than the stated levels of 2000 and 3000 pots per week.

82 2.4. Abundance estimation

2.4.3. Results and Discussion

In figure 10, the data are plotted as monthly CPUEadj, against cumulative catch as for a Leslie estimate of abundance with assumed zero natural mortality. The fitted line intersects the abscissa at N q = 45329. The nine data points can not be said to be a good fit to the line, although the weights applied to each data point (table 4) must be taken into account when examining residuals. The first CPUEadj for December is particularly high (partly as a result of its own low weight). Possible explanations for this outlier have been noted in the previous section, including an increase in catchability of crabs after moulting and the subjective estimation of the crew selectivity at this time.

Facing this uncertainty around the December data point, the model has also been run starting from January, using only eight data points in the regressions. In this case, the estimated parameters obviously refer to the stock size in January. However, the initial population for December and its confidence limits can still be derived, again assuming the catch to have been taken in the middle of the period, using the approximate difference equation of Pope, (1972):

N, = - C t_i) or rearranging for the present notation:

NDec = NJan^ + CDec .

The estimates of initial population size (ATq), for both models, along with other regression statistics and 95% confidence limits, at four levels of natural mortality are given in table 5. For all models, N q indicates the stock at the start of December, after the yearly pulse of recruitment (ie. the above correction has already been made for those runs of the model starting in January).

The estimated N qs vary between 45 and 65 thousand crabs depending on the

83 2.4. Abundance estimation model used (table 5). Excluding the December data from the estimation gives greater linearity to the plot, the variance of residuals (Resid MS in table 5) being approximately halved. This action also increases N q by around 20-25 per cent, by decreasing the slope of the line. The increase is less than might have been expected, however, again due to the low weighting of the December data point.

The effect of introducing M is also to reduce the slope of the line (ie. q), this time by attributing the observed decline to natural mortality instead of fishing mortality. A range of M between 0 and 0.15 has been investigated here. The likely magnitude of the total natural mortality over the whole year is unlikely to be above 0.15-0.2 as discussed later in section 5.2.2.. Under the reasonable assumption that most of this mortality occurs during, or close to, the moulting season, then the level of M during the months examined here (deliberately excluding the moulting period) must be very low, probably well below 0.1.

As shown in table 5, N q *s increased by between 4 and 7 per cent per 0.05 increment in M. As the fitted line becomes shallower, the significance of the slope, q, decreases at each step. For the model starting from December, raising M to 0.1 lowers the significance of the regression to below 95%, at which point the upper confidence limit simultaneously reaches infinity. Due to the lower initial slope of the January model, the upper confidence limit, in this case, is already at infinity even at M = 0. These results, however, should not cause undue concern. The usual significance level of 95% may be considered too restrictive for this type of data: all the art, signify*** ** tV^ 10% \tvel in any case (table 5).

To clarify the situation, further confidence intervals have also been calculated at lower probability levels. These are presented graphically for four of the models in figure 11. For each graph, the two curves enclose a ’region’ of N q along the abscissa, within which the true value of N q may be expected to lie, at the probability level given on the ordinate. The confidence intervals are highly

84 2.4. Abundance estimation asymmetric for all models (figure 11). The simple distribution of probability around the limits may, however, be seen as symmetrical. Thus, if the confidence limits enclose the region of N q at, say P = 80%, then we may assert that there is an equal chance (10% in this case) that the true N q lies either above or below the limits shown. For the December data at M — 0.1, for example, there is a

10% chance that N q exceeds 103100 crabs and a 10% chance that iV0 is less than 36200 crabs.

Figure 11 provides a more useful investigation of the results than the single confidence interval usually provided. For the eight situations investigated, the value of N 0 given in table 5 is the best available estimate. The confidence intervals illustrated in figure 11, though, show that there is a good chance that

N q is considerably greater than these values. Due to the asymmetry of the intervals the lower limits are less variable: for all the models, there is a maximum probability of less than 2.5% that the true N q is below 30000 crabs (table 5).

When considering these statements, it must be borne in mind that the confidence levels presented are based only on the presumed random variability within the raw data (ie the scatter of points around the line, seen in figure 10). The uncertainties and assumptions noted in sections 2.4.1. and 2.4.2. still exist, but the extra contribution of such factors to the probability levels is not considered in the statistical process.

To summarise, the estimate of abundance is relatively unaffected by the exclusion of the December data, or by the level of M used, varying only between 45 and 65 thousand crabs. The higher estimates are obtained from the model starting in January with the highest natural mortalities. M, however, is not likely to be high during this period. Furthermore, it can not be proven that the December data point is in error for the reasons given above, any more than the (heavily weighted) February data point, and others, may be in error due to ineffective targeting or the expansion of the inhabited area in the summer. In

85 2.4. Abundance estimation view of the various uncertainties (section 2.4.1.), including the probable increase in catchability with experience and more particularly as a result of the late discovery of the Centre Island mating ground, the most likely estimates from table 5 will be the lower ones. As a working figure, allowing for a small amount of natural mortality, a stock size of around 50000 crabs > 80mm is probably a conservative but reasonable estimate.

86 2.4. Abundance estimation

Figure 10. The monthly CPUEadj plotted against cumulative catch (total number > 80mm from December 1987 onwards), with the fitted line from the weighted Leslie estimate of total abundance with M — 0.

Table 5. Leslie method regression statistics for the estimation of stock size at four levels of natural maturity. The estimated abundances (Nq) for all models are the number of crabs > 80mm in Choiseul Sound at the start of December 1987 (see text).

M $(*10'5) SE^(*10‘6) Sig q Resid MS * 0 95% Cl for N 0

Starting from December

0 2.24389 8.78990 0.0379 0.02455 45329 30094 -► 430853 0.05 2.15266 8.80231 0.0444 0.02556 47361 30813 -*■ 995572 0.1 2.06101 8.81570 0.0520 0.02660 49584 31556 -*■ oo 0.15 1.96895 8.83007 0.0610 0.02768 52025 32334 -»• oo

Starting from January

0 1.71652 7.15990 0.0535 0.01330 53986 33852 -* oo 0.05 1.62313 7.17123 0.0642 0.01373 57804 35196 -»• oo 0.1 1.52928 7.18342 0.0773 0.01418 60741 35874 -*■ oo 0.15 1.43496 7.19647 0.0932 0.01464 65059 37102 -*■ oo

87 2.4. Abundance estimation

Starting Decenber Starting January

Initial population size (thousands of crabs)

Figure 11. Confidence intervals (% probability) for the true initial population size, Nq, for the December and January data sets, at two levels of natural mortality, M (from results given in table 5). See text for detailed explanation.

88 2.5. Biomass estimation

2.5. Estimation of the commercial biomass of Choiseul Sound for 1987

The estimated abundance of P. granulosa in Choiseul Sound after the 1987 recruitment pulse (section 2.4.) relates only to those male crabs with carapace lengths greater than or equal to 80mm. Above this length, all crabs are thought to be fully selected at all times and by all gear types (section 2.2.2.). Many crabs below this length, however, are equally suitable for processing and have been retained in the past in large numbers, at times of low crew selectivity.

The equivalent abundances of crabs in these smaller commercially important size classes have been calculated with the aid of a length frequency of crabs captured in Choiseul Sound from the small meshed creel pots (figure 12a). This size composition represents all the male crabs sampled from this pot type during the whole of phases 1-5 from all areas in Choiseul Sound (n = 22074). At least for the declining upper limb of the catch curve, it is assumed to be an unbiased reflection of the average relative abundances of crabs in each 1mm size class for this period. The mesh of these pots prevents the escape of crabs over approximately 50mm. The under-representation of crabs between around 50 and 70mm (figure 12a) is thought to be due to some biological effect such as the gradual recruitment of small crabs on to the adult feeding grounds or the inhibition of smaller males by larger ones already inside pots.

These relative numeric abundances have been converted to biomasses of male crabs in each size class using a weight for length relationship calculated from those male crabs measured for weight during this period. Crabs parasitised by the rhizocephalan B. callosus have been excluded from the estimation of weight at length. In addition, only the data from crabs over 55mm CL have been used, as juvenile crabs do not fit the adult pattern due to changes in morphometry. The relationship of log variables is, however, linear above 55mm. Using the natural logarithms of the mid-points of the length and weight classes (1mm and lg respectively) the equation used is:

89 2.5. Biomass estimation

In Weight = 3.450059 (In CL) - 9.20250 with n = 1316 and R 2 = 0.96096. The individual body weights of crabs predicted from this equation have also been illustrated in figure 12a as a smooth curve. The line should only be considered accurate for those crabs over 55mm. The total weight of crabs sampled in each 1mm size class (from Choiseul Sound and from creel pots) has been calculated as the product of these data and shown in figure 12b.

In section 2.4., the abundance of male crabs > 80mm in Choiseul Sound, after the 1987 recruitment pulse, has been estimated to be around 50000 animals. In the samples, 1013 crabs of equivalent size have been measured, with a total (predicted) weight of 446 kg. The initial biomass of male crabs > 80mm in Choiseul Sound at the start of December 1987 is therefore (446 * 50000 / 1013 = ) 22053 kg. Using similar calculations, the numbers and biomasses of crabs of smaller size classes have been estimated, also for the whole of Choiseul Sound (table 6). The numbers and biomasses over each length may be taken to be the best available estimates of the Choiseul Sound stock size under conditions of knife edged selectivity at each length.

Finally, the cumulative numeric catch between December 1987 and July 1988 was 24463 male crabs > 80mm. The exploitation ratio for these catches, used in the Leslie estimation, is therefore (24463 / 50000 = ) 0.48926. Almost half the total stock size of these large crabs is estimated to have been caught in this season. As discussed further in sections 4.3. and 5.2., such high exploitation rates can only be sustained, in equilibrium situations, by species with fast growth rates and high mortalities. As is shown in later sections, it is very unlikely that P. granulosa falls into this category.

90 2 .5 . Biomass estimation

Carapace Length (nn)

Figure 12. a) The number of male crabs sampled from Choiseul Sound from creel pots (n = 22074) and the predicted live body weights (g) of individual crabs in each 1mm class of carapace length and b) the weight (kg) of crabs sampled at each length.

91 2 .5 . Biomass estimation

Table 6. The estimated total numbers and weights of male crabs in Choiseul Sound at the start of December 1987 in 1mm size classes of carapace length and the total numbers and weights of crabs over each size limit. The lengths given are the lower limits of each 1mm class.

Length Within length class Greater than length class Class (mm) number weight number weight (kg) (kg)

70 48716 11680 351283 107249 71 46643 11739 302566 95569 72 41066 10843 255923 83829 73 37611 10411 214856 72986 74 32033 9291 177245 62574 75 26406 8019 145212 53283 76 20878 6635 118805 45264 77 19151 6365 97926 38628 78 15004 5213 78775 32263 79 13770 4997 63770 27051 >80 50000 22053 50000 22053

92 Chapter 3

93 3.1. Size at maturity

3. Biology of Paralomis granulosa in the Falkland Islands.

3.1. Size at Maturity

3.1.1. Introduction

Stocks of commercially exploited crabs and other Crustacea are commonly managed by restricting landings to male animals only, and only above a certain size limit. Female crabs are often too small to process commercially and are excluded from capture to maximise the reproductive potential of the stock. Legal size limits are used to ensure that males can reproduce before becoming available to the fishery. King crabs in the north Pacific are allowed 3 years of reproductive activity (Jewett et al, 1985; Somerton & Macintosh 1983(a)); other crabs, including the brachyurans Chionoecetes bairdi, Cancer magister and Callinectes sapidus, are granted only one year of growth while mature (Miller, 1976; Somerton 1981(b)). Such legal size limits are determined from estimates of size at maturity and annual growth rate: this section is devoted to the estimation of the first of these factors for P. granulosa.

3.1.2. Definitions of maturity and patterns of growth.

Various definitions of maturity have been proposed for crabs, including physiological or gonad maturity. Physiologically mature animals are characterised by the presence of spermatophores or ova in the reproductive tracts (Campbell & Eagles, 1983; Conan & Comeau, 1986), or by the large size of the ovaries or the opaque, convoluted appearance of the male sperm ducts (Hartnoll, 1963; Watson, 1970; Brown & Powell, 1972; Powell et al, 1973; Campbell & Eagles, 1983).

94 3.1. Size at maturity

Physiological maturity can only be detected internally. Many crabs, however, change their overall body shape at maturity, displaying adaptive sexual dimorphism (Hartnoll, 1974). This appearance of external secondary sexual characteristics can be defined as morphological maturity. Courtship in crabs often involves a long pre-copulatory embrace with much competition between males for available reproductive females. Morphological maturity in males is thus, usually, expressed by a relative increase in the size or growth of the chelae or claws, to better adapt them to this role. In female crabs, the fertilised eggs are carried beneath the abdomen during development, and morphological changes at maturity of females are related to this function. Thus, the abdomen generally increases in size to create the brood chamber, and the pleopods develop increased setation for attachment of the eggs (Hartnoll, 1984). These modifications at morphological maturity bring the secondary sexual characteristics to functional size when required, without wasting resources on their development during the juvenile phase (Hartnoll, 1982). The size at morphological maturity has been estimated in king crabs by Wallace et al, 1949; Somerton, 1980(b); Somerton, 1981(a); Somerton & Macintosh, 1983(a); Jewett et al, 1985 and Somerton & Otto, 1986 and in brachyuran crabs by Hartnoll, 1963; Watson, 1970; Brown & Powell, 1972; Somerton, 1980(b); Somerton, 1981(b); Campbell & Eagles, 1983; Conan & Comeau, 1986 and Davidson & Marsden, 1987.

A final expression of reproductive development can be defined as functional maturity, when a crab is actually capable of the physical act of reproduction, in its normal environment. All ovigerous females are obviously functionally mature: this does not, however, imply that all non-ovigerous crabs are not functionally mature. Where courtship behaviour involves a pre-copulatory embrace, those male crabs observed in the process of ’grasping’ females, prior to copulation, have been identified as functionally mature (Powell & Nickerson, 1965; Brown & Powell, 1972; Watson, 1972; Powell et al, 1973; Conan & Comeau, 1986).

At what relative sizes do these different interpretations of maturity occur? In both anomuran and brachyuran females, the act of copulation and ovulation, at

95 3.1. Size at maturity least on the first occasion, at the size of functional maturity, must occur immediately after ecdysis (Hartnoll, 1984). For the ova to become fully developed, prior to this moult, physiological maturity must be recognisable, for a brief period at least, at a size one moult increment smaller than the size at functional maturity. Thus, Powell et al (1973) were able to distinguish ’pubescent’ female red king crabs, Paralithodes camtschatica, externally immature, but with oviducts full of ova, ready for release at the next moult. Campbell & Eagles (1983) found that nearly all ovigerous rock crabs, Cancer irroratus, were considerably larger than the average size at physiological maturity.

All majid females are physically incapable of mating until morphological maturity (Hartnoll, 1963). In this group, the ’puberty moult’, at which the secondary sexual characters suddenly develop, is also the terminal moult (Hartnoll, 1963; Watson, 1970). No further growth occurs in mature animals, and morphological and functional maturity are thus achieved at the same size, a single moult increment larger than the size at physiological maturity. The pattern of maturation in other species, where growth continues after maturity, is largely unknown. Theoretically, it would still be most efficient for morphological and functional maturity to be achieved at the same moult, as the secondary sexual characteristics are unnecessary until this time. In the portunid, Ovalipes catharus, however, abdomen width increases gradually after morphological maturity and females are not ovigerous until a larger size (Davidson & Marsden, 1987).

The pattern in male crabs is even less obvious, as functional maturity can not be detected by simple observation. This is unfortunate, as the functional maturity of males is the particular parameter most desired by the managers of the many male-only crab fisheries. Again, it is intuitive that all males must attain physiological maturity either before, or at, the size at which they reach functional maturity. The majority of estimates of size at male maturity in the literature, however, are based on the analysis of morphological maturity, often with little justification, or consideration of other patterns of maturation. To what extent, then, is the size at morphological maturity in males related to the sizes at

96 3.1. Size at maturity physiological or functional maturity?

Males of several species of majid crabs may be found with mature gonads before growing large chelae (Hartnoll, 1963; Brown & Powell, 1972; Conan & Comeau, 1986). Similarly, male rock lobsters, are physiologically mature before attaining the long front legs characteristic of morphological, and in this group functional, maturity (George & Morgan, 1979). In other majids, however, physiological and morphological maturity are apparently achieved at the same sizes (Hartnoll, 1963).

There is evidence that a size factor is involved with the functional maturity of male crabs. In the absence of competition from larger males, small males of both anomuran and brachyuran species close to the sizes of physiological / morphological maturity have been found capable of successful matings. Thus, small individuals of both Chionoecetes opUio (Watson, 1972) and Paralithodes camtschatica (Powell et al, 1973) proved themselves functionally mature when enclosed in experimental isolation with receptive females. In addition, small male Chionoecetes bairdi (Brown & Powell, 1972) were found grasping females in a natural but shallow location where larger males were absent.

However, only the largest of the morphologically mature specimens of C. opilio were found to be grasping in the wild (Conan & Comeau, 1986). The vas deferens of small, morphologically mature males were loaded with sperm, while larger crabs had comparatively empty tracts. This emptiness was attributed to greater reproductive activity in large specimens. Equally, red king crabs, P. camtschatica, at sizes found to be capable of mating in isolation, were not found grasping in their natural environment (Powell et al 1973). The authors concluded they were non-aggressive and did not compete with the larger males. In partial explanation of this size effect, in P. camtschatica at least, the relative size of the chelae does not, in fact, change greatly at morphological maturity, only the relative growth rate is adjusted. Thus, the chelae may not reach a large, functionally mature size until some moults later at the new growth rate.

97 3.1. Size at maturity

In male crabs, then, there is little evidence on the relative sizes at which the three types of maturity are reached. The extent to which the patterns shown, in the few species studied, are generally applicable, is unknown. As found for female crabs, no morphologically immature males have been found to be functionally mature. In addition, males may also be physiologically mature before the morphological ’moult of puberty’, although this has not been observed in all species studied. In contrast to females, large body size may be of great advantage to the functional maturity of males.

It has been mentioned that male maturity is usually estimated morphologically. This is perhaps primarily due to the relative ease of the methods involved and the trend is continued in the present work. However, in view of the previous discussion, it is important to note that the parameter serves only as a lower limit for the size at true functional maturity, which remains unknown. This uncertainty must be well considered when making recommendations on the management of the stock.

3.1.3. Estimation of the size at morphological maturity of males.

Methods for the estimation of size at morphological maturity work by finding the average size at which the secondary sexual characteristics appear. They have developed from the study of relative growth, where ’morphometric’ measurements are taken of certain dimensions of an organism. By sampling a suitable size range of specimens in this way, even slight changes in shape related to particular growth patterns may be seen.

The relative growth of the secondary sexual characters of crabs often follows an ’allometric’ pattern, the growth rate of the character and the overall growth rate of the animal being proportional to each other (Huxley, 1932 in Hartnoll, 1963, 1982). In such cases, the size of the character, Y, is related to the overall body

98 3.1. Size at maturity size, X , by the equation Y = aJ&. The logarithms of the measurements therefore follow the linear function:

log CY = logea + blog^X the slope of which gives the ’growth ratio’, b, of the character. For certain characters, the relative size may remain constant with time, so that b = 1 and growth is described as ’isometric’. When the feature is growing faster than the body, b > 1 and the growth, of that feature, is described as positively allometric. Other characters grow at a slower rate than the body and show negative allometry, in which case b < 1.

The growth ratios of the secondary sexual characteristics of crabs are not constant throughout life, but generally adhere to one relationship while juvenile and change to a new constant ratio after morphological maturity. Plotting logeY on lo g ^ then, usually results in not one, but two, straight lines, of different slopes, giving the two phases of allometric growth of the animal. The two lines may intersect at a point of inflection. The maturity of animals close to this size cannot then be detected on sight, as only the relative growth rate of the character is altered. In addition to this change in growth rate, there may also be a sudden change in the relative size of the character. In such cases, two non­ intersecting clusters of points will occur, differing both in slope and in elevation. When this change in size is sufficiently pronounced, juveniles and adults can be distinguished by eye, even when newly matured. The former pattern of intersecting phase lines has been called Type A allometiy, while the latter pattern may be known as Type B (Somerton, 1980(b); see also Hartnoll, 1978, 1982).

Male, anomuran crabs usually follow Type A allometry, for the growth of the chelae (Wallace et al , 1949; Somerton, 1980(b); Somerton & Macintosh, 1983(a); Jewett et al , 1985; Somerton & Otto, 1986). In this situation the estimation of size at morphological maturity involves finding the point of inflection between

99 3.1. Size at maturity the juvenile and adult growth phases. For some time, this has been done simply by graphing the data, and estimating the point of inflection ’by eye’ (e.g. Wallace et al , 1949; Watson, 1970; Brown & Powell, 1972; Davidson & Marsden, 1987). Subjectivity is slightly decreased by the method of ’intersect analysis’, proposed by George & Morgan (1979), for rock lobsters. Regression equations are fitted above and below the region of inflection, and, if the slopes are significantly different, the intersection of the two fitted lines estimates the size at morphological maturity. This approach has finally been extended to the simultaneous fitting of a two-line model including the point of inflection as one of its parameters. The size at morphological maturity is chosen as the point of inflection producing the minimum residual sum of squares around the model (Somerton, 1980(a); Somerton & Macintosh, 1983(a), Jewett et al , 1985; Somerton & Otto, 1986).

Materials and methods.

The size at morphological maturity of male P. granulosa has been estimated by the ’MATURE2’ algorithm of Somerton & Macintosh (1983(a)), based on the change in chelae allometry at maturity. In this and other similar methods, precision is maximised by measuring the widest possible size range of crabs (Somerton, 1980(b); Somerton & Macintosh, 1983(a)). To ensure representation of the smallest crabs, samples have therefore been obtained from special small meshed pots in addition to the regular sampling of the commercial pot types.

The analysis is based on a sample of 2283 male crabs measured for carapace length (CL) from the eye socket to the central posterior margin of the carapace, and for the maximum length of the major (usually the right) chela. All measurements were made to the nearest mm below using vernier calipers. The mid-points of 1mm length classes have been used in the calculations.

Crabs infected by the parasite Briarosaccus callosus and those showing the scar

100 3.1. Size at maturity of a previous infection were excluded from the analysis. Infected males do not follow the normal allometry pattern of healthy crabs and are thought to be castrated and feminised by the parasite (see section 4).

As maturity is estimated on the basis of chelae size, those crabs with chelae in the process of regeneration must also be excluded from the data set (Wallace et al , 1949; Jewett et al, 1985). Obvious cases, with very small claws relative to the size of the body have been rejected during sampling. More borderline cases only become apparent on plotting the morphometry data. In previous studies, negative outliers have been excluded from the data set until the change in the residual error around the model becomes negligible (Somerton & Macintosh, 1983(a); Somerton & Otto, 1986). In the present case 5 negative outliers stood out from the remaining cluster of points, with much larger deviations than the largest positive outlier. Deletion of these 5 data points resulted in an approximately symmetrical distribution of deviations around the subsequently fitted model (Somerton & Otto, 1986).

The MATURE2 method (Somerton & Macintosh, 1983(a)) works as follows. The point of intersection of the juvenile and mature phase lines is estimated by finding the best fit of the data to the following model:

Y = a + b X XX*

where X and Y are the logarithms of carapace length and chelae length respectively. X* is the desired parameter, the point of intersection of the two lines on the abscissa. Y is the equivalent point of intersection on the ordinate (ie Y* = a + bX*). The upper line is thus constrained to meet the the lower ♦ __ _ j|c one at the point X . The model has four parameters a, b , c and X .

101 3.1. Size at maturity

Finding the best fit of the model involves choosing a range of carapace lengths so that the point of intersection is contained within the range. Such a range should be obvious to the eye, even when the exact point of inflection is slightly obscure. The model is then fitted repeatedly, once for each possible value of X within the chosen range of carapace lengths. For each fitting, the slope and intercept of the lower line are estimated by least squares regression analysis using the data where X < X . The upper line is then similarly fitted with the constraint that it passes through the point X*,Y* as shown above. The parameters a , b and c are thus obtained for all possible values of X and the residual errors about each fit of the model are derived. The carapace length which best separates the data is that which produces the minimum residual sum of squares about the two fitted lines.

The significance of the fitted 2-line model has been tested against the fit of a single line to the data by the following partial F test:

F2jiA df = (RSS1 line ‘ RSS2 line) ! 2

RSS2 line / (n-4) where RSS^ line is the residual sum of squares (RSS) about a single line fit to the data, RSS2 \[nQ is the RSS about the two line model and n is the number of data points used (Somerton, 1980(b)). For samples in which the two line fit is not significantly better than a single linear regression, there is no justification for using the available morphometric data to estimate size at maturity.

The standard deviation of X* has been estimated by the statistical technique known as bootstrapping (Efron & Gong, 1983; Jewett et a\, 1985). The original data have been randomly subsampled with replacement, with each sample equal in size to the full data set. The best fitting X* has been found for a number of such subsamples and the standard deviation of these estimates has been used to estimate the standard deviation and confidence limits of the parameter.

102 3.1. Size at maturity

Results.

The crabs used in this analysis ranged in size between 24 and 97mm CL. The best fit of the data to the two-line model was obtained when the intersection, X , was set at 52mm. The partial F test was significant at P < 0.001 and the standard deviation of 175 bootstrapped estimates of the best fitting X* was 1.09. The estimated size at sexual maturity (±95% Cl) of male Paralomis granulosa in the Falkland Islands is therefore 52 ± 2.15 mm CL (see Figure 1).

In comparison with some estimates of size at male maturity in the literature, the size at maturity of male P. granulosa has been estimated with some accuracy. The coefficient of variation (CoV) of this parameter for golden king crab, Lithodes aequispina varies between 3.0 and 4.9% (Jewett et a\, 1985; Somerton & Otto, 1986). The CoVs for blue king crab, Paralithodes platypus , from standard deviations estimated by Monte Carlo simulation (Somerton & Macintosh, 1983(a)) are generally above 10%. The CoV estimated here for P. granulosa , however, is only 2.1%.

The chelae allometry method works best for species having a pronounced change in shape at maturity. Species showing only a slight change, such as the anomurans of the genus Paralithodes necessarily have a large variance associated with their maturity estimates (Jewett et al , 1985). The high accuracy reported here is partly due to the obvious change in allometry shown by P. granulosa. The large sample size and the extra sampling effort made on small crabs, are also thought to be contributory factors. Note that it is not implied that individuals of the species P. granulosa mature at a more constant size than those of other species. These methods do not give the state of maturity of individual crabs in the sample, nor the range of sizes at which maturity is attained. The allometry pattern of P. granulosa and the sampling programme followed have simply enabled the population size at maturity to be estimated with more confidence than usual.

1 0 3 3.1. Size at maturity

L o g C a ra p a c e L e n g th (mm)

Figure 1. Chelae length (mm) plotted against carapace length (mm) on logarithmic scales for 2283 male Paralomis granulosa. The best fitting 2-line model is shown, with the intersection point giving the estimated size at maturity at a carapace length of 52mm (dashed line).

1 0 4 3.1. Size at maturity

3.1.4. Estimation of the size at functional maturity of females.

Fem ale P. granulosa, on average, grow to much smaller sizes than males. Only a very small proportion reach a size at which they can be economically processed by hand picking. It is likely therefore that any fishery for P. granulosa in the

Falkland Islands would operate on a males-only basis, with the added benefit of maximising the reproductive capacity of the stock. The size at maturity of females is therefore unnecessary as regards setting size limits. It is of interest, however, to the investigation of the life history of the species and is estimated here for that purpose.

Of the three sizes at maturity, defined in the introduction, the parameter most commonly estimated for female crabs is functional maturity. In many lithodid species (e.g. Paralithodes platypus, Somerton & Macintosh, 1983(a); L ith o d e s a e q u isp in a, Jewette t a l, 1985), the eggs are released immediately after mating.

In such cases, it is possible to assume that the functional maturity of individual females can always be detected by the presence of either the ripening eggs or their remains beneath the abdomen. The estimation of size at functional maturity in these species is then a simple procedure yielding the most useful of the three parameters.

Not all individuals of a species mature at the same size. Indeed, the largest immature crab may be around three times the size of the smallest mature one

(e.g. Campbell & Eagles, 1983). In data-limited situations, it may only be possible to present the range of sizes at which maturity is attained (Brown &

Powell, 1972; Powell e t a l, 1973).

From a management aspect, it is more desirable to condense this range into a point estimate of the average size of maturation within the stock. A simple estimator of this size is found from the length at which half the animals in the stock are juveniles and half are adults. If the size at maturation of individuals follows a normal distribution, then this ’size at 50% maturity’ will be equal to the

105 3.1. Size at maturity mean size at first maturity within the stock (Wenner e t a l, 1974). In such circumstances, a plot of the percentage mature at length against size, will follow a cumulative normal distribution. The population size at maturity may be read directly from this graph (e.g. Watson, 1970 for physiological maturity). Plotting the percentage mature data on probability paper, however, will result in a straight line, over the range of maturity of the species, and may allow easier fitting of the data (Wenner e t a l 1974; Wenner e t a l, 1984). This approach also facilitates the easy approximation of the standard deviation around the size at maturity from the distance along the abscissa between the 16th (or 84th) and the

50th percentiles.

Alternatively, the percentage mature data may be fitted to the very similar logistic function, and the mean size at maturity estimated from the fitted parameters. This may be easily accomplished by weighted linear regression of the linear version of the logistic function (Berkson, 1944, in Somerton, 1980(b)).

More precise estimates may be obtained by non-linear least-squares fitting of the untransformed function (Somerton, 1981(a); Somerton & Macintosh, 1983(a);

Campbell & Eagles, 1983; Jewett e t a l, 1985; Somerton & Otto, 1986). In the case of non-linear fitting, the variance can be estimated by the Delta method

(Somerton, 1980(b)).

Given reasonable data, all these approaches will give similar estimates of the mean size at maturity. For species in which the eggs are held for long periods and moulting is followed immediately by ovulation, percentage mature data based on the presence or absence of eggs are often a good fit to the chosen sigmoid function. If, however, there are serious departures from the underlying assumptions, a degree of subjective interpretation will be necessary, and fitting

’by eye’ may be safer. Wenner e t a l, (1974), for example, found that not all functionally mature female mole crabs (Emerita analoga) were always ovigerous, particularly in the larger size classes, and were content to fit only the lower portion of a normal distribution, by eye, to their data.

106 3.1. Size at maturity

Materials and Methods.

The estimation of functional maturity of female P. granulosa has been made on data collected in the Choiseul Sound area between September 1987 and

December 1988. A total of 13793 female crabs between 22 and 80mm in length have been examined during five phases of sampling in the Falkland Islands.

For each crab, carapace length (CL) has been measured to the nearest mm below, from the eye socket to the central posterior margin of the carapace.

Four stages of female maturity were recognised: 1) non-ovigerous, 2) carrying uneyed eggs, 3) canying eyed eggs and 4) with empty egg cases. Crabs in the latter stage have hatched their eggs and carry the remnants until the next moulting, mating and ovulation. Crabs in classes 2-4 are mature. It has initially been assumed that non-ovigerous crabs are immature. The size at 50% functional maturity has been estimated from the percentage maturity in each

1mm class, based on this classification.

Crabs infected by the parasite Briarosaccus callosus have been excluded from the analysis, as have those showing the scar of a previous infection. B. callosus parasitism results in sterilisation of female P. granulosa (see section 3.4.).

Infection is revealed by the presence of the reproductive sac of the parasite, which protrudes from the ventral surface of the host’s abdomen in the normal position of the eggs. Parasites at an internal stage of development only were not detected. Certain recently infected crabs may therefore have been classed as juveniles when their non-ovigerous condition was, in fact, due to castration by the undetected parasite. However, as the overall prevalence of B. callosus is below 1% in females, the error associated with this misclassification is likely to be small.

107 3.1. Size at maturity

Results.

For female P. granulosa the proportion ovigerous in each length class does not follow the normal sigmoid pattern seen in other similar species (Figure 2a). The data approach, but do not quite reach, the expected maximum of unity in the middle size classes. With further increases in size, the proportion of females carrying eggs falls away from the asymptote, so that the largest females are mostly non-ovigerous.

Assuming that the largest females are, in fact, mature, the presence of reproductive material may not be a reliable indicator of sexual maturity, at least not for all size classes, of female P. granulosa.

The observed pattern may be due to several factors. The first questions the assumption that moulting is immediately followed by mating and ovulation as it is in other lithodid species (Powell e t a l, 1973; Somerton, 1981(a); Somerton &

Macintosh, 1983(a); Jewett e t a l, 1985). Two behaviour patterns are possible, either of which could lead to mature females being non-ovigerous for a short period during the moulting season. For females which do not immediately find a mate, there may be a short non-ovigerous period in-between moulting and mating. Alternatively, a period of time may be needed by a ll mated females between mating and the subsequent release of the fertilised eggs.

The data in Figure 2a are from samples collected during all seasons, including the mating season. If moulting is not immediately followed by release of the eggs, samples taken during the moult season would not be expected to show the normal sigmoid pattern. Data collected outside of the moult season, however, may still conform to the expected pattern. The moulting/mating season of fem ale P. granulosa occurs in the spring in the Falkland Islands (section 2). A combined data set taken from samples collected between May and July 1988 in the southern autumn/winter still does not take a sigmoid form (Figure 2b). The curve, however, is shifted to the left for this data set, suggesting that the above

108 3.1. Size at maturity effect is at least partially true.

It is evident that a proportion of mature females do not ovulate every year.

This may be the normal behaviour pattern for P. granulosa, with females taking a break from reproductive activity every few instars. Such strategies have been reported for many crustaceans (see Hartnoll, 1984 for a review). Alternatively, females may only be receptive for a short period after moulting, perhaps until the final hardening of the shell. Females which did not find a mate during this time would not ovulate for the duration of that instar. This is perhaps the most likely explanation. Assuming that females are mated only by males larger than

themselves (Powell & Nickerson, 1965; Powell e t a l, 1973) larger females would find it increasingly difficult to find a suitable mate in time, thus explaining the

decreasing proportion ovigerous by size seen in figure 2.

Both the above proposals would have a limited effect on small, newly matured

females. In the first case such crabs would be expected to mate and ovulate at

their first available opportunity. Secondly, the smallest mature crabs have the

greatest chance of finding a mate larger than themselves.

Therefore, the proportion of females ovigerous, in small size classes at least, may

closely follow the true curve of the proportion functionally mature. While it would be incorrect to fit cumulative normal or logistic functions to such data, a

reasonable estimate of the size at 50% functional maturity may still be obtained

by fitting the lower portion of the data only, by eye (Wenner e t a l, 1974). Using

only the data from the autumn/winter sampling period, the size at 50%

functional maturity has thus been found to occur at approximately 46mm (figure

2b).

The available data set does not allow accurate estimation of the standard

deviation around this parameter. Nor is it possible to give a range of sizes at

first maturation, although the smallest ovigerous female measured was 44mm in

carapace length.

109 3.1. Size at maturity

o

Carapace Length (mm)

Figure 2. The proportion of female P. granulosa in ovigerous condition (including those carrying empty egg cases) in 1mm classes of carapace length. Unconnected data points signify size classes with less than 10 animals, a) Data from all seasons combined, n = 13793. b) Data from samples taken during autumn and winter to exclude the spring mating season, n = 3787.

11 0 3.1. Size at maturity

3.1.5. Summary

The mean size at morphological maturity of male P. granulosa has been estimated from the change in the relative growth of the major chela, a secondary sexual characteristic, as 52mm CL. The estimate has more precision than those seen in the literature for other lithodids, due partly to the pronounced change in allometry shown by this species. Like other lithodid species, however, P. granulosa shows a change only in the relative growth rate of the chelae at morphological maturity. The relative size of the chelae thus changes gradually, possibly only achieving a functional size after a few adult moults. The estimate must therefore be regarded only as a lower limit for the true size at male functional maturity. The implications of these results are further discussed in a number of later sections.

The size at 50% functional maturity of female crabs has been estimated directly as 46mm CL, on the assumption that all newly matured females are ovigerous during the winter incubation period. The great majority of females between 50 and 60mm CL are in reproductive condition at this time. In contrast to other lithodid species, where all the largest females would be carrying eggs, female P. granulosa over and above this size are increasingly non-ovigerous. Harvesting the few females caught larger than the present size limit used for males would therefore have little effect on the reproductive capacity of the stock.

I l l 3.2. Life History

3.2. Life History

3.2.1. Introduction

Very little is known about the life history of Paralomis granulosa, particularly so for populations from the Falkland Islands. In Chile, male crabs have been reported to moult over an extended period during winter and early spring. Female crabs hatch their eggs in spring and moult shortly afterwards, followed immediately by mating and the subsequent release of the eggs. Adult crabs of both sexes are thought to moult annually in Chilean waters (Campodonico et al, 1983). Adult males are also apparently believed to occupy slightly deeper water than females during most of the year, and to migrate upwards on to shallow water to mate in the spring (Campodonico pers com , in Fortoser, 1986(b)).

The life history of P. granulosa in the Falkland Islands has previously been assumed to follow the pattern described above. However, the frequency of moulting and the timing of the moult seasons have important implications both for the estimation of growth rates and for the protection of vulnerable animals, by closed seasons. Knowledge of the seasonal migration pattern of the stock is equally essential for the correct interpretation of apparent changes in localised abundance. This section attempts to answer these demands, by describing the moulting pattern of crabs by sex, size, locality and season and examining the reproductive activity of the stock both in time and space.

3.2.2. The effect of depth / habitat on the size distribution of crabs

The distribution of crabs smaller than about 50mm CL was largely unknown during the period of commercial fishing operations, for two main reasons. Firstly, even the smallest-meshed of the commercial pots would not retain crabs smaller than this approximate size and secondly, as shown in this section, it

112 3.2. Life History appears that the fishing gear was simply never set on the main nursery grounds.

In the coastal regions of Chile, small specimens of both P. granulosa and the larger king crab, Lithodes antarctica, have been found living among the holdfasts of the Giant kelp, Macrocystis pyrifera (various authors in Campodonico et al, 1983). Extensive beds of this kelp are also found in the shallow waters of Choiseul Sound and throughout the Falkland Islands. The species is distributed in waters up to 15m deep, attached to rocky substrates by large, branched holdfasts with long fronds reaching up to the surface waters. During the commercial phases, however, the gear was never set among these kelp beds possibly due to the supposed lack of large crabs in such habitats but also because of the increased risks of either fouling the gear or clogging the water intake of the vessel.

In order to test if small crabs were also associated with kelp beds in the Falkland Islands, strings of special small meshed pots were set in dense beds of kelp, and the catches compared with those taken from the edges of the kelp beds and in deeper open water. The resulting size distributions (see figure 1 for males and figure 2 for females) are aggregations of several samples taken from different locations in Choiseul Sound representing each ’habitat type’. The open water samples were collected over an extended period between January and July 1988 while the remaining shallow water samples were taken only during the austral spring in November and December 1988. It is initially assumed that the samples obtained are unbiased representations of the community structure on each habitat, for the year as a whole.

Considering only the distributions labelled a and d, it is evident that crabs of both sexes inhabit the kelp beds while small and are found in open water mostly at larger sizes. For both sexes this ontogenic migration from the shallow water kelp beds to deeper, open water occurs at approximately 50mm and is, therefore, likely to be correlated with the onset of maturity.

113 3.2. Life History

The distributions found at the edges of kelp beds (figures lb and 2b) and in deeper water but still close to large areas of kelp (figures lc and 2c) show that both juveniles and adults may be found in these locations. It may be more correct to say that both types of crabs may be attracted to baited pots set in these locations. The size distributions of male crabs from these two peripheral areas are more similar than those observed for females. It is possible that juvenile females are less inclined to leave the protection offered by the holdfasts of the kelp.

The distribution of juveniles outside of the spring period remains unproven. As they were captured only in small numbers in the deeper open water throughout both summer and autumn (figures Id and 2d), it is assumed that they continue to be associated with the shallow water kelp beds during these seasons at least. It is possible that the juveniles migrate deeper in winter to escape the coldest waters.

Finally, the distribution of the very smallest crabs also remains unknown as very few crabs smaller than 30mm were captured from any of the habitats sampled (figures 1 and 2). Their absence can not be explained by the selectivity of the gear as the fine meshed pots used would certainly have retained crabs much smaller than 30mm. It is thought most probable that these smallest animals do also live in the sheltered kelp beds, but that they are inhibited from entering the pots by larger individuals or, alternatively, that they do not lead a scavenging lifestyle at this size and were simply not attracted by the baits used.

114 water iue . Lengthfrequencies 1mmFigure crabsmale classes in 1. of from: deep waterdeepadjacent beds kelp to ) ep beds kelpa) Frequency (n 483). = (n = 168), b) the edges of kelp beds of edges the 168), b) = aaae egh (mm) Length Carapace 115 (n 50 ad ) ep open deep and d) 560) = (n 84, c) 814), = .. f History ife L 3.2.

3.2. Life History

Figure 2. Length frequencies in 1mm classes of female crabs from: a) kelp beds (n = 194), b) the edges of kelp beds (n = 451), c) deep water adjacent to kelp beds (n = 278) and d) deep open water (n = 549).

116 3.2. Life History

3.2.3. Temporal organisation of the moulting and mating cycles

During routine sampling in the Choiseul Sound region of the Falkland Islands, data have been collected in order to examine the timing of the moult cycles of both sexes of crab and the seasonality of the reproductive activity of female crabs. In their final form, the data estimate the percentage of the total number of adult crabs of each sex in Choiseul Sound in each combination of moult and maturity stages for each month of sampling. The raw data have been collected and prepared as follows.

Collection of the raw data

The basic sampling unit of this analysis has been the pot and only the small- meshed type of creels (or CR pots) have been used. The large mesh sizes of the other commercial inkwell pots and the escape holes tied into the creel pots to improve commercial selectivity cause the samples from these pot types to be biased towards larger crabs only and to be vulnerable to changes in sample composition caused by the escape of small crabs after long soaktimes. The unmodified small-meshed creel pots, without escape holes, produce far more representative and consistent samples and only these samples have therefore been used. The mesh of the CR pots retains crabs over approximately 50mm, so that the analysis can reasonably be considered to be restricted to adults only. The close correlation of the selectivity of the pots with the sizes at maturity of both males and females also means that the estimates produced for the percentages in each moult stage etc. may be taken to represent the percentages of virtually the whole adult populations. Any size-specific effects are thus ignored at this stage and the timing of the cycles is estimated here for adults only, as two homogenous groups, males and females.

As many pot samples as possible have been taken from each string, depending on the time available and on the fullness of the pots. Each crab in a sample

117 3.2. Life History has first been classified by sex, detectable macroscopically on the basis of abdominal structure at all sizes encountered. Normally, all the crabs in the selected pot have then been measured for carapace length (CL) and further classified according to moult stage and also, in females, by maturity stage. Apart from a small contribution to the weighting procedure, the length data have not been used in this analysis: the raw data thus take the simple form of the number of (adult) crabs in each category of sex, moult stage and maturity stage in each sample.

Three moult stages have been recognised: 1) soft, with a completely unhardened shell after moulting, 2) recently moulted, with a hardened, but still clean and bright shell and only 5 or less epifauna growing on the carapace and 3) intermoult, with an abraded shell and more than 5 epifauna living on the carapace. As only a tiny percentage of crabs have been recorded with ’soft’ shells (0.03%), this moult stage has been included in the recently moulted class for analysis. In the results, recently moulted and intermoult crabs are coded R and I respectively. The analysis of male crabs is restricted to the cyclic variation in the proportions of these two categories only.

Female crabs, however, have also been classified according to their reproductive condition in four stages: 1) non-ovigerous (coded N), 2) carrying uneyed eggs (U), 3) carrying eyed eggs (E) and 4) carrying empty egg cases (C). Non- ovigerous females may be either juveniles or, in some cases, adults which have moulted and not yet released eggs. The eggs, or more correctly fertilised embryos, as seen in the brood pouch under the abdomen, are uneyed when first extruded and become eyed during the incubatory period. Females carrying empty egg cases have hatched their eggs and are awaiting their next moult. Lithodid females do not store sperm and must moult immediately before copulating, at the beginning of each reproductive cycle (Powell et al , 1973; Somerton & Macintosh, 1983(a), Jewett et al, 1985). Intermoult females may be in any of these four classes but recently moulted females have only been found to be either non-ovigerous or carrying uneyed eggs. In all, six categories of

118 3.2. Life History

female crabs have thus been recognised in this analysis, coded as follows: IN, IU, IE, IC, RN and RU.

Infection by the rhizocephalan barnacle Briarosaccus callosus has been recorded as the presence of the reproductive sac or ’externa’ of the parasite, or as the scar of a previous infection. B. callosus is thought to cause castration in both sexes of P. granulosa (see section 3.4.) and such infected animals have been excluded from the analysis.

Samples have only been taken from scientist-observed strings. The selection of pots for sampling has not been on a random basis, but biased towards the fuller pots to reduce the interference of sampling on the fishing activities. Abundance, as measured in terms of catch per pot, is therefore overestimated in these data but the composition of the samples by sex, moult stage and so on is still thought to be reasonably unbiased.

Due to the great natural variation in the patterns of moulting and mating, not only with time but spatially around the sound, a great deal of information is necessary to produce accurate analyses of these phenomena. Effort has therefore been deliberately directed towards sampling the small meshed creel pots. During the period of this research, 287 strings of creels have been observed, leading to 653 samples, each sample generally being the whole contents of a single pot. A total of 55369 crabs have thus been sampled during the project, of which 39326 have been measured from samples taken from CR pots in Choiseul Sound. Of these, 30335 have also been categorised by moult stage and maturity stage (in the case of females) and were not carrying the extemae of the parasite B. callosus. The analysis has been made on the latter sample size.

With the exception of August, September and most of October 1988, sampling in Choiseul Sound has been almost continuous between September 1987 and December 1988. The data thus form a fairly comprehensive examination of the

119 3.2. Life History full years moulting and reproductive activity of P. granulosa , with replication of sampling during the important months November and December.

From this extensive data set, the many pot sample results have been aggregated to estimate the proportions of the total adult stock in each combination of moult stage and reproductive condition in each month. Unfortunately, sampling has not been a spatially random procedure; neither has sampling effort been proportional to localised abundance. This aggregation has, therefore, not been the simple matter of taking just the mean of all the pot samples in each month. During the first four phases of commercial exploitation and sampling, the setting of the gear has been completely under the direction of the skipper of the Laura Jay. Effort has understandably been concentrated on portions of the stock with the largest numbers of the largest male crabs. Other areas, with low abundances of large males, but possibly large numbers of females or small males, have been visited occasionally and then avoided. In these four phases, the majority of sampling has thus also been limited to the areas of greatest commercial attraction so that an unadjusted monthly average would represent mostly the situation in these areas. To compensate for these effects, various weightings have therefore been necessary to the aggregation procedure, as explained in the next section.

Aggregation of the raw pot-sample data into monthly estimates

In terms of the distribution of crabs, Choiseul Sound is far from a homogenous area. Various categories of crabs, moulting males for example or large females, have been observed to be aggregated in certain areas at certain times often with great variations in relative densities. In order to take this variability into account, Choiseul Sound has been divided up into 36 ’grounds’ of variable size, delimited partly by geographic features such as islands and shallow reefs and partly by concentrations of fishing effort both in space and time. Sampling has been conducted with the aim of producing data from as many of these grounds

120 3.2. Life History as possible in each month. The aggregation procedure has then been weighted to take account of the relative stock sizes on each of the different grounds, so that the averaged monthly estimates are the best possible reflection of all the different activities occurring in the area as a whole, at each time.

Obviously, with the commercial direction of fishing effort followed in phases 1 to 4, ftwer grounds have often been sampled than would have been desirable. However, it is assumed that in each month, a sufficient range of grounds have been visited and sampled to identify most of the current moulting and reproductive activities of the stock. During phase 5 of sampling, the activities of the Laura Jay were wholly under scientific direction. During November of this phase, all the major grounds of Choiseul Sound have been sampled and it has been possible to divide this month into two fortnightly periods for more detailed analysis.

As described in the previous section, the raw data are in the form of the number of adult crabs in each of the specified categories, from each pot sample. In the first stage of the analysis, all the pot samples from each string have been combined and the strings have been classified according to the month and the ground from which they were taken. For each sex separately, the total numbers in each category have then been expressed as percentages of the total sample sizes from the string. Each string thus produces two sets of percentage data (one for each sex) in the form P denoting the percentage of crabs in category i, in month m , from ground g and from string s. The eventual aim of this section is to reduce these data sets into the form P ^ , as the percentages in each category in each month for Choiseul Sound as a whole, single unit. The aggregation procedure thus uses two separate weighted averages, the first over all replicate strings to get P[mg and the second over all the grounds sampled each month to produce Pim . These procedures are slightly different for each sex, so the general method is described first for the males and later amended for the females.

121 3.2. Life History

In both parts of this procedure, the averages have been weighted by the relative abundances of crabs in the different sub-units concerned, in the first case within each string and in the second case, each ground. Thus, the percentages, of crabs in each category, in each month and in each ground sampled (or in each month/ground unit, or MGU) are estimated as the weighted averages of all the string results from the MGU, as given by:

mg p . E P. A ung- * imgs * mgs (i) s = 1

n mg ^ m g s s = 1

where nmg is the number of strings sampled in month m and ground g, and A m^s is the CPUEadj (see section 2) of the relevant string. The parameter A thus represents the relative abundances of the catches from the different strings and the result is consequently weighted towards those samples taken from the most densely populated parts of each ground.

The second average, giving the final proportions in each month for Choiseul Sound as a whole, is similarly weighted, thus:

p . y P. A un.. ^ img. * m g (2) g= 1

^ ^ m g 1

where nm is the number of grounds sampled during month m and, now, A ms represents the relative abundances of the crabs in the different MGUs. This second abundance parameter is somewhat more complicated than the first and

122 3.2. Life History

has been calculated as:

A mg CPUEwg . AREAg. SIZERATIOg

where CPUEmg is the overall CPUEadj for all the strings hauled from the MGU (not just those contributing samples),

AREAg is the area of ground g , and

SIZERATIOg is the ratio, in ground g , of the total number of male crabs sampled over the number >80mm in length.

The reasons for including these factors are as follows. The CPUE^g is the

relative d e n s ity of crabs o v e r 8 0 m m in length within the MGU concerned (see section 2). The use of AREAg thus weights the analysis by abundance, rather than density and the use of SIZERATIOg further weights the analysis by the abundance of the whole adult male population, instead of the abundance of only those animals over 80mm. The monthly averages, are thus weighted according to the relative contribution of each ground to the total (numerical) size of the whole adult male stock in Choiseul Sound. The size ratio correction is necessary to avoid the possible under-representation of any activities occurring on grounds containing mostly small adult crabs (and with consequently low CPUE^gS). These complications were not necessary to the first step of the procedure (eq. (1)), because all replicate strings were taken from single MGUs and it may be reasonably assumed that the size composition is approximately constant within such local areas.

The monthly proportions for females (in six categories, instead of the two for males) have been estimated in exactly the same way, except that, in the second reduction of the data (eq. (2)), the average has been weighted by the relative

abundance of adult females, not males. The parameter, A m s for females has thus been calculated as:

A mg CPUEmg . AREAg . SIZERATIOg . SEXRATIO^g

123 3.2. Life History where the new factor, SEXRATIO^ has been estimated as the ratio, within each MGU, of the total number of females captured over the total number of males.

Both SIZERATIO^ and SEXRATIO^ have been calculated in a similar way to equation (1), weighted by the CPUEadj of each string contributing samples. Unfortunately, it has not been possible to calculate the SIZERATIO^ parameter separately for each month (hence the single subscript), for the following reason. In certain grounds with very few large crabs, all the samples taken in one or more months did not contain any male crabs over 80mm, so that calculation of the necessary ratio for these MGUs is impossible. Increasing sample size by aggregating the whole years data provided the necessary measurements of large crabs in these grounds. A small amount of smoothing of the results is to be expected from this approximation.

Using the methods outlined, all the samples taken have been utilised in a manner which should be unbiased either by sample size or fishing effort. Although different grounds have been sampled in each month, given the available data, the monthly figures produced are thought to be the best possible estimates of the true, overall percentages in each of the specified categories among the whole, adult stock of Choiseul Sound.

As a final comment, it may be noted that the assumption is made, that the crabs of Choiseul Sound, as far as moulting and reproduction are concerned, do actually form a unit stock. This is not to say that individual crabs do not migrate into or out of Choiseul Sound at certain times of the year. It simply implies that all the components of the moulting and reproductive cycles do, in fact, take place within the sampled area of the Sound, as they are presumed to do in other similar stocks around the Falkland Islands. Thus, by estimating the percentage of animals in each category in each month in Choiseul Sound, it is assumed that the resulting estimates reflect all the different behaviour patterns within the unit stock at that time. If this were not the case and only non­

124 3.1 Life History moulting crabs, for example, migrated out of the sound into deep water at a certain time of year, then the proportion of crabs moulting (within the unit stock) at this time would be overestimated. This assumption is thought to be reasonable as the great majority of crabs in the Falkland Islands have been found to occupy the central regions of large inlets like Choiseul Sound. Progressively lower abundances are obtained as one moves away from such areas towards the open sea, and very few crabs have been found around the more exposed headlands separating the stocks of individual sounds (Fortoser, 1986(b)).

Results

The aggregated monthly data (P^ of the previous section) for both males and females are given in table 1, as are the total number of crabs sampled in each month and the average surface sea temperatures. The latter measurements were taken at berth, once each fishing day, in the early mornings. It is thought that the shallow depth of Choiseul Sound and the regular strong winds would cause fairly rapid transmission of surface water temperatures to all depths within the sound.

Before examining the actual proportions, it may be noted that sample sizes were relatively small during all of 1987 and in April and October of 1988. Results obtained for these periods may, therefore, be less accurate than those of other months. In addition, the statistics for October 1988 have been derived from only a single days sampling at the end of the month and must be taken to represent the situation at only that time. Similarly, the data for December 1988, while fairly comprehensive, were collected during only the first week of the month. No samples were taken during August and September 1988.

125 3.2. Life History

Timing of the moult cycles

Recently moulted adult males have mostly been found in the catches taken during the austral spring, between the end of October and early December (figure 3b). As with many other crustaceans (Conan, 1984), a second moult period also occurs in the autumn. For P. granulosa in Choiseul Sound, though, it is evident that the great majority of crabs moult in the spring season (figure 3b). Recently moulted adult females have been caught slightly later than the males, mostly during the second half of November and early December (figure 4e,f). This pattern is also found in many crab species and is thought to be an adaptation for the mating of hard-shelled males with soft-shelled females (Conan, 1984). The stocks of both sexes, however, have never been found to be in 100% recently moulted condition in any of the months sampled. This result is further examined in the following section (3.2.4.) on moult frequency.

The periods quoted are the times when ’recently moulted’ crabs have been caught: given the definition of this moult stage, these times must be slightly after the actual moult seasons. As soft crabs have been caught so infrequently, a short period must exist between moulting and the subsequent capture of the crabs in ’R’ condition. The time then taken by these crabs to become ’intermoult’ depends on the rates of deposition and growth of epifauna on the shell of the host. Both these periods, unfortunately, are unknown. Assuming that hardening of the shell takes around one week and that the achievement of intermoult condition takes approximately another month, then ’recently moulted’ crabs would be found in the catches from a week after the start of the moult season to a month after the end. On these assumptions, which are thought to be reasonable, the male moult period would take place between early October and late November; female crabs, similarly, would moult between the middle of November and the middle of December.

These moult seasons are correlated with the warming of the inshore waters in the austral spring (figure 3c). Females moult approximately one month after

126 3.2. Life History

males. Assuming that both sexes take an equal amount of time to become ’intermoult’ after moulting, female moulting activity is more synchronised than that of males.

Timing of the reproductive cycle

The mating period of P. granulosa, if it is associated with the female moult

period as in other lithodids (Powell e t a l, 1973; Somerton & Macintosh, 1983(a);

Jewette t a l, 1985), therefore, also takes place in late November and early December. The uneyed eggs of recently moulted females are released predominantly in December (figure 4f). If December 1988 had been more evenly sampled, a greater percentage of recently moulted females may have been expected to have been ovigerous at this time, as found in the previous year. By January 1988, the majority of females had ovulated and become intermoult. The small percentage of recently moulted females observed in April 1988 is largely due to a heavy weighting coincidentally applied to a single small sample.

Females with eyed eggs formed an increasing percentage of the samples taken between February and July (figure 4c). The eggs, therefore, mature as water temperatures decrease in the austral autumn (figure 3c). Females carrying empty egg cases, after hatching their eggs, were never found to comprise a large percentage of the samples taken (figure 4d). However, as females with eyed eggs had virtually disappeared from the catches of October 1987 and were completely absent from the samples at the end of October 1988, the eggs are assumed to hatch at some time between August and October in the austral winter. As the females carrying eyed eggs were not replaced in equal proportions by crabs with empty egg cases, it must be assumed that the latter do not feed greatly during preparations for their forthcoming moult. A sharp decline in CPUE at the time of moulting and mating, attributed to ’disinterest in feeding’, has similarly been shown for stocks of Paralithodes camtschatica in

Alaska (Powell e t a l, 1973).

127 3.2. Life History

In the period between October and early November, leading up to the female moulting and mating season, catches of females were virtually restricted to those in intermoult condition carrying uneyed eggs. Such crabs would not be expected to moult in the present years moult season and it is concluded that the reproductive cycle of such females has a duration of longer than one year. This conclusion is further supported by the observed percentages of both females with eyed eggs and those in recently moulted condition, neither of which completely dominate the catches at any stage in the cycle.

Given the synchronisation of the female moult season at only one time of year, seen in figures 4e and 4f, the female reproductive cycle is further assumed to have a period of some multiple of one year, most probably two years. Those intermoult females with uneyed eggs captured in October and November are all presumed to have moulted the previous year, and dominate the catches at this time due to the inactivity of crabs with recently hatched eggs. After the moult season, around January and February half the intermoult females with uneyed eggs would be last years ’cohort’ and the other half would just have moulted, mated, ovulated and finally become newly ’intermoult’. Only the former group are assumed to ripen and hatch their eggs in the coming autumn and winter, to produce the patterns seen in figures 4b and 4c. In the field, during autumn, females with the most abraded and encrusted ’intermoult’ shells have invariably been found to be carrying eyed eggs. Such females are thus presumed to have spent considerably longer (probably one year longer) in intermoult condition than females with uneyed eggs. If this interpretation is correct, the normal incubation period of P. granulosa is between 20 and 23 months in duration.

The pattern shown by non-ovigerous female crabs (figure 4a) is not fully understood. In section 3.1.4. it has been shown that not all females, particularly in the larger size classes, ovulate after every moult. Non-ovigerous females are, therefore, to be expected as a small component of the catches in each month. Large, non-ovigerous females were noted to have been particularly common in the peripheral, shallow water grounds during the summer. Increases in the

128 3.2. Life History percentages of non-ovigerous females observed during the austral summer and autumn (figure 4a) may, thus, be due to the increase in fishing effort (and hence sampling effort) which was applied to the peripheral areas at this time.

129 3.2. Life History

Table 1. a) The percentages of adult male crabs in Choiseul Sound in each moult stage (I = intermoult, R = recently moulted) in each month of sampling, b) the equivalent percentages of adult female crabs further subdivided by reproductive condition (N = non-ovigerous, U = uneyed eggs, E = eyed eggs, C = empty egg cases), c) the monthly sample size, and d) the average surface sea temperature in each month. Samples taken during November 1988 have been divided into two fortnightly periods. No samples were taken during August and September 1988.

a b c d

Sex M ale Fem ale

Moult Stage I R I I I I R R

Reproductive N U E C N u C ondition Surface Sam ple sea temp, Year M onth size (°C )

87 Sep 94 6 9 68 23 0 0 0 320 3.5 87 Oct 66 34 2 95 2 1 0 0 492 6.7 87 N ov 47 53 0 98 0 0 1 1 286 9.7 87 D ec 90 10 11 52 0 0 6 32 344 11.8 88 Jan 97 3 10 84 0 1 1 5 2436 11.9 88 Feb 100 0 14 83 2 0 0 1 2136 11.4 88 Mar 100 0 17 65 16 1 0 1 1158 11.6 88 Apr 98 2 16 69 11 0 0 3 611 8.8 88 May ' 98 2 10 52 37 1 0 0 1614 5.4 88 Jun 99 1 10 51 39 1 0 0 3856 2.8 88 Jul 99 1 6 33 60 1 0 0 3195 2.4 88 Aug 88 Sep 88 Oct 25 75 2 98 0 1 0 0 210 5.7 88 N ov 1 50 50 4 90 0 5 1 0 4854 8.5 88 N ov 2 32 68 2 80 0 2 13 3 6581 88 D ec 40 60 3 61 0 1 15 19 2242 9.3

130 3.2. Life History

100 -J 90 - 3. 80 - m 70 - bi 60 - •p(d tn 40

o n ao CDcd R (D Clt 40(0 P CJCD CD>4 P4

9 10 11 12 1 2 3 4 5 6 7 6 9 10 11 12

Time (months of year)

CJ CDCO CD H cn CD •a CD >H 40p >ocd CD 0P i CD Eh CD a •+HClJ >H P cn Time (months of year)

Figure 3. The monthly percentages of adult male crabs in Choiseul Sound between September 1987 and December 1988 in a) intermoult and b) recently moulted condition, and c) the average surface sea temperature (°C) in each month. No samples were taken during August and September 1988.

131 3.2. Life History

2D n S ID - 1 M M, I I I JUU l ioa -i 50 - 80 - Q) 70 - bi (0 60 - p cn 1) 50 - >, 40 - p •H 30 - P 20 - 2 P 10 - cd m 0 4 p i—i 2 o

o cd CD

•p CD fcn cd p C a) o p CD P-i

Time (months of year)

Figure 4. The monthly percentages of adult female crabs in Choiseul Sound between September 1987 and December 1988 in the following categories of moult stage and reproductive condition: a) intermoult, non-ovigerous b) intermoult, with uneyed eggs c) intermoult, with eyed eggs d) intermoult, with empty egg cases e) recently moulted, non-ovigerous f) recently moulted, with uneyed eggs.

132 3.2. Life History

3.2.4. The effect of size on moult frequency

One of the main objectives of this analysis has been to investigate the moult frequency of both juvenile and adult P. granulosa. The extensive data on the moult stages of individual crabs, collected during the 1988 moult seasons (sampling phase 5) are therefore examined in this section as a function of crab size.

The samples used in this analysis have been taken from both the unmodified creel pots used in the previous section and from the special, small meshed pots also used to examine the effect of depth and habitat on size distribution (section 3.2.2.). A size range covering both juveniles and adults has thus been examined. Morphological maturity of males is initially assumed to occur, on average, at 52mm as found in section 3.1. Functional maturity of females is likewise assumed to take place at approximately 46mm.

To illustrate the changes in the observed moulting patterns during the progression of the moult seasons, the data have been subdivided into the following three periods. As in the previous section, the data from November have been divided into two halves. The samples taken in the first week of December form the third time phase. The few animals sampled at the very end of October have been included in the first class.

The complicated weighting of samples, employed in the last section (3.2.3.), has not been used in this analysis for the following reason. It has been necessary to sample from the special, small meshed pots to include juveniles in the data set. These pots, however, have regularly been set in unusual habitats in ’grounds’ without any other commercial pot hauls for the period. No CPUEadj data are thus available to weight these samples. However, a wide variety of locations, distributed throughout Choiseul Sound, have been sampled in each of the three time periods defined. It is thought that the aggregation of the data without weighting provides a fair reflection of all the activities taking place within all the

133 3.2. Life History components of the unit stock at each time. The data are thus simply presented, for each sex in each time period, as the proportion of all the crabs measured in each 1mm class of carapace length which were in recently moulted condition.

The tiny proportion of crabs captured in ’soft* condition have again been included in the recently moulted class.

In previous analyses of size-specific moulting probabilities (W eber & Miyahara,

1962; M ohr & Hankin, 1989), similar data have been presented but as the proportions of crabs in each length interval actually intending to moult in a forthcoming moult season. This is achieved by reducing the size of the recently moulted animals by one moult increment each, to find the length frequency of the same animals before the moult season. This distribution is then compared to that of the unmoulted crabs (which is obviously unchanged during the season) to find the correct probability of moulting from a particular length class. A further correction may also be made for the probable increase in mortality rate among the moulting animals (M ohr & Hankin, 1989).

The above corrections have not been made in this analysis, however, because neither the moult increments nor the increase in mortality due to moulting are k n o w n fo r P. granulosa. Because of these omissions, the observed proportions of animals in recently moulted condition are slightly greater than the real probabilities of moulting. This bias only affects the older animals (those which moult less than annually) but is increasingly significant in the very largest size classes. The actual magnitude of the effect depends on the amount by which the ’R ’ length frequency needs to be adjusted. Assum ing that growth and mortality rates are relatively low in P. granulosa (see sections 3.3. and 5.2.2.), the bias is probably fairly small in this case. In the absence of further information, the observed proportions must simply be interpreted as upper limits to the true probabilities of moulting from each size class. In terms of intermoult periods,

(being the reciprocals of the yearly moult probabilities), the results suggested in the next section should therefore be taken as lower limits to the true values for

P. granulosa.

134 3.2. Life History

Results

In the previous section on the timing of the adult moult cycle, neither sex has ever been found to be in 100% recently moulted condition in any of the months sampled. However, virtually all the juveniles captured during both halves of November have been found to be recently moulted (see figures 5a,b for males and 6a,b for females). It is thus concluded that the great majority of the juvenile population of P. granulosa moults at some time during October. By the first week of December, the proportion of recently moulted juveniles had been much reduced, as crabs became ’intermoult’ again due to epifaunal growth (figures 5c and 6c).

Moulting is concluded to take place at least once a year for all juvenile crabs of both sexes. In contrast to the larger juvenile females, note that the smallest females, on average, were intermoult in early November, and had recently moulted by December. The smallest crabs, (probably including the males), are thus assumed to have a different, most likely more frequent, moulting pattern than older, larger juveniles. In the absence of data on the moulting of juveniles during the rest of the year, it is impossible to predict with certainty the true moult frequency of these crabs. Assuming that juveniles, like adults, only moult at this time of year, it is thought most likely that the larger juveniles moult annually, with the smaller crabs moulting twice per year, and probably even more frequently at the very smallest sizes.

In the case of adult crabs, each sex must be considered separately, due to the different timing of the two moult seasons. Adult males have been assumed in section 3.2.3. to moult between early October and late November. In both early and late November (figures 5a and 5b) virtually all the small adult males (over 52mm) had recently moulted, but only around half of those in the larger size classes had done so. It is proposed that small adult males continue to moult (at least) annually after becoming mature, for perhaps one or two years, but that moulting thereafter is less frequent, probably a biennial occurrence. Note that

135 3.2. Life History

the largest males are even more rarely found in recently moulted condition (even less would be apparent if the correction for moult increment noted in the previous section had been made). Moult frequency is therefore likely to decrease still further, probably to a three year period, in these largest adult males.

Adult female crabs have been assumed in section 3.2.3. to moult between the middle of November and the middle of December. Allowing for a short delay (for the hardening of the shell) between moulting and subsequently finding recently moulted females in the samples, the present analysis upholds this interpretation. Very few recently moulted adult females had been captured by the first half of November (figure 6a), and the proportion had only increased slightly by the second half of the month (figure 6b). By early December,^ however, a significant proportion of the sampled adult females had moulted (figure 6c).

In contrast to the male pattern, figure 6c does not obviously suggest either annual or biennial moulting in adult females. It does, however, imply that moult frequency is reduced in older adult females. This reduction occurs more immediately after maturation than is the case for males, which may be due to the increased energetic investment of females in reproductive activity (Hartnoll, 1984).

It is unfortunate that the later weeks of December 1988 were not sampled. It is possible that sampling has been interrupted before the end of the 1988 female moult season. In that case, figure 6c may underestimate the proportion of adult females moulting in this season. However, virtually no adult females were found in recently moulted condition in the January succeeding the 1987 moult season (figure 4 in section 3.2.3). If the moult seasons occurred at the same time in both years and all the females moulting in 1988 were to become intermoult by January of the next year, the proportions of adult females moulting in 1988 would be unlikely to increase greatly beyond those seen in figure 6c. Whatever

136 3 . 2 Life History assumptions are made, it is unlikely that moulting is an annual occurrence in adult females.

137 3.2. Life History

Carapace Length (mm)

Figure 5. The proportion of male crabs in recently moulted condition in 1mm classes of carapace length in a) early November ( n = 3877), b) late November (n = 5219) and c) early December (n = 1766) during the 1988 moult season in Choiseul Sound. Unconnected data points represent length classes with less than 10 measurements.

138 3.2. Life History

Figure 6. The proportion of female crabs in recently moulted condition in 1mm classes of carapace length in a) early November (n = 2670), b) late November (n = 2280) and c) early December (n — 711) during the 1988 moult season in Choiseul Sound. Unconnected data points represent length classes with less than 10 measurements.

139 3.2. Life History

3.2.5. Spatial organisation of the moulting and mating cycles

In section 3.2.3., the timing of the moulting and mating cycles has been examined by considering the whole of the Choiseul Sound stock as a single, homogenous unit. In this section, the spatial organisation of these cycles is determined, using the same raw data, but with the information from each ground kept separate within each month.

As for the temporal analysis, the percentages of crabs in each sex, moult stage and reproductive condition have first been calculated for each month / ground unit (MGU) from which samples have been collected. In this spatial examination, the technique of cluster analysis has then been used to define relatively homogenous clusters or communities of crabs. Both temporal and spatial changes in community structure have thus been examined simultaneously, so that neither seasons nor areas needed to be specified in advance of the analysis. For each defined cluster, the average composition of the stock is described along with the area, depth and time period that the community occupies.

As described in the following section, the clustering method treats the MGU as the ’sampling unit’ and the percentage composition of the stock as a multivariable. Such an approach has the advantage of greatly simplifying the large and unbalanced data set. An alternative method might have been to present the equivalents of figures 3 and 4 for each ground sampled. However, with 36 grounds, such a presentation would have been very difficult to interpret. The incompleteness of the data across both months and grounds would further have reduced the value of this approach.

Collection and aggregation of the raw data

The raw data from the regular sampling of the small meshed creel pots, as used

1 4 0 3.2. Life History in section 3.2.3., have been used again in this analysis. As before, a sample size of 30335 crabs has been used and the analysis can be considered to be restricted to adults only. The classification of sampled crabs into moult stages and reproductive condition (in the case of females) is as given in section 3.2.3.. The samples were collected from the Choiseul Sound area only, between September 1987 and December 1988.

In section 3.2.3., the temporal organisation of moulting and reproductive cycles has been analysed separately for each sex. In the present analysis of the spatial organisation of communities, both sexes are considered together. The prepared raw data thus take the form of the percentages of sampled crabs in each of the following eight categories in each MGU: I and R males and IN, IU, IE, IC, RN and RU females. Apart from this distinction, data preparation has been broadly the same as in equation (1) of section 3.2.3. Thus, the final estimate of community structure in any given MGU is the average of all the results from the sampling of individual strings, weighted by the CPUEadj of each string sampled. Assuming, as before, that the size structure and sex ratio of crabs is fairly constant, at least within single MGUs, weighting by the CPUEadj- should be directly equivalent to the more correct method of weighting by the total CPUE (of all sizes of both males and females) of the string.

Method of cluster analysis

The community structures, estimated as above for 101 MGUs in the form of eight-category multivariables, have next been submitted to a hierarchical cluster analysis. The percentage composition of the stock has been used rather than the actual abundances of each type of crab to avoid problems with the changes in CPUE caused by the amount of previous fishing in the area (as opposed to natural migrations of crabs between grounds). The analysis therefore clusters together those MGUs which have similar community structures, irrespective of abundance.

141 3.2. Life History

Cluster analysis first computes the similarity or, alternatively, the distance between all possible pairs of cases (MGUs). Many different measures of distance or similarity are available for this purpose, depending both on the characteristics of the data and on the analysis to be made. In this case, the simple ’absolute’ distance measure has been used. For each pair of cases, it is just the sum of the absolute distances of the values over all the variables. As the data are in the form of percentages, each variable has a relative scale, and this absolute distance is, therefore, equivalent to the popular Bray and Curtis index, much used in ecological work (see Norusis, 1986; Ludwig & Reynolds, 1988). The measure has a range between 0, in the case of two identical samples, up to 200 for complete dissimilarity.

Having computed the distance matrix, cluster analysis then starts a process of agglomeration, building clusters, starting with the most similar pair first and working upwards until all cases have been combined. Again, many different ’agglomeration schedules’ are in use. These differ in the way distances are estimated between clusters at each successive step, and hence in the order in which clusters are combined. In this analysis, a method known as UPGMA (un­ weighted pair group method using arithmetic averages) has been used. This standard schedule defines the distance between two clusters as the average of the distances between all the possible pairs of cases, where one member of the pair is taken from each of the two clusters.

The result of a cluster analysis is often given as a ’dendrogram’, which is a branched diagram showing the levels of similarity at which clusters are joined and the relationships between them. A number of clusters are then chosen which give the simplest interpretation of the data, with the maximum within- group homogeneity and the maximum between-group distances.

142 3.2. Life History

Results

The above process of cluster analysis has produced seven reasonably interpretable clusters of MGUs. The characteristics of these clusters are shown in table 2, which includes a simplified, approximate dendrogram illustrating the relationships between the clusters identified.

For each cluster in table 2, the average community structure has been calculated as the means of all the eight percentage composition variables weighted by the CPUEadj of each MGU comprising the cluster. While this procedure is similar to eq. (2) of section 3.2.3., the more complicated weighting (by the factor A mg) is not needed here because the stock structure is assumed to be reasonably constant among those MGUs comprising each cluster. The mean depth and bottom type have also been calculated using the same weighting factor, to show the average environment in which the majority of the community lives. Three categories of bottom type have been recognised and noted for each string sampled. The classification is derived from the colour shown by the colour video depth sounder. The lowest value of 1 represents a soft (probably muddy) bottom, while the highest value of 3 is given for a hard bottom type (probably sand or rock). The total CPUEadj- has also been calculated as the total catch of males over 80mm, taken from the MGUs in the cluster, divided by the total number of pots fished. Note that this value represents the abundance of large males only, and not necessarily of other classes of crab.

The maximum ’absolute’ distance between any two MGUs in a single cluster is just less than 60 units. As this distance measure ranges between 0 and 200, all the units within any identified cluster are less than 30% different from each other. In other words, the minimum similarity within a cluster is 70%. The final merging of the last two clusters (numbers 2,4,7,3 and 8,5,6 in table 2) occurs at an absolute distance of 122 units (61% different).

The cluster ’numbers’ given in table 2 are the product of the computer program

143 3.2. Life History

used for the analysis (SPSS/PC+ ’CLUSTER’) and simply depend on the order of the cases in the data set. Note that the characteristics of cluster 1 have not been given. This cluster contained only a single MGU, and has been included with its closest neighbour, cluster 3.

The temporal distribution of the clusters (communities!

Examination of the data in table 2, shows that the seven clusters can be further simplified into three generalised classes. Clusters 2, 4 and 7 are all dominated by intermoult crabs and form a non-moulting group. Clusters 8, 5 and 6 all contain significant numbers of recently moulted crabs of both sexes and may be considered as a separate moulting group. The remaining cluster 3 falls between the other two groups, having many moulting males but virtually no moulting females.

As the cluster analysis has clearly divided the data into moulting and non­ moulting groups of communities, the spatial distribution of the clusters is next presented separately for two periods, chosen to represent the non-moulting or ’off season (figure 7) and the moulting season (figure 8) of crabs in Choiseul Sound. For this purpose, the moulting season has been taken to occur between September and December. This division of the data gives the best allocation of the non moulting clusters 2, 4, and 7 into the off season and of the moulting clusters 8, 5 and 6 into the moult season. The few data points from 1987 are thus merged with the heavily sampled phase 5 (of 1988) in the moulting group.

The spatial distribution of the clusters (communities')

Figures 7 and 8 are simplified charts of the central Choiseul Sound area, bounded by the ’North Shore’ of East Falkland to the north, the Lafonia mainland to the south-west and Lively Island to the south-east. Choiseul Sound

144 3.2. Life History narrows off gradually to a dead-end at Goose Green, to the west of the area shown. The sound is open to the sea by two channels, one to the east and one to the south. The 36 defined grounds are shown as (mostly) rectangular blocks of uneven sizes. All the main concentrations of the stock are thought to be contained within these grounds.

The numbers shown in figures 7 and 8 indicate which grounds have been assigned to which cluster. A single digit has been placed in each ground for each month the ground fell into the cluster indicated. For example, the ground immediately to the north-west of Centre Island has been assigned to cluster 2 in both the two months it was sampled during the off season (figure 7). During the moult season, however, this same ground was included in cluster 3 for two months and also in cluster 5 for two later months (figure 8).

It is immediately obvious that the clusters or communities are not randomly distributed within Choiseul Sound. The curved lines have thus been drawn on the figures to suggest the best possible divisions of Choiseul Sound into areas containing homogenous communities of crabs. In the off season, cluster 7 forms a central group, surrounded by cluster 2, with the crabs of cluster 4 occupying grounds further to the north and the west (figure 7). A remarkably similar spatial separation of the remaining clusters has been found in the moult season (figure 8). The characteristics of these different communities are considered in more detail in the following sections.

The spatial distribution of communities during the non-moulting or ’off* season

It is perhaps simplest to interpret the ’off season (figure 7) first. As expected, the clusters found in this season are the non-moulting clusters 2, 4 and 7 (table 2). Neither males nor females have moulted in significant numbers in any of these three communities. Moving out from the central area occupied by cluster 7, through clusters 2 and then 4, the proportion of males increases at each step,

145 3.2. Life History the depth decreases and the bottom substrate becomes harder. In relation to the males, therefore, the females generally are aggregated in the central, deeper waters of Choiseul Sound over soft, muddy grounds.

The most dissimilar of the three clusters (see the dendrogram in table 2) is the central cluster 7, located just to the east of Centre Island. In this community, most of the ovigerous females are carrying eyed eggs (71%) at this time of year. It must be viewed as an aggregation of those females preparing to hatch their eggs, moult and then mate in the forthcoming season. In cluster 2, only 18% of the females are brooding eyed eggs. This intermediate community is therefore dominated by those females which will not moult, nor mate in the approaching season. In the peripheral cluster 4, the few females present are again mostly carrying uneyed eggs.

The spatial distribution of communities during the moult season

In the moult season, depicted in figure 8, the three clusters, 6, 3 and 5 are distributed over similar grounds to clusters 7, 2 and 4 found in the off season. Cluster 8 forms a new community inhabiting the shallow water in the west of Choiseul Sound.

The communities of this season are slightly more difficult to interpret. As predicted from the off season data, the highest proportions of moulting females are to be found in the central cluster 6, previously 7. This community is now apparently dominated by males: the high CPUEadj reflects the good catches of the largest adult males taken from this area. On the evidence of both the moult season and the off season, this deep water area to the east of Centre Island is presumed to be the primary spawning ground of P. granulosa in Choiseul Sound.

Further support for this interpretation has been provided by the sampling of small crabs from kelp beds, summarised in section 3.2.2. Of the few locations

146 3.2. Life History sampled, juvenile crabs have only been captured from those kelp beds close to the proposed spawning areas. Thus, juveniles have always been found in large numbers in the kelp beds surrounding Centre Island and around Johnsons Island on the eastern north shore. However, no juveniles have been captured from four kelp beds sampled around the small islands in the vicinity of cluster 8.

If it is assumed that pre-moulting females become disinterested in feeding, as suggested in section 3.2.3., then the proportion of females is particularly underestimated in the central spawning community at this time. In that case, the percentage of males may then be seen to increase consistently as one moves away from the central area through clusters 3, 5 and finally 8. Again, the females are found to be aggregated in the deeper central waters of Choiseul Sound in the moult season, as in the off season, in comparison to the males.

Also as found in the off season, those females in the community now dominated by members of cluster 3, are again mostly in intermoult condition and carrying uneyed eggs. As before, these are the females which would not be expected to moult in the present season. This cluster is derived mostly from grounds sampled early in the ’moult season’. In late November and early December, when the females started to moult, several grounds in this area became cluster 5. These grounds contain some moulting females, but not as high a proportion as found in cluster 6 (see table 2). Finally, a high proportion of the female stock of cluster 8 have been found to have moulted, but as females are relatively uncommon in this area they do not form a large portion of the total moulting stock of females in Choiseul Sound.

The distribution of moulting male crabs follows a different pattern to that of females. Only 3 7 % of males are in recently moulted condition in both the central clusters 6 and 3. The proportion is higher in cluster 5 (67%) and highest in the peripheral cluster 8 (89%). In general, therefore, non-moulting males stay in the central deep water grounds presumably to attend the mating aggregation. Those males, mating in the present year, however, migrate out to the shallower,

147 3.2. Life History harder grounds along the north shore and the western islands off Lafonia. Such regions would have the warmest waters in the austral summer and may provide better feeding for these crabs.

148 3.2. Life History

Table 2. The characteristics of the seven communities identified by the method of cluster analysis. The cluster numbers are an arbitrary product of the cluster method used. The simplified dendrogram shows the relationships and relative distances between the seven clusters. The main portion of the table shows the percentages of crabs in the cluster, in each category of sex, moult stage and (female) reproductive condition. Categories with missing data points signify the total absence of the crab type from the cluster, to distinguish from those categories where the actual percentage has been rounded to zero. The CPUEadj represents the abundance of large male crabs only. Bottom hardness has a range between 1 (soft, probably muddy) and 3 (hard, probably sand or rock).

Cluster Number 2 4 7 3 8 5 6

Sex Moult Reproductive Stage Condition

Male Intermoult 40 68 27 22 10 24 38 Male Recent 1 1 0 13 80 48 22

Female Intermoult Non-ovigerous 5 7 3 2 1 1 1 Female Intermoult Uneyed eggs 41 16 20 58 5 21 25 Female Intermoult Eyed eggs 9 7 49 0 Female Intermoult Empty egg cases 1 0 0 2 0 0 0 Female Recent Non-ovigerous 0 0 1 3 4 3 Female Recent Uneyed eggs 3 0 0 1 2 9

CPUEadj 0.72 0.58 0.80 0.76 0.84 1.54 3.27

Sample size 6210 4635 4366 4939 1637 7788 760

Mean depth (m) 28.57 23.49 32.29 28.62 21.07 28.46 31.50 Mean bottom hardness 1.77 2.05 1.28 1.73 2.12 1.81 1.48

149 3.2. Life History

Figure 7. The spatial distribution of clusters (communities) during the non-moulting or ’off season, between January and August, within the 36 grounds defined in Choiseul Sound. A single number, representing a cluster, has been written in each ground for every month the ground has been assigned to that cluster. For example, the number 444 in the top, left comer of the figure, signifies that this ground was classified into cluster 4 in all the three months that it was sampled, during this time period. Cluster numbers superscripted by apostrophes indicate MGUs with sample sizes of less than 50 crabs. The curved lines provide the best possible division of Choiseul Sound into areas where all the grounds belong in the same cluster.

150 3.2. Life History

Figure 8. The spatial distribution of clusters (communities) during the moulting season, between September and December, within the 36 grounds defined in Choiseul Sound. For further comments, see caption to figure 7.

151 3.2. Life History

3.2.6. Summary and Conclusions

The life history of the stock of P. granulosa in Choiseul Sound has been described in four sections. In section 3.2.2., it has been shown that juvenile crabs of both sexes inhabit the dense kelp beds in the shallow waters of Choiseul Sound. Adult crabs, in comparison, occupy the deeper, open waters, well away from the protection offered by the kelp.

In section 3.2.3., the timing of the moulting and mating seasons has been investigated, by taking the crabs of Choiseul Sound as a single, homogenous stock. The moult season of adult males has been estimated to occur between early October and late November. The moult season of adult females appears to be more synchronised, occurring around a month later between the middle of November and the middle of December. These seasons are cued by the warming of the inshore waters in the austral spring. Uncertainty about the exact timing of these events arises from the unknown period that crabs remain in the ’recently moulted’ classification after moulting, which has been assumed to be approximately one month.

Observations on the proportions of female crabs in each reproductive stage in each month, suggest that mating of P. granulosa takes place immediately after the female moult, as with other lithodid crabs. A short period exists when recently moulted crabs are non-ovigerous; new clutches of uneyed eggs are released mostly in December. The incubated eggs become eyed between February and July, maturing as water temperatures decrease in the austral autumn. Mature larvae hatch between August and October in the subsequent winter. Females carrying empty egg cases after hatching their brood never comprised a large part of the catches. It is concluded that such crabs feed less while preparing for their forthcoming moult.

At the same time that many females are preparing to moult after hatching their eggs, large numbers of female crabs have been sampled in intermoult condition

152 3.2. Life History carrying uneyed eggs. Such crabs dominated the catches taken both prior to and even during the moult season and would not be expected to moult in the present year. Similarly, neither females with eyed eggs, nor those in recently moulted condition ever completely dominated the Choiseul Sound stock at any time. It is concluded that the moulting and reproductive cycle of female P. granulosa takes longer than one year to complete. Due to the synchronisation of the female moult season, the cycle must have a period of some multiple of one year, most probably two years for the majority of adult females. In support of this conclusion, it has been observed in the field that those females carrying eyed eggs during autumn always had more abraded and encrusted shells than females with uneyed eggs. Such an observation would be expected if the former type had spent one year longer in intermoult condition, as proposed. If this interpretation is correct, the incubation period of P. granulosa in Choiseul Sound is between 20 and 23 months in duration.

Conclusions on the duration of the moult cycle and the moult frequency of male crabs are less certain for the following reasons. The percentage of crabs in recently moulted condition in any time period not only depends on the actual percentage moulting, but also on the balance between the synchronicity of moulting and the time taken by recently moulted crabs to return to ’intermoult’ condition again. Thus, if the time spent ’recently moulted’ is short, relative to the synchronisation, then all the crabs in a population may moult in a given season, and yet never produce samples of 100% recently moulted crabs. This occurs when the early moulters have already returned to intermoult before the latest individuals have moulted. However, the same pattern may also result from only 50% of the stock moulting, but with high synchronicity and a long period spent in recently moulted condition. From the information presently available, the previous years intermoult crabs are indistinguishable from the present years and a choice can not be made with certainty between the two interpretations. For females, the reproductive stages identify separate cohorts at certain times of year, but no equivalent information is available for males.

153 3.2. Life History

With the above comments in mind, it has been shown in section 3.2.4. that virtually all the juveniles of both sexes captured in November were in recently moulted condition. Moulting, therefore, must take place at least once a year in juveniles, during October. Unlike adult crabs, both sexes of juveniles moult at the same time. By December, many small crabs had returned to intermoult condition suggesting that juveniles, like adults, only moult at this time of year. Assuming that only one moult occurs in this short time, moulting is likely to be annual in these large juveniles.

Almost 100% of the smaller adult males are also in recently moulted condition at this time of year. In contrast, only around half the stock of larger males had recently moulted in each of the three short, successive time periods. As shown above, this, in itself, does not necessarily mean that only half of the larger adult crabs moult in any given year. However, it is fairly certain that moult frequency is reduced in these crabs. If moulting in juveniles and small adult males is annual, it is most likely that moulting in the larger males is biennial.

For adult females, sampling may have been insufficient to cover the whole moult season. The available data, though, do support the biennial moult cycle proposed in section 3.2.3. Moult frequency also appears to decrease more immediately after maturation than is the case with males which may be due to the high energetic demands of egg production in females.

In section 3.2.5., the spatial organisation of the moulting and mating cycles has been examined. The technique of cluster analysis has been used to define a few relatively homogenous communities of crabs, on the basis of the sex ratio, the proportions moulting in each sex and the reproductive condition of the females. Three such communities have been found to occur in the non-moulting or ’off season, occupying three distinct areas within Choiseul Sound. Later, in the moulting and mating season, the same areas have been found to be occupied by communities with different characteristics, revealing the activities taking place in each area. The following interpretation of the spatial organisation of the

154 3.2. Life History moulting and reproductive cycles of P. granulosa in Choiseul Sound has been proposed.

At all times of the year, females have a more concentrated distribution than males, being most common in the deeper water in the middle of the sound. The centre of this area, in the deepest water over the softest (muddy) ground, has been found to be the main mating ground of the Choiseul Sound stock. Thus, those females with eyed eggs (approaching hatching, moulting and mating) are congregated here in the off season. The same area, in the moult season, then has the largest percentages of recently moulted females accompanied by the highest concentrations of large adult males.

Around this central area, many females may always be found in non moulting condition, even at the time of the moulting and mating season. These are the females, reported in section 3.2.3., which will not moult until the next season and may now be seen to have migrated off the mating ground at this midway point in their two-year reproductive cycle.

The highest proportions of moulting male crabs, however, have been found on the shallowest grounds on the edges of Choiseul Sound during the moult season. The proportion of crabs in recently moulted condition is much lower among those males remaining with the females on the central mating grounds. Male crabs presumably alternate between moulting and feeding on the warmer shallow grounds in some years, and attending the central mating aggregation, without moulting, in other years. The less synchronised timing of the male moult period, compared to the females (section 3.2.3.), may be due to the wider distribution of males over many different grounds in Choiseul Sound.

155 3.3. Growth rates

3.3. Growth Rates

3.3.1. Methods of estimating growth rates of crustaceans

The rate of growth of an animal is the rate of change in some bodily dimension, say length or weight, with time. To estimate growth rates, it is thus necessary to have information on both the size of the animal and, in one form or another, the time taken to reach that size.

In the simplest methods of estimating growth rates (see Gulland, 1983; Pauly, 1984), the ’time’ factor used is the age of the animal. For many fish species, particularly in temperate waters, the individual growth pattern of any specimen is recorded on various ’hard parts’ as a series of rings. These rings, or annuli, are the result of alternating periods of fast and slow growth, broadly corresponding to periods of feeding in summer and fasting during the winter. For such animals, simply counting the number of rings gives the age of the specimen (Blacker, 1974).

The growth of crabs and other Crustacea, however, is achieved as a sequence of moults. At each moult, the exoskeleton and all the hard parts are shed to allow the animal to expand in size. As a result, only one growth ’ring’ ever exists, as all the previous ones are lost during moulting. The ages of individual crabs, then, can not be determined by simple inspection and growth rates can not be obtained in the usual ways.

Alternative methods of estimating growth rates have therefore been developed which do not need actual ages as input data. In all such methods, two or more lengths are compared with each other, without knowing the actual ages at each length, but instead knowing the periods of time taken for the amounts of growth observed. These techniques fall into two broad classes; those involving mark and recapture and those using sampled length frequency data.

156 3.3. Growth rates

In the first case, which has been particularly useful for the analysis of growth in crustaceans, captured animals are measured, marked in some way for later identification and then measured again after a known time interval. In certain studies, the tagged animals have been released into the wild during the interval, to allow growth in the most natural environment (eg. Hoopes & Karinen, 1972; Bennett, 1974). Due to the low chances of recapturing tagged animals, other studies have retained the specimens in the artificial conditions of tanks or cages on the sea bed (eg. Butler, 1961; Powell e t a l, 1973). These methods lead to a realistic interpretation of the growth of crustaceans, as they quantify the two real processes of the discontinuous growth format; the moult increment and its frequency of occurrence. Many crustaceans fit a pattern of decreasing percentage increment combined with increasing intermoult period over their lifetime (Mauchline, 1977; Hartnoll, 1982). Discontinuous, empirical growth functions may easily be fitted to such information (eg. Weber & Miyahara, 1962; McCaughran & Powell, 1977).

In the second case, the analysis of length frequency data may be used to estimate growth rates. Length frequency data often contain several overlapping distributions of length at age with separate but identifiable modes. To obtain growth rates from these modes, the necessary ’time factor* is the time interval between the modes. In the easiest analysis, this period may be known to be one whole year, so that the modes represent different age classes or cohorts of the stock (various references for small crustaceans in Hartnoll, 1982). Alternatively, these modes may represent, not age classes, but instars (Butler, 1961; Klein Breteler, 1975; Bailey & Elner, 1989). To estimate growth rates from the latter type of data, the intermoult period between the various instars must also be known.

Several methods are used to estimate the positions of these modes in length frequency data, or to estimate growth rates from them. If only ’stationary’ data are available from, say, a single sample at one point in time, the modes may be separated by various graphical methods (eg. Cassie, 1954; Bhattacharya, 1967) or

157 t 3.3. Growth rates

by more efficient mathematical procedures (eg. MacDonald & Pitcher, 1979). Further information will then be needed to ascertain if the modes represent instars or age classes. When a sequence of length frequencies is available, spaced over several months or years, the actual data can sometimes be used to quantify the time factor, by observing the progression of the modes through the samples (eg. Blau, 1986).

When the discontinuous, stepped growth of crustaceans is viewed as a whole and growth takes the common format noted above (percentage increment and moult frequency both decreasing with time), the growth curve is seen to be broadly asymptotic in shape. The smoothed curve, in fact, can be reasonably approximated by the continuous von Bertalanffy growth function (VBGF) (von Bertalanffy, 1938; Brander & Bennett, 1989). Several methods have recently been developed (primarily for the study of growth in tropical fish, which are also difficult to age), which use sequential length frequency data to fit the parameters

of the VBGF (eg. ’ELEFAN’ (Pauly & David, 1981), ’Projmat’ (Rosenberg e t a l, 1986), ’SLCA’ (Shepherd, 1987)). Any of these techniques may be used to estimate the average growth of those Crustacea with suitable growth formats.

All these length frequency based methods obviously assume that the required information is actually contained in the data at hand. This, however, may not always be so, even when large numbers of animals have been sampled. All the methods rely on the existence of modes in the length frequencies. If the modes represent instars, their successful discrimination is dependent on the variability of the moult increment between individuals. If, on the other hand, the modes are due to separate year classes, their identification is dependent on the variability of the overall growth rate between individuals. In either case, this variation is normally such that only the first few modes can be distinguished in length frequency data, and less when the modes are cohorts than instars (see review in Hartnoll, 1982). Length frequency methods, then, are most likely to be successful when the samples include the smallest possible animals. Indeed, when only larger animals are sampled, and many cohorts or instars merge together,

158 3.3. Growth rates only one single mode may be apparent in the data. Serious biases can then result with the methods above, several of which will give the best solution as that which incorrectly interprets the single mode as a single cohort (Rosenberg & Beddington, 1987; Basson et al , 1988).

Great care must therefore be taken when analysing length frequency data of only the larger animals of a population. If the natural variability in growth is enough to eliminate the individual modes, and the only apparent mode is not believed to be a single cohort/instar, then it will not be possible to determine growth rates from length frequency methods.

3.3.2. Estimation of growth rates bv tagging methods

In view of the above comments, the first intention had been to estimate growth rates for this stock of crabs using mark and recapture methods. The relationship between moult frequency and size has been investigated in section 3.2.4. It had been hoped that the second component of crustacean growth, the moult increment, could be estimated by tagging. Firstly, a controlled experiment in cages was designed to ensure some ’recaptures’. For comparison, the release of tagged crabs was planned, to allow moulting to take place in the most natural environment, before the subsequent recapture and second measurement.

Five thousand ’streamer’ tags were obtained of a design known to work on lobsters and prawns, and thought to be most suitable for P. granulosa. One crab, which had been tagged with a streamer tag and released during earlier trials, was recaptured in healthy, recently moulted condition, with the tag still in place. It had grown 4mm during the 7 months since its release.

Due to the synchronised moulting period of P. granulosa (see section 3.2.3.), the timing of these experiments was known to be of great importance. It was intended to tag the crabs a few months before the moult season, to allow the

159 m 3.3. Growth rates

tagged animals sufficient time to recover before their moult. Unfortunately, for various reasons, the start of these experiments was delayed until the beginning of November, 1988, by which time the great majority of the stock had already moulted. The mark, release and recapture experiment was therefore postponed, but the holding experiment was still carried out. A balanced, randomised design was employed, with 360 crabs in three size classes and two holding densities. An equal number of untagged controls were included and the crabs were divided between 24 store pots in two separate strings. Sadly, none of these crabs moulted during the five weeks of subsequent observation. As expected, the experiment was simply too late.

3.3.3. Examination of available length frequency data

With the failure of the tagging experiments, only the length frequency data remain as a potential source of information on growth rates. Samples have been taken on a regular basis from Choiseul Sound, during the whole of the five phases of exploitation. A short (16 months) but well sampled time series of data is thus available of the average structure of the Choiseul Sound stock for this period. The main problem with these samples is that the great majority have necessarily been taken from the commercial pots fished over the ’adult’, deep water ground (see section 3.2.2.). As a result, only the larger animals have been regularly sampled, which, as noted above, are not always suitable for the estimation of growth rates.

Of the 52977 crabs measured in Choiseul Sound during this project, the majority, 39326, have deliberately been sampled from the smallest meshed, commercial, ’CR’ pot type so as to obtain the smallest animals for this analysis. As with most of the biology of crabs (section 3.2.; Hartnoll, 1982), the size compositions differ greatly between the sexes. The length data from these pots have therefore been separated by sex and plotted as the monthly relative frequencies in 1mm intervals of carapace length (figures 1 and 2). Note that the length scales differ

160 3.3. Growth rates for the two figures and that, for both sexes, the scales start at 20mm and not at the origin. It is seen that the length frequencies of both sexes mostly contain animals over about 50mm. This is due to the selection characteristics of the mesh used in the CR pots. Thus, even with the smallest meshed of the commercial pots, only the upper half of the size range of male crabs is sampled effectively and only the upper quarter or so in the case of females. Unfortunately, even though the sample sizes are large, these size classes do not contain sufficient information to permit the estimation of growth rates, as will now be shown.

For both sexes, the length frequency data are basically unimodal, each having only a single main peak (figures 1 and 2). The overall shapes of the length distributions are functions of both the relative abundances and the catchability coefficients of the crabs in each size class (Miller, 1989). Male crabs over about 75mm are thought to be caught more or less in proportion to their abundance (cf section 2.2.2.). Below this size, catchability of males appears to decrease, possibly due to the inhibition of small crabs by larger ones already present in pots, or to the gradual recruitment of smaller crabs on to the adult grounds.

As mentioned earlier it is possible that the single broad modes shown by both sexes are representative of single age classes of the stock. At this end of the size range, however, they are much more likely to be mixtures of modes which have merged together due to the variability in growth rate between individual animals. The broadly unimodal size compositions are not completely smooth, but comprise a number of smaller peaks and troughs (see eg. September ’87 for males and October ’88 for females). If the samples represent mixtures of modes, these smaller peaks may instead be interpreted as age classes or instars from which growth rates could be obtained. This supposition is now examined.

The pattern to be expected in such length frequencies is a function of the growth format of the species. In fast growing tropical fishes, for example, growth continues all year round, so that the average size of the fish in each

161 * 3.3. Growth rates

cohort increases significantly each and every month. A gradual progression of modes may then be observed in the length frequencies in each of the months sampled. In the case of P. granulosa , however, moulting, and hence growth, only occurs at one time of the year during the moult seasons in spring (section 3.2.3.). In this case, the modes should occupy the same positions in all the months between the moult seasons and no progression should be seen on a monthly basis. Any movement of modes will only be observable on a yearly scale, and even then, only if there is variability in recruitment and abundant cohorts can be followed. If, on the other hand, recruitment is constant, or nearly so, the modes should not only occupy the same positions at all times, but also be of the same relative sizes. The overall shapes of the length frequencies should then be exactly the same in all months and in all years.

Now, the homogeneity of the 14 monthly distributions has been tested by means of the chi-square test. At this overall level, a significant difference does exist between the 14 samples, both for males (chi^o^f = 1632, P < 0.00005) and for females (chi2^ ^ = 404, P < 0.00005). In these tests, the data for lengths on the edges of distributions have been combined, so that the expected frequencies exceed unity in all cells (Snedecor & Cochran, 1980).

The above test merely tells us that the length frequencies do change in shape with time, but not whether these changes occur from month to month or between years. A more refined form of the chi-square test, using a log-linear model, has therefore been used to examine simultaneously the change in shape of the distributions on both the monthly and yearly scales. The frequencies in each cell are examined as functions of the variables, month, year and carapace length (see section 4.2.4. for further details of this type of test). Only the data for October, November and December have been used, so as to balance the model across these three months for the two years available (see figures 1 & 2). Significant interactions have thus been found to exist between carapace length and month of sampling (partial likelihood ratio chi-square or G270df = 196, P < 0.00005 for males and G236df = 55, P = 0.0211 for females). The interaction

1 6 2 3.3. Growth rates between carapace length and year of sampling, however, would not be considered significant at the normal levels (G23 5df = 37, P = 0.3902 for males and G218(lf = 23, P = 0.1727 for females).

These tests show that the observed non-homogeneity in the shapes of the length frequencies is due to changes between the months, and not between the years. As noted above, a change between, say, October 1987 and December of the same year, could be due to the progression of dominant cohorts during the moult season; but the new shape should then persist until the next October, producing further differences in the yearly contrasts. These do not exist, so that the observed pattern can not be explained under the known growth format of the species. There are no horizontal shifts in the positions of the peaks with time and no strong year classes can be followed through the series.

The significant differences in the shapes of the distributions are therefore thought to be due only to changes in the catchability or availability of certain sizes of crabs with time. The mean sizes of the crabs in each sample have been plotted against time in figure 3, in addition to the monthly mean surface water temperature. For males at least, small crabs appear to be more available in summer: perhaps they are more inclined to compete with the larger males at this time. The females do not show any obvious pattern, possibly due to the much narrower length range sampled.

Finally, as noted before, even when a progression of modes can not be observed, this does not necessarily mean that modes do not exist. With fairly constant recruitment, a ’stable’ modality may be seen, with peaks occurring in similar positions in all monthly distributions. Even this does not appear to be the case. Indeed, as monthly sample size increases, the smaller peaks mostly disappear (eg. November ’88 for both sexes). The small peaks in the data are, therefore, presumed to be the result of natural sampling variability around the true relative frequencies of each length. No real modes are believed to be present in this data set.

163 3.3. Growth rates

Prior to these conclusions, the data for both sexes (figures 1 & 2) were extensively analysed by the ’SLCA’ method of Shepherd (1987). This method uses a score function to assess the fit of the data to any chosen combination of the parameters K and of the VBGF. The method is easily adapted to model the growth of animals with sudden length increments at only one time of the year. The results, however, were not encouraging and led to the analysis above.

For both sexes, the T>est’ solution from SLCA (with the highest score) is any combination of K and which interprets the basically unimodal length frequencies as a single cohort. This, obviously, is not a sensible answer for a species which only moults once or less a year. A second broad solution also occurs at lower values of K with the data being interpreted as two overlapping cohorts. Still further solutions, with increasingly smaller X’s, suggest that the distributions comprise more and more overlapping modes. This is the problem of ’multiple maxima’ associated with these length frequency methods (Rosenberg & Beddington, 1987; Basson et al, 1988). In the absence of secondary data supporting one particular estimate, and with the lack of obvious modality in the available data set, it is impossible to choose between the various solutions.

The only other potentially useful source of length frequency data is that from the special, small meshed sampling pots used to investigate the spatial distribution of small P. granulosa (see section 3.2.2.). These pots select much smaller crabs than the commercial CR pot type, giving a greater chance of detecting modes before they merge together. Unfortunately, these pots have only been regularly deployed in the final sampling phase of November/December 1988 so that even less of a time series exists in this data set. Furthermore, even though large samples have been taken, including animals as small as 25mm (n = 2025 for males and n = 1472 for females), the length frequencies still do not show interpretable modes (see section 3.2.2., figures 1 & 2).

Stable recruitment is fairly rare in nature. Red king crabs (Paralithodes camtschatica ) in Alaska show great recruitment variability (Otto, 1986; Incze et

164 3.3. Growth rates a l, 1986). Even with the moderately fast growth of this species, the progression of strong year classes can still only be seen in long time series of data (eg. 12 years in Blau, 1986). Instead of being due to relatively constant recruitment, the lack of change in the available length frequencies for P. granulosa may therefore suggest that growth is comparatively slow in this species and that the stock structure simply has not changed appreciably in the 16 months of observation. A slow growth rate would also be supported by the less than annual occurrence of moulting in the larger P. granulosa (section 3.2.4.). As would be expected, when growth only occurs once every other year or so, several years of good data, and not only a few months, are needed to detect changes in population structure.

165 Relative Frequency (25) iue . otl lnt feunis fml cas ape from sampled crabs male of frequencies length Monthly 1. Figure and 1988 (total (total 1988 and ml mse C pt i al ein o hiel on drn 1987 during Sound Choiseul of regions all in pots CR meshed small 1987 n 22024). = aaae egh (mm) length Carapace 166 0 1 0 1 0 1 0 2 4- 6 8 0 2 4: 6 g (H 2- 6 Bar, 1-43&0 I

- 3 m y . * - i 0J 2 B = - : - : Z tfT. 3

------>>629 - -- -- 1988 3.3. Growth rates Growth

Relative Frequency (&) rm ml mse C pt i al ein o hiel Sound Choiseul of regions all in pots CR sampled crabs meshed small female from of frequencies length Monthly 2. Figure during 1987 and 1988 (total (total 1988 and 1987 during 15 0 1 0 1 16 0 1 15 0 1 15 0 5 0 5 0 5 0 5

D 0 0 0 0 0 0 80 60 40 20 80 60 10 2D 1987 aaae egh (mm) Length Carapace n 17302). = 1988 3.3.

Growth rates Growth * 3.3. Growth rates

Month.

Figure 3. The monthly mean carapace length of (a) male crabs and (b) female crabs sampled from Choiseul Sound from CR pots during 1987 and 1988 and (c) the monthly mean surface sea temperature (°C).

168 * 3.3. Growth rates

3.3.4. Summary and conclusions

Unfortunately, it has not been possible to estimate growth rates of P. granulosa from the data available.

Even with total sample sizes of around 20 thousand crabs for each sex, the length frequency data still do not appear to contain sufficient information on growth. The shapes of the length frequencies have not changed significantly over the two years observed, except for monthly changes in the relative numbers of small crabs in the samples. These have been attributed to changes in the availability of small crabs at different times of the year. Whatever the reason, the samples do not show any progression of modes during the period observed. Neither do they show a stable, repetitive pattern of small modes as may have been found under conditions of constant recruitment.

Growth rates can only be estimated from length frequency methods when the data are from the smallest sizes of animals. The finest meshed commercial ’CR’ pots apparently do not select crabs small enough for this purpose. Not even the special sampling pots have produced suitable samples. However, even if growth rates could be estimated for the youngest crabs by further sampling, they would probably be very different to the adult rates, and would thus have limited use for the stock assessment of this fishery. Length frequency methods are therefore of

little use for the analysis of P. granulosa.

Several modem, computer-aided methods could have been used to investigate growth. However, all such methods produce several different estimates for this type of data depending on whether the length frequency is interpreted as a single mode or as a mixture of two or more modes. With no supporting information for any particular solution, and no consistent pattern in the raw data, a single estimate can not be obtained. The success of any method, computer aided or not, is still dependent on the data submitted to it. The length frequency data alone are insufficient for this purpose.

169 ♦ 3.3. Growth rates

The lack of any change in the length frequency data may be due to fairly constant recruitment of the Choiseul Sound stock. In this case, a progression of modes may actually exist, but it is never apparent: all the cohorts are the same size and the whole stock simply moves up one mode at the time of the synchronised moult season. Such constant recruitment, however, seems unlikely.

An alternative hypothesis may be that growth of P. granulosa is so slow, at least in these larger animals, that no progression of year classes can be seen during the short period observed. Further support for a slow growth rate is given by the infrequent moulting of adult crabs of both sexes (section 3.2.4.). For such slow growing species, the progression of abundant year classes can only be observed in a long time series of length frequency data. This, obviously, is not a practical solution for a preliminary assessment of a largely unfished stock.

As with many other crustacean species, then, it is still the mark and recapture

techniques which are most likely to produce growth rates for P. granulosa. It is thus doubly unfortunate that these methods could not be applied successfully in the time available.

170 3.4. Parasitism

3.4. The effect of parasitism by B. caUosus.

The effects of the parasitism of P. granulosa by Briarosaccus callosus have been investigated during this research and published in the journal Crustaceana (attached as annex 1). The main results are summarised here, with comments on the importance of such results to the assessment and management of a fishery for P. granulosa.

B. callosus is a rhizocephalan parasite which affects the growth and sexual reproduction of lithodid crabs throughout the world (O’Brien & Van Wyk, 1984). In the commercially important king crab fisheries in the north Pacific, B. callosus is found with localised prevalences as high as 76% for blue king crab, Paralithodes platypus and 40% for golden king crab, Lithodes aequispina (Sloan, 1984; Hawkes e t a l, 1985; Hawkes e t al, 1986). Overall prevalences in Falkland Island stocks of P. granulosa are, however, below 1% at present.

Infection is revealed externally by the presence of the reproductive sac of the parasite. This ’externa’ is usually found in a protected position beneath the abdomen. Scarred crabs are also found where the externa has been lost. It is assumed that such losses are due to the natural death of the parasite.

Both sexes of crabs, with extemae and with scars have been found in the Falkland Islands in recently moulted condition. B. callosus, therefore, does not entirely prevent moulting in P. granulosa. A qualitative correlation has been observed between the relative sizes of host and parasite. It is concluded that, like other lithodids (Bower & Sloan, 1985; Hawkes et a l, 1987), P. granulosa is infected early in life and that both parasite and host grow together.

Both sexes of P. granulosa have been found to be castrated by B. callosus, both during and after the period of infection. All parasitised females, with externae and with scars, are non-ovigerous. Infected males do not attain the morphological maturity indicated by the relative size of the chelae (see section

171 » 3.4. Parasitism

3.1.2.). At any given size, males carrying extemae have smaller claws than even juvenile males. In view of the parasitic feminisation frequently observed in other hosts of rhizocephalans (Hartnoll, 1982; O’Brien & Van Wyk, 1984), it is likely that parasitised males take on the relative claw sizes of uninfected females. It is unfortunate that the chelae of a small sample of females were not measured for comparison. Scarred males, after loss of the parasite, return to the relative chelae sizes of juvenile male crabs, even at sizes at which they would normally be mature.

Crabs with extemae are significantly more prevalent at smaller sizes, particularly in the case of male crabs. Prevalence of scarred crabs, however, increased with host size in females, while scarred males showed no consistent trend. These patterns have tentatively been attributed to the effect of the parasite on the growth rate of the host. The energetic cost of supporting a parasite may result in smaller mean sizes of crabs with extemae, while scarred females in the absence of both the parasite and the normal demands of egg production would be capable of enhanced growth.

B. callosus thus has a considerable effect on the biology of both male and female P. granulosa. Both sexes are castrated. Parasitised crabs should therefore be excluded from samples used in the estimation of size at sexual maturity. Considering the low prevalence currently observed in the Falkland Islands, parasitic castration by B. callosus is unlikely to have a large effect on stock production. Any increase in prevalence would, however, be undesirable. Infected crabs are rarely encountered in the commercial catches due to the decrease in prevalence with size. Even so, it is recommended that any parasitised crabs captured, regardless of sex or size, be either destroyed or processed with the rest of the catch (Sloan, 1984; Hawkes et a l, 1986; Hawkes et al, 1987). Such crabs contribute nothing to the recruitment of the host stock and serve only for the further propagation of the parasite larvae.

172 Chapter 4 4.1. Introduction to comparative biology

4. Comparative biology of Paralomis granulosa

4.1. Introduction

The comparative biology of P. granulosa is discussed at two levels. Firstly, the biology of two possibly separate substocks within the Falkland Islands are examined. Secondly, the Falkland Island stock as a whole is compared to the almost certainly separate stock of P. granulosa living in Patagonia and also to several other commercially important species of lithodid crabs. The reasons for these analyses are now briefly discussed.

The intention of this research has been to examine the potential for an inshore crab fishery within the Falkland Islands. However, for logistic and commercial reasons, only one small part of the Falkland Islands has been sampled on a regular basis. The biology of this area, Choiseul Sound, is now reasonably understood (section 3.). Regular sampling in this single location has at least allowed a short, but useful, time series of catch data to be assembled, in addition to important information on the timing of the moulting and mating cycles, neither of which would have been possible if sampling had been more dispersed. On the other hand, it must now be questioned whether the information gathered in Choiseul Sound is also applicable to other crabs in different parts of the Falkland Islands.

Only two other areas, besides Choiseul Sound, have been fished by the Laura Jay. A very brief examination of the Berkeley Sound / Port William area, to the north of Choiseul Sound, found only very small numbers of crabs; not enough for a reliable comparison. Greater fishing and sampling effort has been applied to the more productive area of Adventure Sound, further to the south. An examination of the applicability of the Choiseul Sound results to the Falkland Islands as a whole is therefore limited to a comparison of these two sounds.

174 9 4.1. Introduction to comparative biology

The two locations, however, were identified in the earlier work of Fortoser (1986(b)) as the two major concentrations of P. granulosa in the islands. In addition, they are the closest concentrations of crabs to the processing plant in Stanley, and, hence, the most likely to be exploited.

Secondly, in section 4.3., certain elements of the biology of P. granulosa are discussed, in comparison with stocks of the same species in Patagonia and with other species of lithodid crabs around the world. In particular, factors important to the likely productivities and yields of the various stocks are considered. These include the relative sizes of the different species, their growth rates, reproductive rates and relative abundances and densities.

The maximum annual yield of P. granulosa achieved in Chile was 952 tonnes in 1979 (CORFO, 1981). In comparison, the harvest of red king crab (Paralithodes camtschatica) in the Bering Sea peaked at 58,944 tonnes in 1980 (Otto, 1986). These and other species and stocks are thus compared, at a fairly crude and qualitative level, to assess the reasons for such variability in yields and to see if the Falkland Islands might support a similar amount of exploitation as the other stocks.

175 4.Z Comparison o f Choiseul / Adventure sounds

4.2. Comparison of P. granulosa, from Choiseul Sound and Adventure Sound

4.2.1. Introduction

Of the principal fishing grounds identified by Fortoser (1986(b)), Choiseul Sound is the closest to the processing factory in Stanley. Furthermore, the harbour at East Cove in Choiseul Sound is the only place close to any of the grounds where the catch can presently be landed and safely transported, by road, back to Stanley. For these reasons, both fishing and sampling have been concentrated in Choiseul Sound.

Due to the size and the lack of living space aboard the Laura Jay, fishing anywhere other than Choiseul Sound has proven veiy difficult. Visits to any of the more southerly grounds involve passages via the often treacherous waters around the headlands of the south west of the Islands. In the event of rough weather, a frequent occurrence in the Falkland Islands, a safe return to the landing facilities at East Cove is often impossible for such a small craft.

However, in July 1988, two separate 5-day visits were made to Adventure Sound, adjacent and to the south of Choiseul Sound, to examine the fishing potential and the biology of the area. 98 pots were taken and tied into 6 short strings, between 9 and 20 pots in length, so as to cover the maximum possible area. A total of 481 pot hauls were made in 29 separate locations, although 3 whole days were lost to bad weather over the two periods. On hauling, many pots were found to be empty, as much of the fishing was located in ’experimental’ areas. Nevertheless, 21 separate samples have been obtained for a sample size of 2044 crabs. Most of the samples were taken from the usual small meshed CR pot type but others had to be taken from the CRE2 pots when the former were all empty on poor grounds.

The two trips were made in the second and fourth weeks of July 1988. In the

176 # 4.2. Comparison o f Choiseul / Adventure sounds

first and third weeks of the same month, the Laura Jay fished in Choiseul Sound, from which samples have also been taken for comparison. Due to the overlapping of the sampling periods, it is assumed that the slight differences in the times of sampling are negligible in comparison with any differences between the two areas. Several samples were also taken from CRE2 pots in Choiseul Sound, so as to compare with those collected by necessity from this pot type in Adventure Sound.

Adventure Sound has only been sampled in this one month. It must also be assumed, therefore, that any differences found for the single month of July are valid as a comparison of the two areas for the year as a whole, and that similar differences would also exist at other times of the year.

In both Choiseul Sound and Adventure Sound, the stock is concentrated wholly within the central, sheltered parts of the inlets: no animals have been caught in the open sea or aroynd the headlands separating the two sounds (Fortoser, 1986(b)). It is possible that crabs do migrate between the two grounds, maybe at certain times of year or along some presently undiscovered migration routes. However, in this examination, the two sounds are considered to contain separate,

self regenerating substocks of P. granulosa.

The following biological characteristics have been compared between the two areas: the abundance of large male crabs, the size distributions of both males and females, the size at maturity of female crabs and the proportions of crabs in each moult stage, female maturity stage and level of infection by the parasite

Briarosaccus callosus. The different sexes, sizes and life stages of crabs, however, are not evenly distributed over the sea bed, even within a known fishing ground. As a result, the values obtained for several of the above parameters are functions of the locations sampled (see section 3.2.). For the limited number of data collected in this month, it has not been possible to divide the samples into small homogenous areas, not least because such areas have not yet been identified for Adventure Sound. However, in both locations, a wide variety of

177 4.2. Comparison of Choiseul / Adventure sounds different grounds have been fished and sampled during July 1988. For the comparative analyses, the samples have, therefore, been simply aggregated within each area. It is initially assumed, then, that the combined samples are representative of the general situations within the two stocks in the month of July. In certain analyses, this assumption is further questioned.

4.2.2. Physical Environment

The fishing grounds in Adventure Sound are of a similar size to those of Choiseul Sound. Both areas are sheltered from the worst of the weather, facing the open sea on the south east of the Falkland Islands. Adventure Sound, however, is around 10m deeper, on average, than Choiseul Sound with depths commonly between 30 and 40m.

A very limited examination of the two physical environments is given in table 1 . The early morning surface water temperatures for the month were similar in both sounds (pooled variance t test: f16<= 0.48, P = 0.641). Table 1 also shows the mean depths and the bottom types of the areas fished. Note that these are not the same as the average depths, nor the proportions of different substrate types in the two areas. With the exception of depth, the two sounds are thought to have fairly similar physical characteristics. Generally speaking, crabs were found to be distributed on the same types of grounds in Adventure Sound as in Choiseul Sound. The data simply show that sampling effort has not been evenly distributed across the different types of ground for the two areas.

In Choiseul Sound, fishing effort in July was directed at known concentrations of crabs, mostly in deeper water at this time of year. In Adventure Sound, on the other hand, the fishing had a more experimental nature, with several different depths and bottom types being tried out to assess the distribution of crabs. The variance of the depths sampled in Adventure Sound is thus greater than in

Choiseul Sound (^29 54 = 4.549, P < 0.0005). In addition, more strings have

178 ft 4.2. Comparison o f Choiseul / Adventure sounds

been hauled on harder substrates (generally shallower and less productive in

winter) in Adventure Sound (chi22(jf = 25.30, P < 0.00005).

This varied sampling regime soon showed that the crabs were, indeed, distributed on the same types of ground in the two different areas. Later sampling concentrated on the deeper, softer areas in Adventure Sound and it is from these that the majority of crabs have been sampled in both locations.

179 4.2. Comparison o f Choiseul / Adventure sounds

Table 1. A comparison of the biological characteristics of crabs sampled from Choiseul Sound and Adventure Sound during July, 1988. For further information and statistical details see text.

Choiseul Sound Adventure Sound Probability of no difference between areas

Physical Environment Depth (JP,s , n)1 31.484 4.020 64 34.655 8.574 29 0.066 Temperature (r, s, n) 2.586 0.689 7 2.432 0.658 11 0.641 Bottom Type (S, M, H)2 53 10 1 9 15 5 <0.00005

Abundance CPUEadj (*, s, n) 0.599 0.438 64 0.806 0.618 29 0.111

Size Distributions (see figure 1) Males (total n) 1173 867 0.0007 Females (total n) 1346 1177 <0.00005

Moult Stages Males (R, I)3 18 1155 18 849 0.3613 Females (R, I) 0 1346 0 1177

Weight at Length Males (a, by 0.0002198 3.2703 0.0002180 3.2858 0.0001 Females (ay b) 0.002446 2.6553 0.002051 2.7124 <0.00005

Female Maturity Size at 50% maturity Approx. 47mm Approx. 49mm (see figure 2) Maturity Stages (N, U, E, C)5 85 409 843 9 127 633 402 15 <0.00005

Parasitism by R caUosus Males (N, Y, S)6 1171 2 0 860 5 2 0.0016 Females (N, Y, S) 1345 0 1 1168 4 5

1 x = mean, s = sample standard deviation, n = sample size. 2 Number of strings set on soft (S), medium (M) and hard (H) grounds, as determined by the colour of the echo sounder picture. 3 Number of crabs sampled in recently moulted (R) and intermoult (I) condition. 4 a and b are the parameters of the relationship, Weight(g) = a Length(mm) b, as fitted by the regression of In Weight on In Length. 5 Number of female crabs sampled in the following reproductive conditions: non-ovigerous (N), with uneyed eggs (U), with eyed eggs (E) and with empty egg cases (C). 6 Number of crabs sampled in the following stages of parasite infection: without externa (e) (N), with extema(e) (Y) and with the scar of an earlier infection (S).

180 * 4.2. Comparison o f Choiseul / Adventure sounds

4.2.3. Relative Abundance

The relative abundances of the two areas have been compared by estimating the average catches per unit of effort or CPUEadj. The CPUEadj is the number of male crabs over 80mm per pot, corrected to a soaktime of one day (see section

2.). In Adventure Sound, all retained crabs have been measured (n = 1839) and the CPUEadj is an exact measure for each string. The great majority of landed

catches from Choiseul Sound in July, 1988 were also measured ( n = 4738), so that very little error exists in these data.

The abundance or CPUEadj, then, has been found to be higher in Adventure

Sound than in Choiseul Sound at this time, though not significantly so (table 1 ,

separate variance t test, f413df = 1*63, P = 0.111). However, as noted in the previous section, the fishing and sampling in Adventure Sound was deliberately spread over a wider range of often less productive grounds, just to see if they held crab or not. The variance of CPUEadj is correspondingly greater in

Adventure Sound (table 1, ^29 54 = 1.99, P = 0.0125), reflecting the occasional poor catches (as expected) on poor grounds. Therefore, if the fishing had concentrated only on the best grounds in Adventure Sound, as it did in Choiseul Sound, then it is thought that the abundance of crabs in Adventure Sound would have been seen to be significantly higher. This would be as expected, as the stock in this area has never been commercially exploited.

4.2.4. Size Distributions

Samples of crabs have been taken both from the smallest-meshed commercial ’CR’ pot type and also, by necessity, from the larger meshed ’CRE2’ pots. In

section 2 ., it has been shown that mesh size has an effect on the sizes of crabs selected by the various types of pot. The aggregated samples from the two pot types are, therefore, analysed separately between the two areas. The size compositions and sample sizes of each sex of crab, in each pot type and from

181 * 4.2. Comparison of Choiseul / Adventure sounds

each area are plotted in figure 1.

Statistical differences between these size compositions have been analysed by the use of hierarchical log-linear modelling, a refined form of chi2 analysis (see eg. Marascuilo & Serlin, 1988). The expected frequencies in each size class of each distribution are generated as if all the samples came from the same underlying distribution. The deviations from this pattern, within certain samples, may then be attributed to one or both of the variables, area and pot type. The contribution of each variable to the total observed deviation may also be calculated, in a similar way to the contribution of each independent variable to

the total R 2 in a multiple regression.

In log-linear analyses, the real dependent variables are the frequencies of animals in each cell of the classification. However, in this situation, the variable, length, may also be envisaged as a ’dependent’ variable. The significances of the ’independent’ variables, area and pot type may then be calculated by tests of partial association or interaction between the length variable and the ’independent’ variables, either individually or in combination. For example, a significant interaction between carapace length and area may be thought of as a test of the ’main effect’ of area on the shape of the observed length frequencies.

The partial likelihood ratio chi2 or G2 statistic has been used for these tests. To validate the analyses, it has been necessary to aggregate uncommon lengths on

the edges of the distributions so that the e x p e c te d frequencies of all cells have values greater than one (Snedecor & Cochran, 1980).

Using the above methods and the data illustrated in figure 1, it has thus been found that the observed length compositions do not differ significantly between the two pot types (for the interaction of pot type and length in males, G238df =

46, P = 0.1869 and for females, G22 2df = 22, P = 0.4645). This lack of significance is thought to be due to the fairly short soaktimes allowed for most of these strings. Differences in mesh size only become apparent in samples

182 4.2. Comparison o f Choiscul / Adventure sounds when crabs start attempting to escape and only the larger ones find themselves trapped. This may only occur after a few days when the bait is exhausted.

However, significant differences have been found between the size structures of the catches from the two different areas. For the interaction of area and length in males, G23 = 72, P = 0.0007; for females, G222(jf = 210, P < 0.00005. Observation of figure 1 shows that these differences are due to the greater proportions of large crabs, of both sexes, in Adventure Sound.

183 Relative Frequency (%) on fo to o tps C ad R2 drn Jl, 1988. during July, CRE2) and (CR types pot two from Sound n ml cas ape fo Cosu Sud n Adventure and Sound Choiseul from sampled crabs male and iue . h sz cmoiin ad ape ie ( sizes sample and compositions size The 1. Figure Females aaaeLnt (mm) Length Carapace 184 4.Z Comparison o f Choiseul f o Comparison 4.Z n Males ) of female of ) / detr sounds Adventure

4.2. Comparison of Choiseul / Adventure sounds

4.2.5. Moult Stages

The proportions of crabs in recently moulted condition at this time of year have also been compared between the two sounds by a log-linear analysis. As the effect of pot type has been found to be insignificant in determining the sizes of crabs selected, pot type has been excluded from the remaining analyses. In this case, the data have been tested, as presented in table 1, taking sex and area as ’independent’ classification variables and the proportions of animals in recently moulted and intermoult condition as the ’dependent’ variable.

As expected, significant differences do exist between the sexes (G2ldf = 59, P < 0.00005). No females have been found in this month in recently moulted condition while a very small number of males had moulted in each location in the minor, autumn moult season (see section 3.2.3.). No significant differences exist, however, between the two areas (G2ldf = 0.8, P = 0.3613).

4.2.6. Weight at Length

The weight W, of an animal of length L can generally be expressed by the relationship

W = aLb where a and b are known as the parameters of the weight for length relationship. They can be estimated by the regression of a log-transformed, linear form of this equation

In W = \n a + b In L .

When the value of b is close to 3, the shape of the animal is constant throughout the range of sizes measured. The coefficient a is then a function of

185 4.Z Comparison o f Choiseul / Adventure sounds the average shape of the animals comprising the sample, with correction made for the scales of measurement of the weights and lengths. Rounded or fat animals have higher values of a than thin ones. For this reason, a is known as the condition factor and is often used as a comparison of the ’well-being’ of animals from different stocks (Pauly, 1984). When the value of b is not equal to 3, the condition factors may still be compared as long as the slopes are not significantly different and a similar size range of animals have been measured in each sample (Ricker, 1973).

Usually, these comparisons are made for stocks of fish, not invertebrates. Male red king crab (Paralithodes camtschatica ), however, have previously been found to be heavier at length in the productive region around Kodiak Island than in the more northerly Bering Sea (Wallace et al , 1949, section 4.3., and see also Somerton & Macintosh, 1983(b)).

Small samples of crabs from both locations have therefore also been weighed, partly for this analysis. Similar size ranges of animals were included in both samples; in addition, all but one of the crabs were in intermoult condition. 46 males and 130 females were sampled in Choiseul Sound during the month, the sample sizes from Adventure Sound were 62 and 92 respectively.

The regression coefficients a and b , for males and females from the two different areas, are shown in table 1. The fitted lines have been compared within each sex by analysis of covariance (the comparisons, in fact, have been made with dummy variables in an analogous multiple regression arrangement). For both sexes, the slopes are not significantly different between the areas (^io4df = 0.138, P = 0.8901 for males and f2i8df = 0.433, P — 0.6651 for females). However, for a combined slope of 3.2778 in the males, the intercepts (ie. the condition factors) are significantly different (*io5df = 4.093, P = 0.0001). Similarly, for a combined slope of 2.6870, the a's of the females are also different (^i9df = 5*46, P < 0.00005). In both sexes, the crabs from Adventure Sound had the higher condition factors.

186 4.1 Comparison o f Choiseul / Adventure sounds

Before drawing conclusions from these results, two further factors should be mentioned. The comparison can not he considered to be ’controlled’ in a statistical sense. The samples producing these results were taken on two different days, and travelled long distances from the capture grounds to the weighing machine in the factory at Stanley. Different weather conditions on the two days could have resulted in unequal levels of stress or evaporation being applied to the crabs during transit. Furthermore, it can not be certain that the balance in use behaved exactly the same on the two occasions. While this result must therefore be treated with some caution, it is suggested that both male and female crabs from Adventure Sound are heavier than those of comparable size from Choiseul Sound.

4.2.7. Female Maturity

Two aspects of female maturity are compared in this section, the average size at maturity and the proportions of crabs in different reproductive conditions.

The size at which 50% of the females in Choiseul Sound are carrying external reproductive material has been estimated by eye, in section 3.1.4., as approximately 46mm. It has not been possible to estimate this average size at ’functional’ maturity with greater precision for reasons discussed in that section. Briefly, it appears that a proportion of the large and almost certainly mature females do not carry eggs at all times, so that maturity can not be determined externally for these crabs. Plots of the proportion ovigerous at each length therefore deviate from the true plot of the proportion mature for the larger females and logistic, or equivalent functions can not be fitted statistically for this species. It is assumed though, that the smaller females, at least, always ovulate at the first available opportunity so that the data for these crabs are reasonably unbiased. Fitting the size at 50% maturity ’by eye’, using data from these smaller animals alone, gave the result above (see section 3.1.4.).

1 8 7 4.Z Comparison o f Choiseul / Adventure sounds

Considering only the data of July 1988, the size at functional female maturity has been estimated, also by eye, as 47mm in Choiseul Sound and as 49mm in Adventure Sound (figure 2). The value for Choiseul Sound estimated here for July alone is believed to differ from that given above (estimated from data collected in the whole of the autumn/winter period) only as a result of the smaller sample size. The estimate for Adventure Sound, however, suggests that the females in this location mature at a slightly larger average size.

Secondly, the numbers of female crabs in the different maturity stages (table 1) are compared. All female crabs sampled in this month were in intermoult condition. This comparison therefore comprises only a simple chi2 test of the proportions of animals in each stage between areas. Again, a significant difference exists between the two sounds (chi23df = 203.778, P < 0.00005). The main contribution to this result lies in the proportions of crabs with uneyed and eyed eggs (table 1). Most females in Choiseul Sound at this time were carrying eyed eggs while in Adventure Sound the majority had the less developed uneyed eggs.

These differences may be due to a variety of factors. The mating cycle may be somewhat delayed in Adventure Sound, so that many females had simply not yet reached the eyed egg stage of development in this area. Alternatively, accepting the hypothesis of a two year reproductive cycle proposed in section 3.2.3, it is possible that the relative year class strengths in the two locations are different, so that the proportions observed would perhaps be reversed in the next and the previous years. Finally, as mentioned in the introduction, the result may simply be due to sampling bias, caused by the distribution of sampling effort in the different areas within each sound. Section 3.2.5. showed that the females with eyed eggs in Choiseul Sound were concentrated in a ’mating ground’ in the middle of the sound. If the equivalent area in Adventure Sound was not found or sampled effectively, the proportion of eyed egg females would be lower, as observed.

188 4.Z Comparison of Choiseul / Adventure sounds

The estimated proportions in each reproductive condition, then, may be far from exact. It may only be possible to conclude that females in both stages do exist in both areas at this time of year. The two year reproductive cycle previously indicated in Choiseul Sound, then, is not disputed by the Adventure Sound data.

189 4.2 Comparison of Choiseul / Adventure sounds

o

Carapace Length {m)

Figure 2. The proportion of female P. granulosa in ovigerous condition in 1mm classes of carapace length in a) Choiseul Sound (total n = 1346) and b) Adventure Sound (total n = 1177). Unconnected data points signify size classes with less than 10 animals. The dashed lines indicate the estimated sizes at 50% functional maturity as fitted by eye (see text).

190 4.2. Comparison of Choiseul / Adventure sounds

4.2.8. Prevalence of the parasite B. callosus

Finally, the proportions of animals infected by the parasite B. callosus (see

section 3.4.) are compared between the two areas. Again, a log-linear model has been used for this test. The ’dependent’ variable in this case is the number of

animals in each of the three stages of parasite infection. The two ’independent’ variables are area and sex.

In this case there is no difference between the two sexes (for the interaction between sex and parasitism, G22df — 2.980, P = 0.2254). However, yet again, a

significant difference exists between the two sounds (G 2df = 12.910, P =

0.0016). Reference to table 1 shows that the overall prevalence of B. callosus is

almost seven times higher in Adventure Sound than in Choiseul Sound.

However, in terms of the potential of the two stocks, the observed difference has

little significance: the percentage of crabs infected is still less than 1% in both

locations.

4.2.9. Summary and Conclusions

Adventure Sound is similar in size to Choiseul Sound but somewhat deeper.

Stocks o f P. granulosa have been found occupying similar types of ground in both

of the two areas. The two stocks, however, are geographically distinct and

several small but statistically important differences have been found between

them.

Of all the biological factors considered, only the proportions of crabs moulting have been found not to be significantly different between the two areas. This is not surprising as very few crabs are moulting at this time of year anyway. The

difference in terms of parasite prevalence has little importance to the stock

assessment. Also, the significant difference in the numbers of females in each reproductive condition is difficult to interpret and not considered further. All

191 4.2. Comparison of Choiseul / Adventure sounds

the other comparisons have interesting implications.

The relative abundance of commercial sized crabs at the time of sampling has been found to be greater in Adventure Sound than in Choiseul Sound. This is

to be expected as the former area has never been commercially exploited. It is

somewhat more difficult to compare the original, pre-exploitation abundances of

these regions (the initial catch rates from Adventure Sound in July 1988 should

not be compared to those first taken from Choiseul Sound in September 1987 as

the catchability of the crabs may well be different at these two times of the year). The available data, however, do not suggest that the initial densities in

the two areas would have would-have- been very different. In section 2.5., it has been estimated that over 48% of the male crabs over 80mm in Choiseul Sound were captured during the 1988 fishing season up to the month of July. Doubling the Choiseul Sound catch rate from table 1 to account for these removals

therefore suggests that the relative abundance in this area, if no fishing had

occurred, would have been around 1.2 crabs/pot. As noted in section 4.2.3., if

the distribution of crabs in Adventure Sound had been as well known as that in

Choiseul Sound and if only the best grounds had been fished, then it is likely that the equivalent, unexploited catch rates in Adventure Sound at this time would also have been reasonably close to, or greater than, 1.2 crabs/pot.

Whatever the original densities in these two areas, at the time of sampling, the

crabs in Adventure Sound were undoubtedly more abundant. Under the

commonly accepted theories of density-dependence, the remaining observations may then be seen as slightly unusual. Of the two areas, the catches of both sexes taken from Adventure Sound contained greater proportions of large crabs.

In the case of males, this may be due to the reduction in numbers of large animals during the selective, commercial exploitation of Choiseul Sound: the same can not be said of the females, however. The data therefore suggest, surprisingly, that P. granulosa grows, or survives, to a larger average size in the more densely populated of the two areas. Furthermore, it has also been shown that the female crabs mature at a larger average size in Adventure Sound and

192 * 4.2. Comparison of Choiseul / Adventure sounds

that both sexes are (probably) in better condition. Neither of these observations

can be explained by the exploitation of Choiseul Sound, nor by the densities in

the two populations. Indeed, if both the grounds were equally suitable for the

growth and survival of P. granulosa, on the basis of density-dependence,

completely the opposite effects should be apparent. It must therefore be

concluded that Adventure Sound is more densely populated than Choiseul Sound

because it really is a better habitat for the growth of this species and that the

secondary observations on size, maturity and condition are simply further

reflections of this fact.

Finally, returning to the purpose of this comparison, from a stock assessment

point of view, Adventure Sound may be considered at least as productive as

Choiseul Sound. The parameters estimated in section 3., from Choiseul Sound

alone, may thus be used as lower limits of the same parameters in Adventure

Sound. In the absence of further data, it is assumed that the Choiseul Sound

results are acceptable, at least for a conservative stock assessment, of the

Falkland Islands as a whole.

193 m 4.3. Comparison of Lithodid species

4.3. A qualitative examination of the commercial potential of P. granulosa in

comparison with other lithodid crabs

4.3.1. Introduction

In this section, the relative productivity of the stock of P. granulosa in the

Falkland Islands is compared with that of other stocks of lithodid crabs both in

nearby Patagonia and in other parts of the world. In the absence of a robust

estimate of sustainable annual yield for the Falkland Islands, this comparison is

made simply to see if the stock might be capable of producing yields similar to

those taken in the other fisheries.

Seven different species of lithodid crabs are compared, including the red, blue

and golden king crabs, Paralithodes camtschatica, P. platypus and L ith o d e s

a e q u is p in a, of the northern Pacific Ocean and Bering Sea. The red king crab

formed the mainstay of the large Alaskan crab industry until its collapse in the

early 'eighties. At this time, the latter two species became more intensively

exploited. Limited attention is also given to the presently unexploited species, L.

c o u e s i , found on isolated deep seamounts in the Gulf of Alaska. The remaining

species represent the family in waters of the southern hemisphere. L . M u r r a yi

exists in many parts of the southern seas but has only been briefly exploited

from the deep waters off South West Africa. Both L. antarcticus and P a r a lo m is

g r a n u lo s a are found in relatively shallow waters in both southern South America

and the Falkland Islands. Where possible, comparisons are made between stocks

of the same species occupying different locations. Particular attention is given to

the differences between the two stocks of P. granulosa in the Falkland Islands

and in Chile.

As is shown in section 4.3.2., some of these stocks do not support even a single

vessel while others support multi-million dollar industries. The reasons for these

differences are explained in this section in terms of 'productivity', which, in this

194 * 4.3. Comparison of Lithodid species

context, is defined as the amount of new mass produced each year within a stock. Under a given exploitation pattern, the maximum sustainable yield of the stock and hence its commercial potential are both directly related to this productivity. As all fisheries for lithodids are managed on a males only basis, only those factors affecting the productivity of the male portion of the stock are considered.

Productivity depends on two basic factors; the size of the population and its rate of turnover. The available information on stock sizes is examined in section 4.3.2. and explains much of the differences between the fisheries. The observed stock sizes are maintained by reproduction and recruitment. Reproduction is thus the female contribution to the productivity of the (male) stock. For lithodids, as for most animals, the relationship between the adult stock size and the consequent recruitment is unclear. In all cases, a wide range of environmental factors are likely to be at least as important as the number of adults. However, it is assumed that those species or stocks producing the most reproductive material have the greatest chance of taking advantage of suitable environmental conditions, when they occur. The likely effects of the various lithodid reproductive strategies on such potential recruitment rates and hence on productivity are examined in section 4.3.4.. The ’turnover’ of the male stock is a function of the growth and mortality rates of the individual male crabs. Though neither of these are well known for any of the species, certain factors associated with growth may still be used at a theoretical level as indicators of relative production. These comparisons of male productivity are somewhat simpler than for the females and are considered first in section 4.3.3..

The upper limit of this productivity is ultimately determined by the carrying capacity of the local environment; the amount of usable space and food resources. Within this limit, the characteristics of certain species will enable them to be more competitive and to exploit the resource more fully than others. In this section, however, it is largely the productivity of the different grounds which is compared, rather than the species themselves. The characteristics of

195 * 4.3. Comparison of Lithodid species

the various stocks are examined simply as indices of the potential of the different locations.

Such a comparison is necessarily of a fairly qualitative nature. Much of the information needed for a complete analysis of this topic, particularly on growth, is not fully available. Furthermore, many of the data which have been used have been estimated, often *by eye’, from information published in a variety of formats, and collected in many different ways. Such a procedure inevitably has a fairly low level of accuracy and it is stressed at this stage that the eventual comparisons should only be taken as ’order of magnitude’ estimates of the true differences between the stocks. It is still felt, however, that several useful observations can be made.

4.3.2. The relative commercial importance of the exploited lithodid crabs

This section, first of all, looks at the actual landings and catch rates of the different stocks as indications of their commercial values. The observed differences are then partially explained by the sizes of the different stocks and also the areas they inhabit. A final, parenthetical section looks at the apparent variation in the catchability coefficient between the stocks.

Variability in annual landings and CPUEs between stocks

The available information on the commercial importance of the different stocks of lithodid crabs is shown in table 2. For both the annual landings and CPUEs, the maximum recorded values are presented. These maximum values are thought to be the best indication of the relative importances of the different

stocks for the following reasons. The fishery for P. camtschatica in Alaska has been shown to be particularly dependent on small numbers of strong cohorts

196 m 4.3. Comparison of Lithodid species

(Blau, 1986; Incze e t a l 1986). Such variability in recruitment has little relation to the size of the perceived parent stock and is thought to be mostly dependent on environmental factors (Hayes, 1983; Jamieson, 1986). As a result, both the annual catches and the CPUEs have varied greatly over time in all the stocks

(e.g. Otto, 1986). As noted before, the fishery for P. camtschatica was closed completely in 1983 and much of the effort transferred to the other king crabs of the area. With such differences in exploitation patterns and variabilities in year class strengths, landings or CPUEs averaged over any period of time would be less reliable as indicators of commercial importance than the maximum values that each fishery has so far produced. For comparative purposes, however, it is necessary to assume that all the fisheries investigated have attained their maximum potentials (within the carrying capacities allowed by their environments) at some time during the period observed. In particular, it must

be assumed that the (virgin) biomass of P. g ra n u lo sa in the Falkland Islands was at a relatively high level at the time it was estimated.

The maximum yields and CPUEs taken from the different stocks are extremely

variable (table 2). The catches from the two stocks of P. camtschatica are both

around ten times greater than those of any other fishery. Both P. p la ty p u s and

L. aequispina are mostly found in waters further north than P. camtschatica. The second species is also found in deeper water than the other two, on the edge of the continental shelf. The relatively small yields reported for both of these species were, however, taken with large amounts of effort, transferred from the red king crab fishery after its closure (Otto, 1986; Somerton and Otto, 1986). For this reason, they are unlikely to be repeated.

The Patagonian fishery for L. antarcticus is the largest in the southern hemisphere. The reported catch was taken in 1983 (Fortoser, 1986(a)), after a period of gradually increasing catches. The more recent history of the fishery is unknown.

The reported catch of L . m u rra y i, in comparison, was taken from relatively deep

197 4.3. Comparison of Lithodid species water in only 6 months of exploitation by a single offshore vessel (Melville- Smith, 1982). During this time, the catch rate declined from 3.4 kg/pot to an uneconomic level of 0.4 kg/pot and fishing operations were suspended. The same species has also been reported from deep waters around the Crozet Islands in the south Pacific, but again the catch rates are thought to be too low to support a commercial venture (Miquel e t a l, 1985). Similarly, only low experimental catches have been taken of the remaining deep water crab, L. c o u e s i found on seamounts in the Gulf of Alaska (Somerton, 1981(a)).

Finally, the maximum catch of P. granulosa in Chile is seen to be the smallest of all the commercially operating fisheries for lithodids (table 2). The stated catch was taken in 1979, only two years after the start of the fishery, from the best location in the Strait of Magellan (Campodonico e t a l, 1983). By 1982, the catch rate from this area had dropped by half, from 8.1 to 4.3 kg/pot and even greater declines were seen in landings and estimated abundances. These reductions were accompanied by a considerable expansion of the fished area, but none of the new locations proved as productive as the central zone (Campodonico e t a l, 1983). However, in 1983 and 1984, catches returned to over 800 tonnes (Fortoser, 1986(a)). It is not known whether this increase was due to the discovery of new grounds or to the recruitment of stronger year classes.

In comparison to the above fisheries, the catch of P. granulosa taken from Choiseul Sound in the year from September 1987 to August 1988 is seen to be tiny. Admittedly, this is the catch of only a single boat, but as it represents an apparent exploitation ratio of almost 50% (section 2), it is unlikely that any greater effort could be supported. It is realised that even the small yield mentioned is unlikely to be a sustainable value, as such slow growing stocks do not generally allow such high exploitation rates. However, as the values given for the other fisheries are also maximum yields which have proven equally unsustainable, they may be reasonably comparable.

Data from the Falkland Islands are given both as the actual catches and as the

198 4.3. Comparison of Lithodid specks catches above two ’knife-edged’ sizes of 80mm and 72mm (from data presented in section 2). The latter size is approximately the size at 50% crew selectivity used at the start of commercial exploitation, and below which processing by hand becomes increasingly uneconomic. The values for catches over 72mm estimate the maximum potential yield which could have been taken, with the effort used, had the crew stuck to this consistently low size at selection. Similarly, the catches in table 2 for the other species relate only to animals above their specific legal sizes given later in table 3.

These figures for Choiseul Sound have been projected to the estimated catches which would theoretically have been taken, had the same level of effort been applied to all the known concentrations of crabs, firstly in Lafonia and secondly for the whole islands. For these calculations, the areas of the different grounds estimated by Fortoser (1986(b)), have been used (table 2), with the assumption that the various locations have equal stock densities and would have produced yields in proportion to their areas. The given areas, which are thought to have been reasonably well estimated by an extensive potting survey, represent the total areas within which catch rates were consistently greater than 3 crabs (males over 75mm) per pot (Fortoser, o p c it) .

The majority of the Falkland Islands stock of P. granulosa occurs in Lafonia, in the south east of the islands (table 2, Fortoser, 1986(b)). Besides being the main concentration of the stock, it is also the only part likely to be exploited for reasons of accessibility (this point is discussed further in section 5.3.). The figure of 351 tonnes, quoted as the projected catch from Lafonia of crabs above 72mm (table 2), is therefore the best estimate of the ’maximum annual landing’ which could have been taken from the Falkland Islands had it been as fully exploited as the other regions. Such a catch is considerably smaller than that taken of

Chilean P. granulosa and over a hundred times smaller than the maximum catches of P. camtschatica in Alaska.

Similar differences exist for the observed levels of CPUE. Again, if the Falkland

199 4.3. Comparison of Lithodid species

Islands fishermen had consistently selected crabs over a size of 72mm, the CPUE over the whole year would have been around 1.3 kg/pot. This is in comparison to an annual CPUE for P. granulosa in Chile of 8.1 kg/pot in the early years of exploitation. Again, the catch rate in the Falkland Islands is over a hundred times smaller than the maximum rates achieved in the SE Bering Sea.

The relationships between catch, abundance and area

The intention of this section is to find the reasons for these great differences in productivity. Observation of table 2 shows that the maximum landings from each of the stocks are broadly proportional to their maximum numerical abundances, though somewhat greater weights are landed, per crab, from the Alaskan stocks. However, as will be seen in the following sections, the Alaskan crabs, individually, are much heavier on average than P. granulosa. If, therefore, abundance is expressed in terms of the total weight of each stock, then the maximum landings are a reasonably constant fraction (an average of half) of the total stock biomasses (table 2). The most extreme variations around this value can be explained as follows. A low ratio has been obtained for P. platypus from the Pribilof Islands because the stock was only lightly exploited at the time of its maximum abundance and the maximum catch was actually taken three years later from a much smaller stock size. The high ratio for Chilean P. granulosa is due to the fact that the maximum catch quoted is the total from all fishing zones while the abundance estimate relates only to the central area of the fishery.

As may have been expected, then, the catches depend largely on the sizes of the stocks. However, it is even more interesting to note that the maximum abundances (again, in terms of weight) are also quite closely proportional to the areas of the stocks, so that the densities of crabs (in tonnes/km2) are fairly constant. Thus, both P. camtschatica and P. granulosa in the Falkland Islands have densities (of legal sized crabs) slightly exceeding one tonne/km2 (table 2).

The low density suggested for Chilean P. granulosa is again due to the restricted

200 4.3. Comparison of Lithodid species

area used for this abundance estimate. Unfortunately, either the abundances or the areas (or both) are unavailable for the remaining stocks. However, a

distribution map of P. platypus given by Otto (1986) suggests stock areas around 25 000 km2 for each of the two locations mentioned in the table. Densities of

P. platypus calculated on the basis of these areas therefore broadly support the previous values, with the St Matthew Island stock being the least dense on the

most northerly ground. The unknown abundance of P. camtschatica around Kodiak Island, however, must have been higher than the maximum catch, implying relatively high densities in this stock (table 2).

Nevertheless, the two broad conclusions remain the same: the maximum catches are closely related to the stock biomasses and these, in turn, are largely determined simply by the sizes of the inhabited areas. The small catches from the Falkland Islands may thus be seen to be largely due to the small sizes of the fjords of Lafonia. The larger catch and abundance from Chile was taken from a considerably larger area in the Magellan Strait, though only a fraction the size of

the total area exploited (estimated at 6000 km2 from graphs in Campodonico e t

a l (1983)). Finally, it is interesting to note that Kodiak Island and the Falkland

Islands are actually very similar in size. The distribution of P. camtschatica, however, extends right from the inshore waters of Kodiak Island to the offshore

continental shelf at a maximum depth of around 200m (Blau, 1986). Both P. g ra n u lo sa and L. antarctica, however are found only in the shallower fjords and sounds and the comparatively low yields of these species are therefore partly due to their apparent inability to colonise the similar continental shelf areas in their own regions around South America and the Falkland Islands.

Variation in the catchabilitv coefficient between stocks

The maximum CPUEs given in table 2 are also broadly proportional to the maximum total abundances. This, however, is more surprising as catch rates

should be proportional to lo c a l abundance or density, not to the maximum size

201 ♦ 4.3. Comparison of Lithodid species

of the stock. Thus, if the densities are fairly constant on the different grounds, as noted above, the CPUEs in table 2 imply that the catchability coefficients found in Alaska are as much as a hundred times greater than in the Falkland Islands. In other words, a single pot fished in Alaska takes a proportion of the local stock over a hundred times greater than does a pot fished in the Falkland Islands. This final sub-section examines the possible reasons for this variability.

While such differences in the catchability coefficient or ’ q’ do seem very large for what is basically the same gear type, a number of factors may be responsible.

Firstly, the design of the gear and the way it is operated may affect q . The pots used in Alaska are around 2m square and are fished much further apart than in the Falkland Islands (Blau, 1986). Individual pots can therefore attract crabs from a larger local area, potentially reducing trap competition, and can also trap more of the animals which approach. In addition, the bait used in Alaskan pots is presented in perforated jars and, unlike the exposed baits used in the Falkland Islands fishery, can not be consumed by the occupants of the trap. As a result, the Alaskan pots may continue to attract crabs effectively for a longer period of

time. The pots used in the Chilean fishery for P. granulosa are in-between the sizes used in Alaska and in the Falkland Islands (Fortoser, 1986(a)), which may partly explain the intermediate catch rates observed in this fishery (table 2).

The above factors suggest that the efficiency of the gear used in the Falkland Islands could be improved. Of course, this does not mean that higher total catches could be achieved, only that the same catch could be taken with less effort.

Other potential influences on q relate to the biological characteristics of the

different species. P. granulosa is known to be aggregated on certain good grounds in Choiseul Sound (section 3.2.). If the Alaskan crabs also form similar or even stronger aggregations and the fishery is limited to a fairly small part of the whole distribution of the stock, then the true densities (in localised areas)

may actually be much greater than suggested by table 2 and the q s much lower.

202 4.3. Comparison of Lithodid species

Finally, deep water animals are usually better scavengers than shallow water ones as they are more limited to a supply of food which falls occasionally from the more productive waters above. Such deeper water crabs may thus be attractable from a greater range, thereby increasing the apparent catchability in relation to the local density.

203 4.3. Comparison of Lithodid species

Table 2. The relative commercial importance of different stocks of lithodid crabs. All data relate only to animals over the specific legal sizes given in table 3. For index to references see table 6.

Maximum Maximum Maximum Area of Refs. Annual CPUE1 Abundance2 fishery3 Landings (kg/pot) Numbers Weight (sq. km) (tonnes) (millions) (tonnes)

P. camtschatica Kodiak Is. 42 834 60 18 500 2,21 SE Bering Sea 58 944 154 46.6 121 160 110 889 14,21

P. platypus Pribilof Is. 4 976 86 9.4 33 840 21 St Matthew Is. 4 288 42 6.8 14 280 21

L. aequispina Bering Sea 4 900 29

L. antarcticus Chile 2 633 7,8,10

L. murrayi SW Africa 185 3.4 19

P. granulosa Chile 817 8.1 2.6 1200 6 000 5,7,8

Falkland Is.4 Choiseul Sd. 67 Actual catches 39 0.9 Actual > 80mm 14 0.3 0.05 22 Equiv. > 72mm 55 1.3 0.26 84 Lafonia 433 9 Equiv. > 80mm 92 0.32 142 Equiv. > 72mm 351 1.65 540 Entire islands 611 9 Equiv. > 80mm 130 0.46 200 Equiv. > 72mm 495 2.33 763

1 CPUEs are the averages within the best recorded seasons, corrected to a 1-day soaktime (the value for P. camtschatica in Kodiak Is. is approximate). 2 Abundances for the Alaskan stocks are survey estimates, those for P. granulosa are Leslie method estimates; the estimate for P. granulosa in Chile is only for the major production area of the stock; those for P. granulosa in the Falkland Islands were attained after the 1987 moult season (section 2). 3 Areas for P. camtschatica are the total areas sampled in annual management surveys; the area for P. granulosa in Chile is the approximate total area exploited up to 1982; those for P. granulosa in the Falkland Islands are the sizes of areas producing catch rates over 3 crabs per pot (Fortoser, 1986(b)). 4 Catches from the Falkland Islands are given above two ’knife-edged’ size limits (72mm is an approximate lower limit for commercial processing) and relate to the single year of commercial exploitation from Sep. ’87 to Aug. ’88 (section 2). The ’Equivalent’ values for the larger grounds have been projected from the Choiseul Sound catches, according to their relative areas.

204 ♦ 4.3. Comparison of Lithodid species

4.3.3. Relative production from the individual growth of male crabs

In this section, the relative productivity of the male of each species is examined.

A yield-per-recruit (Y/R ) type of approach is used to provide a simple index of productivity under particular assumptions. As such, the comparison shows the variation in yield which is caused purely by the different growth of the males between the species, given a constant number of recruits to each stock every year.

Simply speaking, the highest Y /R s are obtained from species which grow at the fastest rates to large sizes with low levels of mortality. The effect of size alone is considered first in this section, as good data are available for this simple parameter. Much less is known about the growth and mortality rates of the different species and the combined effect of these is examined later.

The effect of size on male productivity

The growth of animals is commonly described by the von Bertalanffy (1938)

parameters L^, the asymptotic size towards which growth proceeds and K, the

rate at which L <*, is approached. Such parameters, however, have not been estimated for lithodids (see section 3.3.) and some size other than must be used in this part of the comparison. Length frequencies of both the catches and the landings are available for many of the species, from which various distribution parameters could be obtained. These catches, however, have been taken with a variety of different mesh sizes and selectivities so that the mean sizes from such data are not good measurements of the different average sizes of the species. Instead, the largest animal observed in a sample of reasonable size has been chosen as an easily obtained substitute for L^. A range of such ’maximum sizes’, from different authors, is given in table 3, along with the sizes at maturity and the minimum legal sizes of the seven species.

205 4.3. Comparison of Lithodid species

The size of the largest animal in any sample would be expected to vary both due to location and sample size. As far as possible, estimates from different locations are kept separate (table 3). Variation due to sample size has also been reduced by excluding estimates from particularly small samples. However, to illustrate the limited accuracy of this parameter as an indicator of size, it may be noted that the largest crab reported from Adventure Sound is smaller than the largest from Choiseul Sound, even though relatively greater numbers of large crabs were found in the former area (section 4.2.4.). Due to the very large sample size obtained during this survey, the ’maximum size’ of P. granulosa from Choiseul Sound is thought to be relatively overestimated.

In view of the above comments, the ’maximum size’ is simply used as a rough index of the relative sizes attained by the different species. On this basis, four of the species, P. camtschatica, P. platypus, L. aequispina and L. antarcticus grow to similar large sizes approaching 200mm. The unfished species, L. c o u e s i and

L . m u rra y i, in comparison, are intermediate in size and P. granulosa is by far the smallest of the family at around half the size of the largest lithodids.

Furthermore, P. granulosa from the Falkland Islands are between 10 and 20mm smaller still than the same species in Chile (table 3).

Similar differences are also seen in the sizes at maturity and the minimum legal sizes of the different stocks (table 3). In fact, these two sizes form a reasonably constant 56% and 70% respectively of the maximum sizes of each of the different species. This suggests that, beyond the differences in absolute size, the pattern of growth and maturation is fairly characteristic of the family. The minimum legal sizes are also a consistent fraction of the upper limits because all the stocks are managed in the same way, the legal sizes being set to allow a certain amount of growth after maturity for breeding purposes. For all the lithodid crabs then, only around the upper 30% of the potential growth of the males is legally exploitable.

Under such constant patterns of exploitation, the Y/R of the different species

206 4.3. Comparison of Lithodid species depends only on the absolute sizes attained and on the magnitudes of the growth and mortality rates. For other species, the ratio of these growth and mortality rates (M/K) is fairly constant, so that, for example, long lived species tend to grow slowly (Gulland, 1983). If it is assumed that M/K is constant within lithodids as a group, then the Y/R in this case is simply proportional to the maximum size, in terms of weight. In this rough analysis, we may further assume that the weight is approximately proportional to the length cubed. Then, without knowing anything about the absolute rates of M or K, we may conclude that the large lithodids, growing to twice the length of P. granulosa, have average

Y /R s around eight times as large. Similarly, if P. granulosa in Chile are around 10% longer than in the Falkland Islands (table 3), they are over 30% more productive in terms of weight.

This variation in productivity between the different locations occupied by a species is not exclusive to P. granulosa. As shown in table 3, all the other lithodids for which comparative data are available, also have variable sizes at maturity and ’maximum’ sizes. Such variation, in fact, is a common feature of crustacean growth, also shown by the females and usually attributed to such variables as temperature and food availability (Hartnoll, 1982). Indeed, all the Alaskan species in table 3 grow to, and mature at, larger sizes in the more southerly and presumably warmer waters of their ranges, as do the commercially important brachyuran crabs of the area, Chionoecetes bairdi and C. o p ilio (Somerton, 1981(b)). The difference in size between the males of Chile and the Falkland Islands is also assumed to be the result of habitat differences. Whatever the reason, be it the colder waters of the Falklands current or poor food supply, the data suggest that the Falkland Islands are a relatively poor environment for the growth of P. granulosa.

The effect of growth and mortality rates on male productivity

Lithodid crabs, along with many other crustaceans, have ’indeterminate growth’,

207 4.3. Comparison of Lithodid species in which a succession of ecdyses continues until mortality intervenes (Hartnoll, 1982). At each of these ecdyses the relative size of the increment decreases slightly and the length of time until the next moult generally becomes longer and longer (Mauchline, 1977). The overall effect of these changes is that the growth of lithodids, although non-continuous, is still much the same as that of other animals; fast while small and decreasing with size. In other words, lithodids do grow more or less according to the von Bertalanffy growth function from which the parameter K gives the rate of growth needed for this section.

However, as noted before, von Bertalanffy parameters have not been fitted for lithodids due to the difficulties of ageing these crabs. Instead, growth is usually modelled with separate functions for the moult increment and the intermoult period. It is the combination of the rates of change of these two factors which determines K.

The available data on % moult increments and intermoult periods for lithodid crabs are given in table 4. In all the species, the % increment decreases with increasing size from as high as 20% in young P. camtschatica to below 10% in all the older specimens. It is interesting to note that the most highly productive

P. camtschatica has the largest increments of all the species observed.

Unfortunately, the moult increments for P. g r a n u lo s a are completely unknown (section 3.3.).

The data on intermoult period have been summarised from graphs of the percentages of sampled crabs in recently moulted condition against their size. It is assumed that the size at which this percentage first falls below 100% is the approximate maximum size at which the animals moult annually. Likewise, the size at which the percentage of crabs moulting is reduced to 50% gives the size at which moulting only occurs, on average, once every two years (see also notes to table 4 and section 3.2.4.). Above these sizes the moult frequencies decrease even further: frequencies as little as only once or twice in 9 years have been recorded for tagged P. camtschatica (Hoopes & Karinen, 1972).

208 » 4.3. Comparison of Lithodid species

From table 4, it is evident that the intermoult period of P. granulosa is raised to one and then to two years at much smaller absolute sizes than in the other

crabs. In addition, these life stages are also reached by P. granulosa at smaller

r e la tiv e sizes than in the other species. Thus, by the time P. granulosa reaches exploitable size at 72mm, it is already moulting less than biennially. In

comparison, P. camtschatica, which are also exploitable from about 70% of their maximum size, have intermoult periods between one and two years at this size.

The data for L. aequispina and L. antarcticus suggest that they are both moulting annually at the sizes at which they are first exploited (tables 3 and 4).

Hence, on the basis of the intermoult period, it appears that the maximum size

of P. granulosa is approached more slowly than that of the other crabs. It is still

possible that K could be more or less the same for all the species but, for this to

be true, the moult increment for P. granulosa would need to compensate for the decreased moult frequency. As these two components of the crustacean growth format are usually correlated (Hartnoll, 1982), this is unlikely. It is fairly certain,

then, that the growth rate, K, is comparatively low in P. granulosa.

This fact, on its own, does not necessarily affect the Y/R of P. granulosa for the following reason. Assuming that most of the natural mortality occurs during

moulting, if K is low in P. granulosa, then M is also likely to be low as a result

of the reduced moult frequency. The ratio M/K , then, should still be reasonably

constant within the group. The Y /R s of the different species therefore remain

proportional to their average maximum weights and individual P. granulosa are still around eight times less productive than the larger Alaskan crabs. The implied low mortality rate, however, does have another important implication.

As stocks with low M are comprised of a relatively large number of year classes, only a small fraction of the biomass is renewed with the entry of each new cohort and a larger stock is needed to maintain the same level of annual yield. Therefore, if the yield from a given number of annual recruits is eight times

smaller for P. granulosa, the relative yield from a given total numeric abundance would be expected to be even smaller still. This argument is further developed

209 4.3. Comparison of Lithodid species in section 5.2., in which the real potential yield is estimated from the size of the initial biomass.

In summary, male P. granulosa from the Falkland Islands have individual productivities around an order of magnitude less than the Alaskan king crabs and probably a third lower than the same species in Chile. These differences are mostly due to the comparatively small size of P. granulosa, but also to their apparently low rates of growth and mortality.

210 m 4.3. Comparison of Lithodid species

Table 3. Relative sizes of male lithodid crabs. All measurements are carapace lengths in mm. For index to references see table 6.

Size at Maximum Minimum References Maturity1 Size2 Legal Size

P. camtschatica Kodiak Is. 195-227 145 2,11,22,31 SE Bering Sea 100-103 201 135 21,25,31,32

P. platypus Pribilof Is. 108 185 135 21,27 St Matthew Is. 77 170 120 21,27 Kodiak Is. 87 160 27 Prince William Sd. 93 27

L. aequispina Canadian f[ords3 114 192 163 16,24 Northern Bering Sea 92 180 123 29 Central Bering Sea 107 195 123 29 Southern Bering Sea 130 134 29

L . cou esi Gulf of Alaska 91 135 26

L. antarcticus Chile 90-102 159-187 120 3,7,10,30

L . m urrayi SW Africa 160 102 19 Crozet Is. 70 133 20

P. granulosa Chile 64-79 110-113 80 4,5,7 Falkland Is. Choiseul Sd. CO miXUl Adventure Sd. 93

1 Size at maturity has been determined from chelae allometiy in all cases. 2 The ’maximum size’ is the largest animal recorded in a sample of reasonable size. 3 The legal size given for Canadian L. aequispina was recommended in 1985 but may not have been implemented.

211 4.3. Comparison of Lithodid species

Table 4. Approximate relative growth rates of male lithodid crabs. For index to references see table 6.

% Increment1 Intermoult Period2

Large Small Large Maximum Size at References Juvenile Adult Adult size at biennial annual moulting moulting

P. camtschatica Kodiak Is. 15’-20 15-17 6-11 130-140 160 1,11,13,18,2 SE Bering Sea 19 13-14 9 115-130 155 13,21,32

P. platypus Pribilof Is. 13 9 21 Glacier Bay 13’ 7 12

L. aequispina SE Alaska 13 9 145 17

L. antarcticus Chile 12-13 9-10 110-130 10

P. granulosa Falkland Is. 56 <67

1 The % Increment is the increase in length during a moult, divided by the premoult length. In crabs with indeterminate growth, the % increment decreases with increasing size. Results have therefore been evaluated at three different sizes: just below the size at maturity (large juveniles), 120mm (small adults) and 180mm (large adults). Increments marked by apostrophes resulted from laboratory studies; unmarked results are from mark and recapture experiments.2

2 Intermoult period increases with size for all lithodids examined, from several moults per year as small juveniles to less than annual in large adults. The table shows the maximum sizes at which 100% of animals may still be found in recently moulted condition and the sizes at which 50% of animals are moulting. For P. camtschaticat these data have been corrected for the increment during moulting and the results are estimates of the maximum size at annual moulting and the average size at which moulting is biennial. Moult increment has not been taken into account for the other data and, while the sizes at annual moulting should still be unbiased, the size at biennial moulting of P. granulosa may be slightly overestimated.

212 4.3. Comparison of Lithodid species

4.3.4. Relative production from the reproductive rates of female crabs

In most lithodids, the males moult slightly before the females in spring time and mating usually occurs between hard-shelled males and soft, recently moulted females in relatively shallow water (see references in table 5). The females do not store spermatozoa and only one batch of eggs is produced in each instar (Hartnoll, 1984).

Beyond these common features of the group, various differences exist in the specific reproductive strategies, only some of which affect productivity. In the

deeper water crabs, L. aequispina and L . c o u e s i , for example, mating is apparently aseasonal as the populations are not tied to the surface variations in production and food availability (Sloan, 1985; Somerton, 1981(a)). P. granulosa is also unusual among the group because it is the only species which does not migrate into the shallows for mating (section 3.2.5.). Such specific differences, however, are not believed to have a large effect on the relative productivity of the females.

Specific differences which do affect reproductive productivity include the sizes of the females and the mating frequencies as shown in table 5. In all the species, the females mature at similar sizes to the males, or slightly smaller, but grow to much smaller maximum sizes (cf. table 3). Like the males, the females also mature at a fairly constant fraction of their maximum sizes. At an average 61%, this is somewhat larger than the 56% found in the males. This is thought to be due to the reduced growth rates of female crabs after maturity, resulting from the energetic cost of brooding their eggs (Conan, 1984; Hartnoll, 1984).

The same broad differences in size exist for the females as for the males, with

four of the species being comparatively large and P. granulosa being notably

smaller than the others. Again, female P. granulosa from the Falkland Islands are around 20% smaller than females of the same species in Chile (table 5).

213 ♦ 4.3. Comparison of Lithodid species

The mating frequencies and incubation periods of the various species are also shown in table 5. Both annual and biennial mating is found within the group.

The most productive P. camtschatica is an annual spawner, as is L. antarcticiis

from Chile (references in table 5). Chilean P. granulosa have also been reported

to mate annually, but the data are largely anecdotal (Campodonico e t a l, 1983;

Campodonico pers com in Fortoser, 1986(b)). In the Falkland Islands, P.

g r a n u lo s a is thought to mate once every two years (section 3.2.3.). In all the seasonal reproducers, the larvae are hatched in spring to take advantage of the

increasing water temperatures and food availability. The biennial P. platypus, however, hatch their eggs after only 12 months and then wait a further 12 months before moulting and mating again (Jensen & Armstrong, 1989). A

different strategy is displayed by Falkland Islands P. granulosa, which release their eggs at the same time of year, but only after almost two years of incubation. They are then ready to mate again almost immediately.

In this section, consideration is given to the theoretical effects of these differences on the relative reproductive rates of the females. As noted in the introduction, it is assumed that those species producing the most reproductive material have the best chances of taking advantage of suitable environmental conditions, when they occur, thereby maintaining large and productive stocks. The examination can be thought of in terms of an eggs-per-recruit type model,

similar to the Y/R comparison made for the males. Such a comparison shows the variation in egg production between the females of each species which is caused purely by their different growth rates and reproductive strategies.

As fecundity has not been measured for P. granulosa, this analysis must be made without reference to this important parameter. However, the number of eggs produced by each lithodid is not likely to be a particularly good measure of reproductive potential, as the eggs themselves are highly variable in size. In general, the genus Paralithodes produces many small eggs while Lithodes species produce fewer eggs of about twice the average size (Sloan, 1985). Such larger eggs are likely to have higher survival rates, presumably balancing their lack of

214 4.3. Comparison of Lithodid species numbers. The same number of viable offspring may therefore result from either strategy, so that, in the end, it is just the total amount of reproductive material produced that is important.

The effect of size on female productivity

At a very rough level, all lithodid females are more or less the same shape so that the volume of the egg chamber forms a relatively constant proportion of the overall size of the animal. If the weight of eggs is limited only by the volume of the egg chamber, it may be further expected that reproductive production is proportional to the weight of the animal and thus approximately to the length cubed (Sastry, 1983; Hartnoll, 1984). Examination of this relationship in lithodids, however, has shown that the fecundity usually does n o t rise as fast as the weight. In L. aequispina, fecundity is proportional to length (Jewett e t a l, 1985; Somerton & Otto, 1986) while egg production in the other Alaskan species is apparently asymptotic (Somerton, 1981(a); Somerton & Macintosh, 1985). In conclusion, as the ratio of eggs to body weight decreases, the relative efficiency of reproductive production is reduced in the larger females of each species.

Now, if similar assumptions are made for the females as for the males in the previous section, then the average reproductive material-per-recruit may also be found to be proportional to the maximum weights of the different species. In particular, it is assumed that all the species are reproductively active from the same 61% of their maximum sizes and that both M/K and the rate of reduction of reproductive efficiency are equal within the family. Since the females of the

Alaskan species are again roughly twice the size of P. granulosa (table 5), then, on the basis of these assumptions, they are also about eight times as productive. This is the simple effect of the different size of the species on female productivity.

A further consideration suggests that individual P. granulosa females may be even

215 4.3. Comparison of Lithodid species less productive than this. In section 3.1.4., it was found that the largest females in the Falkland Islands are frequently non-ovigerous. This occurrence has not been noted in the other lithodids (although it does occur in other anomurans

(Wenner e t a l, 1974)) and the decline in reproductive efficiency may therefore be particularly large in P. g r a n u lo s a .

The effect of reproductive strategy on female productivity

As found in the preceding section on the males, the biennial moulting and reproduction of female P. granulosa does not necessarily affect the simple conclusion on female productivity-per-recruit. Again, it may be assumed that the slow growth rate is balanced by low mortality and a longer life in P. g r a n u lo s a.

However, the total amount of reproductive material from a P. g r a n u lo s a female must be delivered over a longer period of time than in the annual spawners. If the annual production of biennial spawners was half that of the annual ones, then a given number of say P. camtschatica females would produce perhaps sixteen times as much material in one year as the same number of P. g r a n u lo s a.

In fact, biennially spawning P. p l a t y p u s do produce 20-30% more dry egg mass in each instar than annual P. camtschatica but this does not compensate for their decrease in spawning frequency (Jensen & Armstrong, 1989).

Female P. g r a n u lo s a, then, on average, also produce approximately an order of magnitude less reproductive material than the Alaskan lithodids. The difference is similar to that of the Y J R s found for the males, largely because both sexes are an equal amount smaller than those of the other species and both sexes are slow growing, but also because the same broad assumptions have been made in each case.

216 + 4.3. Comparison of Lithodid species

Table 5. Factors affecting the reproductive potential of female lithodid crabs. For index to references see table 6.

Size at Maximum Frequency Incubation References Maturity1 Size2 of mating period (months)

P. camtschatica Alaska 96-110 165-189 annual 11 11,22,23,24)

P. platypus Alaska 80-96 143-160 annual 12 15,27,28 then biennial

L. aequispina Alaska 98-111 160-174 less than 16,24,29 annual

L . cou esi Gulf of Alaska 80 122 26

L. antarcticus Chile 80 138-150 annual 10 3,7,10,30

L . m urrayi Crozet Is. 65 94-110 19,20

F. granulosa Chile 52-66 95-100 annual 10 5,6,7 Falkland Is. 46-49 76-80 biennial 20-23

1 The size at maturity is the size at which 50% of crabs are ovigerous (ie functional maturity) 2 The maximum size is the largest animal recorded in a sample of reasonable size

217 * 4.3. Comparison of Lithodid species

Table 6. Publications referred to in tables 2-5.

1 Blau, 1983 in Hayes, 1983 2 Blau, 1986 3 Campodonico e t a l, 1974 4 Campodonico, 1977 5 Campodonico e t a l, 1983 6 Campodonico pers com in Fortoser, 1986(b) 7 CORFO, 1981 8 Fortoser, 1986(a) 9 Fortoser, 1986(b) 1 0 Geaghan, 1973 11 Gray & Powell, 1966 1 2 Hawkes e t a l, 1987 13 Hayes, 1983 14 Incze e t a l, 1986 15 Jensen & Armstrong, 1989 16 Jewette t a l, 1985 17 Koeneman, T. pers com in Jewette t a l, 1985 18 McCaughran & Powell, 1977 19 Melville-Smith, 1982 2 0 Miquel e t a l, 1985 2 1 Otto, 1986 2 2 Powell & Nickerson, 1965 23 Powell e t a l, 1973 24 Sloan, 1985 25 Somerton, 1980(b) 26 Somerton, 1981(a) 27 Somerton & Macintosh, 1983(a) 28 Somerton & Macintosh, 1985 29 Somerton & Otto, 1986 30 Stuardo & Solis, 1963 31 Wallace e t a l, 1949 32 Weber & Miyahara, 1962

218 # 4.3. Comparison o f Lithodid species

4.3.5. Summary and Conclusions

In section 4.3.2., the m a x i m u m yield from the Alaskan stock of P. camtschatica

has been shown to be well over a hundred times greater than the projected

’ma x i m u m ’ yield from the stocks of P. granulosa in Lafonia (table 2). This great

difference is partly explained by the fact that, at its peak, the Alaskan stock

contained an estimated 28 times as m a n y legal sized animals as estimated in this

part of the Falkland Islands (section 4.3.2.). T h e remaining difference is mostly

due to the m u c h larger size and consequently greater potential yield of each

individual crab in the Alaskan stock (section 4.3.3.). P. granulosa from the

Falkland Islands are also less abundant and less productive individually than the

same species in Chile. Both the species and the location of interest, therefore,

are relatively poor from a commercial point of view.

A s the stock densities are apparently similar between the locations, the greatest

part of the variation in catches is explained simply by the different sizes of the

various grounds (section 4.3.2.). P. granulosa in the Falkland Islands are

particularly limited in their distribution to suitable habitats in the small n u m b e r

of sounds in the locality. A m u c h greater total area of similar habitat is

available to the same species in the extensive seaways of Patagonia (although

m u c h of this area has proven to be less productive than the central area of the

Magellan Straits (Campodonico et al, 1983)). T h e Alaskan king crabs also

inhabit the m u c h larger continental shelves of the Bering Sea and north Pacific.

Neither P. granulosa nor L. antarcticus, however, are found more than

occasionally on grounds of similar depth in the south Atlantic. T h e reason for

their absence is u n k n o w n as these fishing grounds are otherwise highly

productive, notably for squid and finfish (Csirke, 1987).

T h e intraspecific differences in size, and hence productivity, between locations

(tables 3 and 5) are assumed to be the result of habitat characteristics. F o o d

supply and temperature have been shown to be the two most important factors

in determining the growth of crustaceans, with both the frequency and the

219 4.3. Comparison o f Lithodid species increment of moulting being affected by both variables (see Hartnoll, 1982 for a review). All three of the large Alaskan lithodids mature at, and grow to, larger sizes in the m ore southerly (and presumably warmer) parts of their ranges

(tables 3 and 5). Although the environmental differences between the waters of the Falkland Islands and Chile are not known, it seems reasonable to assume that the reduced productivity of both males and females in the former location is due to less than ideal conditions.

In conclusion, the Falkland Islands are not likely to produce yields as great as the other lithodid crab grounds around the world. T h e low productivity of the stock is the result of its small relative size (limited by the size of the usable habitat) and the lower productivity of individual crabs in an apparently sub- optimal environment.

220 #

Chapter 5

221 m 5.1. Introduction to bioeconomics

5. Bioeconomic Analysis

5.1. Introduction

In the previous section, it has been shown that the crab stocks of the Falkland

Islands are relatively small in size and low in productivity. They could not be

expected to produce the sort of large yields taken from either the Alaskan or Patagonian stocks of lithodids. In this section, the annual yield which could be

sustained is quantified and the logistic and economic aspects of exploiting the

resource are examined.

Estimation of the potential annual yield is based around the abundance data of

section 2.4. raised to an estimate of the total population size by the distribution

studies of Fortoser (1986(b)). Likely estimates of the growth and mortality rates

are then used to estimate the proportion of this initial biomass which could be

taken each year as a sustainable yield. Although the method is obviously

approximate, it is a c o m m o n approach in the assessment of undeveloped

resources where the available data are limited (Gulland, 1983). U n d e r

continuous, sustainable exploitation, the estimated potential yields from this stock

are very low. If, however, the stock is only fished for short periods at a time

and left to recover in the years in-between, m u c h higher catch rates can be

achieved, at least in the short-term. Such ’pulse fishing’ activity greatly improves

the economic efficiency of a fishery and m a y be the only wa y the Falkland

Islands’ stocks could be successfully exploited. T h e model is therefore extended

in later sections to estimate the potential of the stock under this type of activity.

A n y potential crab fishery in the Falkland Islands will face the logistical

difficulties of exploiting a resource distributed in small, localised aggregations

over a wide and undeveloped area, with limited shore-based facilities.

Discussions with industry have led to two proposals for developing such a fishery:

222 » 5.1. Introduction to bioeconomics

these are outlined in section 5.4.. Finally, the financial viability of each of these

scenarios is examined, conditional on the estimated annual yields.

223 5.2 Estimation of ESY

5.2. Estimation of the sustainable yield

5.2.1. Estimation of the biomass of exploitable stocks

In section 2.5., the biomass of male crabs over 8 0 m m C L in Choiseul Sound, after the recruitment of the 1987 moult season, was estimated to be 22 tonnes.

A s noted in section 4.3.2., hand processing necessitates a m i n i m u m size limit for this species of 7 2 m m CL: the equivalent ’commercially available’ biomass above this size is 84 tonnes (section 2.5., table 6).

In the previous study of the Falkland Islands inshore zone (Fortoser, 1986(b)), the distribution of P. granulosa was described and the total areas of the different crab-holding grounds were estimated (see table 1). T h e two main grounds were found to be Choiseul Sound and Adventure Sound, which have been shown in section 4.2. to have fairly equal productivities. Assuming that the other grounds also have similar stocks of crabs in proportion to their areas, the biomass of the entire Falkland Islands population can be estimated from the Choiseul Sound biomass simply on the basis of their relative areas, as given by Fortoser

(1986(b)). U n d e r this assumption the available biomasses in Lafonia and the whole islands are as shown in table 1 below.

Table 1. Areas inhabited by P. granulosa (from Fortoser, 1986(b)) and estimated available biomasses of crabs from the Falkland Islands.

Area of crab-holding Biomass of crabs ground (sq k m ) > 7 2 m m C L (tonnes)

Choiseul Sound 67 84 Lafonia 433 542 Entire Islands 611 764

A s shown above, over 7 0 % of the stocks of P. granulosa are to be found in the

Lafonia region in the south east of the Falkland Islands. T h e remaining stocks

224 5.2. Estimation of ESY are found in a few small aggregations scattered over a wide area and it is doubtful that they could be effectively exploited (Fortoser, 1986(b)).

The biomass estimates of table 1 are about three times lower than the equivalent estimates of Fortoser (1986(b)), which represents a serious discrepancy between the two surveys. The stock distribution described by Fortoser is thought to have been well estimated and the same areas have been used in both assessments. The difference between the two biomass estimates is due to the different values used for local density. The density estimate of Fortoser was made by the simple Petersen tagging method (Seber, 1982) with a single release and a single recapture of marked crabs. The tags used were pieces of "soft, bright orange plastic sheet measuring approximately 2cm by 3cm ... tied to the left rear walking leg with thin nylon twine". The experiment took place in the partially enclosed Kelp Bay in Choiseul Sound with an area of slightly over 2km. It is thought that two factors, in particular, may have led to the overestimation of density by this experiment. Firstly, discussions with the residents of adjacent Lively Island have revealed that several tags were found washed up on beaches in the vicinity of the experiment, suggesting that tag loss may have been high. Secondly, the assumption of Fortoser that the density within Kelp Bay is similar to that of the rest of the sound may have been unrealistic.

In contrast, the Leslie method used in this assessment (section 2.4.) examined the decline in catch rates within the whole of Choiseul Sound as a single unit, rather than one small part of it. It is assumed that the present lower estimate is the more accurate of the two, but the uncertainty surrounding the previous assumption of constant catchability, noted in section 2.4., should also be recalled.

5.2.2. Assumptions about growth and mortality

The rates of growth and natural mortality are needed in order to estimate the

2 2 5 5.2. Estimation of ESY

potential sustainable yields of the stock from the biomass. Unfortunately, these rates are not known exactly for P. granulosa and it is therefore necessary to examine a range of values of K and M in this analysis. First, however, it must be decided what range is reasonable.

Growth rates

In section 4.3.3., the limited knowledge of moult frequency by size was examined and it was concluded that P. granulosa probably grows somewhat more slowly than the other lithodids. Of all the species, growth rates have only been fully quantified for the commercially important Paralithodes camtschatiea of Alaska. Empirical growth curves have been produced for this species by combining size specific functions of moult increment and frequency from extensive tagging programmes (Weber & Miyahara, 1962; MacCaughran & Powell, 1977). By fitting the von Bertalanffy function to these two sources of synthesised raw data, the growth rate K has been estimated as 0.14 for P. camtschatica from Kodiak Island and 0.15 from the SE Bering Sea. K for P. granulosa, then, is unlikely to be higher than the 0.15 of this large and productive species. As will be seen, the actual value of K makes little difference to the final assessment and a small range between 0.1 and 0.2 is investigated.

Mortality rates

The mortality rates of even the well-studied lithodid crabs are less well known. A limited insight can be gained from the longevity of these animals. The average age at recruitment of male P. camtschatica in the SE Bering Sea is 8 years (Balsiger, 1974 in Incze e t a l, 1986) with the oldest recorded tagged crab being 17 years old (Hoopes & Karinen, 1972). A total mortality rate of 0.3 would reduce a population to 1% of its initial size after 17 years if equal in all ages. Allowing for a fairly high level of fishing mortality in the recruited portion

226 5.2. Estimation of ESY of this heavily fished stock, the natural mortality, M, is likely to be less than 0.3.

Furthermore, if most of the mortality occurs during moulting (as assumed by Hartnoll & Bryant, 1990), then the infrequent moulting of large crabs would reduce the natural mortality among the fishable stock. This common assumption is thought to be the cause of the unusual shape of the length frequencies of many large decapods (Hartnoll, 1978(a) in Hartnoll, 1982). The slow growth and low mortality among the older animals (caused by decreasing moult frequency and percentage increment) results in a relative abundance of larger crabs as many year classes get "bunched up" in only a few large length classes. Falkland Island P. granulosa also show this type of length distribution, as may be seen in section 3.3.3. figure 1 and section 4.2.4. figure 1. The modal lengths occur at around 70mm in these distributions, well above the selection curves of the CR pots used for the samples.

It has previously been shown (Powell, 1979) that such bunched up length frequencies are only found in species where Z is less than K. In this case, the mortality rate of lithodid crabs, among the older animals at least, may be even less than the growth rate of 0.15. Mortality would obviously need to be higher than this in the smaller animals (as suggested by the more frequent moulting) to keep the average longevity down to a reasonable level.

The assumption of such a low M is somewhat speculative. It is also possible that the shape of the length frequencies is biased by sampling from pots, with smaller crabs being inhibited by any larger males already present (Miller, 1979, 1989). Alternatively, a gradual recruitment on to the fishing grounds may lead to such a pattern. However, none of the populations of small crabs found inhabiting the shallow-water kelp beds (section 3.2.2.) were at all abundant, suggesting that the observed length structure may be a real feature of the population. It is therefore assumed that M is indeed comparatively low among the exploited sizes of crabs. In the analysis, a range of mortalities between 0.05 and 0.2 is investigated.

2 2 7 * 5.2. Estimation of ESY

5.2.3. Estimation of the equilibrium annual yield

In assessments of unexploited stocks, the potential sustainable yield, Y, is commonly estimated as a function of the virgin biomass, B0, by the formula

Y = X M B 0

where X — 0.5 (Gulland, 1970). This simplistic formula illustrates the fact that the maximum yield will be taken by reducing B0 to half its initial value, as predicted by basic surplus yield models. The formula also shows that the potential of a stock is proportional to its natural mortality rate, M. Long lived stocks with low M thus produce small annual yields from a given initial biomass because they are comprised of many age classes and only a small fraction of the biomass is renewed on the entry of each new year class.

The formula given above is a rough approximation which frequently overestimates the annual yield and has now been superseded by the more exact work of Beddington & Cooke, 1983. The correct value for X is calculated by modelling the theoretical equilibrium yield and biomass for each level of growth and natural mortality and applying these results to the formula above. These calculations take the well known yield-per-recruit format of Beverton and Holt (1957) and are most simply applied above a constant defined age at recruitment.

In the case of P. granulosa , however, the age at recruitment is unknown. The functions for yield and biomass, fortunately, can also be calculated on the basis of the size at recruitment instead of the equivalent age. If c is the length at recruitment as a fraction of the asymptotic length then the unexploited recruited biomass of the stock at the beginning of any year is given by:

3 n„ (1 - c f B o R W„ (l-c)MIK n=0 1 - e

228 » 5. 2 Estimation of ESY

where R is the annual number of recruits at age zero, is the asymptotic weight equivalent to the length L mi and n is the summation constant of Beverton & Holt (1957) which takes the values fi0 = +1, % = -3, n2 = +3 and n3 = -1 (Beverton & Holt, 1964; Beddington & Cooke, 1983). This formula assumes a stable structure in the population and gives the sum of the biomasses of all the cohorts which have an age greater than or equal to the age at length c.

The formula above is not quite the same as that used by Beddington & Cooke (1983), although it is derived by the same methods. In the cited work, the average biomass over the year is estimated, while the equation above gives the biomass at the beginning of the year. The latter version is used here as the biomass of Choiseul Sound has been estimated by the Leslie method which gives an instantaneous, not an averaged, result.

Similarly, the annual yield from the same stock is given by:

(1 - z (F+M)) m 3 n„ (l-c)" Y = F ------R Wx (l-c)MK 2 ------F + M n=0 1 - e-(F+M+nK)

Again, this is not the same as the equation used for yield by Beddington & Cooke (1983), in this case due to the particular growth format of these crustaceans. Although the yield is taken over the full fishing period, there is no increase in the weight of any individual crabs during this time, as it is outside the moult season. The portion of the equation from the R term onwards gives the biomass at the start of the year (including fishing mortality, F, this time). The earlier terms produce the yield from this initial biomass in the presence of exponential mortality but no increase in weight during the season.

It has been shown in section 4.3.3. that all the lithodids are managed with a legal size limit of approximately 70% of their maximum observed size. If it is assumed that this maximum observed size is close to the asymptotic size, L and hence that c — 0.7, then the potential annual yields as fractions of the initial

229 * 5.2. Estimation of ESY

biomasses are as given in table 2. The results given are simply the ratios of Y over B0 calculated from the above equations.

As shown in table 2, for such a size structured model, the magnitude of K has little effect on Y/B0, at least within this small range of parameter space. This is because changes in K are automatically compensated for by shifts in the age at recruitment in order to maintain a constant c.

In contrast, Y/B0 is still roughly proportional to M, as predicted by the simple yield model of Gulland (1970). With this unusually high size at recruitment (ie with c = 0.7), the coefficient X slightly exceeds 0.5 for most combinations of K and M (table 2). However, due to the very low rates of M used, the size of the predicted Y/B0 is still very small. Even for the highest value of M — 0.2, only a maximum of 12% of the total biomass could be taken as an annual yield. Furthermore, as noted by Gulland (1970) and Beddington & Cooke (1983), even these yields would only be achievable by very high levels of fishing mortality, which would be difficult in practice even for a more concentrated stock. Indeed, the highest values of Y/B0 would only be attained by F = «, ie by catching every single crab as soon as it reached length cl

The potential annual yields from the Falkland Islands have thus been calculated as the products of the biomasses and the Y/B0 ratios from tables 1 and 2 respectively (see table 3). These potential yields are considerably lower than those estimated by Fortoser (1986(b)) and also lower than may have been expected on the basis of the 1987/8 fishing season in Choiseul Sound. However, the projected seasonal catch of 55t from Choiseul Sound alone (section 4.3.2.) was taken from an almost virginal stock with a Y/B0 ratio of almost 50% (section 2.4.). Such rates could not be maintained in an exploited stock after it had reached equilibrium.

It is assumed that this exploitation pattern would not affect the reproductive capabilities of the stock, as the proposed size at recruitment of 72mm is 20mm

230 m 5.2 Estimation of ESY

above the average size at (morphological) maturity of this species (section 3.1.). This should allow sufficient opportunity for mating before recruitment to the fishery. The warnings of section 3.1.2. should, however, be recalled at this point: the change into the morphologically adult growth phase at 52mm does not necessarily imply full functional maturity at this size.

Other stocks of lithodid crabs have highly variable recruitment (see section 4.3.2.) and it must also be assumed that the recruitment and hence the biomass and the yield of P. granulosa would also show some variability. The figures given in table 3 should thus be taken to represent only the average annual yields which would be available if recruitment continued at the same average levels which have produced the presently observed biomass. At this time, it can not be known whether the biomass at the time of the survey was at a relatively high level or a low one, compared to the long-term average. For this reason among others, a degree of uncertainty must be connected with the potential yields in table 3.

231 # 5 . 2 Estimation o/ESY

Table 2. Potential annual yields expressed as fractions of the unexploited recruited biomasses for the likely range of M and K and c = 0.7.

M 0.05 0.1 0.15 0.2 K

0.1 0.025 0.053 0.087 0.123 0.15 0.026 0.048 0.078 0.111 0.2 0.027 0.048 0.073 0.103

Table 3. Potential annual yields (tonnes) from the Falkland Islands for the likely range of M and K and c = 0.7.

Lafonia, B 0 = 542t

M 0.05 0.1 0.15 0.2 K

0.1 14 29 47 67 0.15 14 26 42 60 0.2 15 26 40 56

Entire Islands, B 0 = 764t

M 0.05 0.1 0.15 0.2 K

0.1 19 40 66 94 0.15 20 37 60 85 0.2 21 37 56 79

232 5.2. Estimation of ESY

5.2.4. Available yield and the pattern of exploitation

The potential annual yields estimated in the previous section represent the average maximum weights which could be harvested on a continual basis into the future; in other words, the equilibrium sustainable yields or ESYs. Such estimates suggest that the commercial potential of the stock is fairly limited: even for the higher levels of M, the ESYs are mostly well below 100 tonnes. Fortunately, by modelling the exploitation pattern in a more realistic manner, the true potential of the resource can be shown to be somewhat greater, at least in the short-term.

Problems with using the ESY model

Estimation of the ESY alone is not a complete examination of the potential of this stock because the ESY is the yield available from a stock at equilibrium, after the accumulated year classes have been fished out. No allowance is made for the potentially much greater yields which are available from a previously unexploited stock during the first few years of a new fishery. It may be reasonably assumed that the Falkland Islands’ inshore crab stock is close to its unexploited level as only a fraction of the resource has ever been fished and no fishing has occurred since 1988. The ESYs therefore underestimate the potential yields which would initially be available from this stock.

The fraction of the virgin biomass which can be taken as a sustainable yield depends on the rate of turnover of the stock, being largely a function of the natural mortality rate, M (section 5.2.3.). In contrast, the fraction of the same virgin biomass which could be caught in the first year of fishing is mostly determined simply by the amount of fishing. At the upper limit, infinite fishing mortality would result in the capture of the whole stock of 542 tonnes in this one year. In the reduced stock at equilibrium, however, the same maximum fishing mortality only produces the maximum sustainable yield, around an order

233 ♦ 5.2. Estimation of ESY

of magnitude smaller. This extreme example illustrates the fact that the CPUE of a fishery is (at least in principle) proportional to the abundance of the stock. Both the annual yields and the economic efficiency are thus at their maximum levels in the first years of exploitation.

The example above also highlights a second, previously mentioned problem, that the ESYs for this stock are, indeed, obtained with infinite fishing mortality. In reality, such fishing mortality is completely impossible but the ESY model, as used in section 5.2.3., gives no indication of the yield which could actually be obtained under realistic amounts of fishing.

The dynamic yield model

An alternative to the ESY model is therefore required to assess the true potential of fishing a virginal resource with known and achievable amounts of fishing effort. Just such a non-equilibrium or dynamic model is described in detail in appendix 2. The model has been derived in the same way and using the same assumptions as for the ESY equations of section 5.2.3. except that fishing effort, and hence fishing mortality, is allowed to vary between years. Exploitation begins with the stock at its virginal biomass and the yield from any future pattern of fishing effort can be easily examined. This more realistic approach is used in section 5.4. to investigate possible development scenarios for this fishery. Like the ESY model, only those crabs over a legal size defined by c = 0.7 are included and the results are again dependent on the input values of K and M.

Exploitation patterns

Use of the dynamic yield model allows the investigation of the effect of any pattern of fishing activity on both the stock and the potential yields. If the

234 5.2. Estimation of ESY

continuously available ESY from constant fishing activity is too low to be economically attractive, alternative patterns of fishing can then be considered. These alternative patterns basically involve taking advantage of the greater catch rates available from stocks at high levels of abundance. The greatest economic efficiency is achieved by fishing in the form of pulses. The initially abundant stocks produce good catches for the minimum effort but are reduced in size by exploitation. When catch rates finally become uneconomic, fishing is stopped, allowing the population to rebuild itself. The length of time until the next pulse of activity is determined by the recovery rate of the stock and the catch rate required by the fishery to make a return visit worthwhile. The main problem with such a pattern of activity lies in the alternative employment of the industry in-between pulses.

The greatest gains of pulse fishing are obtained by fairly high rates of fishing so that the shortest possible time is used in reaping the available harvest. As noted by Clark (1976), such heavy and unregulated pulse fishing may severely damage the marine ecosystem. In the Falkland Islands, however, even the heaviest fishing activity is unlikely to endanger the stock due to the large size limit in use and to the exclusion of female crabs from the catches. The species’ wide and low-density distribution also suggest that any fishing activity would cease due to economic factors long before the stock as a whole was dangerously depleted.

The proposed pattern of pulse fishing, then, is still assumed to be fully ’sustainable’, within the broad definition of the word. The difference lies in the rates at which the catches are taken: a small catch continuously at the ESY level or a series of large but occasional catches by fishing in pulses.

235 5.3. Logistic and financial aspects

5.3. Logistic and financial aspects of development

5.3.1. Introduction

The future development of a fishery is dependent, not only on the biological characteristics of the stock which determine the yield, but also on a variety of external and logistical factors. These factors include the accessibility of the resource, the availability of local facilities such as labour and transport, the marketing of the product and any regulations imposed on the fishery. In the veiy under-developed Falkland Islands, such restrictions have acute effects on the ways in which resources can be exploited. The solutions to these problems almost invariably mean that the costs of harvesting crabs in the Falkland Islands are considerably higher than they would be elsewhere.

As the economic attractiveness of any given stock size is completely dependent on the costs of its exploitation, these various logistical restrictions are at least as important to the future development of this fishery as the available yield. They are therefore discussed in this section in some detail, as individual topics. In view of these comments, two development scenarios are later defined (section 5.4. ) as the most suitable ways of fishing this stock. The financial viability of each of these logistically possible scenarios is finally appraised as the simple balance between the costs of the operation and the value of the estimated available yields.

5.3.2. Relative distribution of stock and onshore facilities

The inshore grounds of the Falkland Islands were surveyed with crab pots by Fortoser (1986(b)). As shown in figure 1 (redrawn from the cited work), the distribution of P. granulosa was found to be centred in the south of East Falkland, around the area known as Lafonia. The remaining concentrations of

236 0 5.3. Logistic and financial aspects

crabs in the north and west of the islands are much more isolated and smaller and it is very unlikely that they could be economically exploited. As reported in section 5.2.1., slightly over 70% of the total stock is located around Lafonia and it is assumed that any future fishing will be directed exclusively towards this most concentrated portion of the stock.

Within the Lafonia inshore zone, P. granulosa is distributed in several small stock units, one in each of the various sheltered bays and sounds around the coast (figure 1). Like most other parts of the Falkland Islands, the whole of this region is sparsely populated and very undeveloped. This section examines the importance of these related factors to the operation of a new fisheiy.

Several small, sheep-farming settlements do exist in Lafonia but each contains only one, or a few, families. None of the settlements are large enough to provide such important needs as supplies of labour or accommodation, vessel provisions or processing facilities and there would certainly be no significant demand for crab meat from within this local area. Most importantly, none of the roads in Lafonia are sufficiently well surfaced to permit reliable overland delivery of either the catches or supplies, to or from any other location further afield. At present, the only place with sufficient cheap local labour to support a shore based processing factory is in Stanley. Furthermore, the only surfaced road from Stanley towards Lafonia only reaches as far as the military harbour at East Cove (figure 1), and is unlikely to be extended any further in the near future. Therefore, at the present time, all the catches from any part of Lafonia, intended for processing in Stanley, must first be taken by sea to East Cove before being landed and finally road-hauled to the factory. Transporting catches to East Cove from the furthest stock units up Falkland Sound would thus entail a journey, by sea, of well over 100 miles. In these waters and the prevailing weather conditions, such a journey would probably take close to 24 hours each way, greatly increasing the costs of the operation and reducing the amount of time available for fishing. Those stock units furthest from East Cove will obviously be the least economic to exploit for this reason and must be expected

237 5.3. Logistic and financial aspects to receive far less than their biologically optimum fishing effort.

In view of the lack of shore based facilities in Lafonia and the wide distribution of this stock, any vessel intended to exploit the whole of this resource would clearly need to spend considerable periods at a time on the fishing grounds, without being restricted to any one particular base. The chosen vessel would thus need to be large and self-contained enough to provide accommodation and reasonable, if basic, living conditions for its crew.

238 * 5.3. Logistic and financial aspects

— f------T CO CO r- OJ in in 61 W 60 W 59 W 58 W

1 JL

Figure 1. The distribution of P. granulosa in the Falkland Islands (redrawn from Fortoser, 1986(b)). In the shaded areas, at least one male crab (> 75mm CL) was caught for each pot hauled.

239 « 5.3. Logistic and financial aspects

5.3.3. Local weather conditions

Lafonia, and the rest of the Falkland Islands, are in a particularly windy location. Weather conditions have been monitored daily during this research, the strength of the wind being recorded on the Beaufort scale (between 0 and 12). The readings were taken, in the mornings, at an average time of just after 8 o’clock. The average wind strength, on those days when fishing was possible for at least

part of the day, was 3.716 units on the Beaufort scale ( n = 194). Even this figure, just below ’force 4’, underestimates the true average wind strength as wind speeds were not recorded on days when they were too strong to go to sea.

Such prevailing weather conditions obviously have a great effect on the ability of small fishing boats to operate successfully. Working in the inshore sounds of Lafonia, it is often possible to continue fishing by working only the gear on the most sheltered, calmest side of the sound. If the whole of Lafonia was to be exploited, however, the chosen fishing vessel would also need to be capable of sailing outside the shelter of the sounds and around the open headlands, in much more dangerous seas, during the regular delivery trips.

During the operations of the 36ft Laura Jay, at least 33 days out of the 203 recorded were affected by the weather in one way or another: either the days fishing had to be cancelled altogether or a late start or an early finish was caused. The Laura Jay, furthermore, fished almost entirely in Choiseul Sound alone. A similar vessel working the whole of Lafonia would certainly be far more affected by the conditions encountered on the open sea while delivering catches.

For a variety of reasons, it is therefore felt that a vessel of at least 60 feet would be necessary to function comfortably in these waters. In a more developed country, smaller and cheaper boats may have been able to work within the sheltered confines of each different sound by selling their catches to larger local populations or exporting them for central processing on a more

240 5.3. Logistic and financial aspects advanced road system. In the Falkland Islands, however, catches cannot be delivered overland from any of the stock units except that of Choiseul Sound, there is virtually no local demand for the product and small boats could not transfer their catches reliably by sea, due to the harsh sea conditions outside the sheltered bays.

In conclusion, the stocks of crabs in the inshore waters of the Falkland Islands would be far more expensive to exploit than a stock in a similar but more developed, or less inclement, location elsewhere. Both the cost of the initial investment on a suitable vessel and the running costs, much increased by the problems of delivery, are relatively high in this location.

5.3.4. Processing, marketing and product value

Like other lithodid crabs, P. granulosa has meat of good flavour and texture, with a very acceptable orange-red colour. Although not expected to fetch the premium prices paid for the deeper red meat of the larger king and snow crabs of Alaska and Canada, it should still be a very marketable product (ERL, 1986).

The processing methods employed for such a species and its final value depend on the country in which it is to be sold. With the Falkland Islands’ population, currently around 2000, local demand for any luxury crab product can be taken to be fairly negligible. Exportation to foreign markets is therefore essential, further increasing the costs of the operation. A local industry probably could not compete in the closest market in Chile, due to the higher catch rates (section 4.3.) and the low-cost, artisanal nature of the Chilean fishery. Two other export markets are further considered in this section: the UK market for processed crab meat and the Japanese market for whole crabs. The first market is examined as products from the Falkland Islands would have preferential market access into the UK, giving the greatest benefits to a locally owned industry. Alternatively, the highest prices are paid by the Japanese for whole, unprocessed (and

241 5.3. Logistic and financial aspects

therefore low-cost) products and this market must be considered the primary outlet for this species, for any fishery able to exploit it successfully.

UK market for processed meat

Although many crabs are bought whole in UK markets, most of these are bought alive, immediately cooked and processed and subsequently resold to the

consumer as crab meat. There is thus relatively little p u b l i c demand in the UK for whole crabs. Crab meat, like most foods, does not respond well to being frozen and then defrosted, processed and finally frozen again. As Falkland Island crabs would need to be exported frozen, it is essential that they be processed to their final consumable form, prior to export. To access the UK market with a high quality meat product, all processing and meat extraction would therefore need to be undertaken on location, in the islands.

Extraction of crab meat is a laborious process, which must be done manually if texture and quality are to be maintained. The freshly boiled crabs are first divided into their various body parts, each of which is processed differently. The best quality meat (and the greatest amount) is extracted from the walking legs using a purpose built mangle, the claws are picked by hand using a long thin instrument and the remaining meat in the shoulders is blown out by compressed air (Van Smirren, 1986). For a given weight of crabs, the labour costs of such manual extraction methods are more or less inversely proportional to the average size of the crabs (hence the insistence of the factory for a reasonable size limit). A Falkland Island fishery is thus further disadvantaged as the

relatively small P. granulosa have relatively high processing costs. Data presented by Van Smirren (1986) suggest the requirement of 5 factory labourers

working for one week, to boil, fully process, pack and freeze one tonne of P. g r a n u l o s a . At current Falkland Island labour rates, the direct cost of processing this tonne of crabs for the UK market, in this way, would be around £700 (Boyd

& Johnson, p e r s c o m , 1990).

242 5.3. Logistic and financial aspects

The value of Falkland Islands crab meat on the UK market is presently unknown and difficult to forecast, as with any new product. Van Smirren used a figure of £6.90 / kg in their assessment in 1986, but all the other economic appraisals of this fishery have worked with a planned retail price of £4 / pound (Fortoser, 1986(c); ERL, 1986). The latter figure, equivalent to £8,820 / tonne (processed meat weight), is still thought to be the best current estimate (Boyd & Johnson, pers com , 1990) and is the retail price used in this assessment. Such a retail price, however, may be quite optimistic, particularly as crab meat is now in competition with surimi-based artificial crab imports from the far-east and elsewhere (ERL, 1986).

The value to the fishery, per tonne fresh weight of catch, is dependent on the meat yield which can be obtained (ie. the weight of extracted meat as a percentage of the total fresh body weight). In early processing trials with P. granulosa , meat yields in excess of 20% overall were realised (Taiyo, 1976; Van Smirren, 1986). However, during the regular commercial operation of the SWB factory in the 1988 season, the yield obtained was only 17.5% (Boyd & Johnson, pers com , 1990). This figure is used in these forecasts, giving an estimated value of P. granulosa , in terms of fresh weight but as sold as crab meat on the UK market, of (0.175 * 8820 = ) £1,544 / tonne.

Given these values and the high processing costs, the net value of a one tonne catch of P. granulosa , if exported as meat to the UK market, is not greatly different to its probable value if exported whole (UK crab currently fetches around £7-800 / tonne in whole, fresh condition). However, as transportation charges are roughly determined by the weight actually carried, the costs of exporting only the meat from one tonne of crabs are only about 17.5% of the cost of exporting the catch as whole crabs. Exporting crabs after processing is, therefore, considerably more economical in this case. As noted before though, the real benefit of this practice would be the quality control and the higher and more guaranteed prices to be gained by processing and freezing in one single operation.

243 5.3. Logistic and financial aspects

Finally, if Falkland Island crabs were to be marketed in this way, it would be essential, for the sake of quality, that all the catches were indeed processed before freezing. In the past, due to labour problems, inconvenient delivery times and other factors, this has proven difficult and many crabs have been boiled and immediately frozen to await processing until a later date. Whatever the difficulties, this practice must be avoided in a future industry. The use of live storage facilities at the factory, with recirculating sea water, has been suggested for this purpose by Van Smirren (1986).

Japanese market for whole crab

The low value of whole crab on the UK markets is in complete contrast to its esteemed position in Japan, where whole, and recognisable products fetch the premium prices. Home-produced crabs in Japan may realise around £4,500 / tonne (whole, fresh weight) (Boyd & Johnson, pers com , 1990) and while an unknown product imported frozen from the Falkland Islands may not have quite such a high value, the economics of an industry using this market would clearly be very different to that of the previous arrangement.

Marketing whole crab would avoid the expensive processing costs associated with meat extraction and greatly reduce the initial investment costs of a new fishery. While transportation costs would be higher, as the full weight of the animal would be exported, they would be relatively small in comparison to the inflated value of the catches. Such a market may not even be restricted to crabs over the same minimum size as deemed necessary for meat extraction and greater yields may be possible by exploiting smaller crabs. The size of crabs generally sold in Japanese markets is, however, unknown at present and it is assumed that such an industry would also be based on a minimum size of 72mm and hence on the same potential yields as any fishery based on meat extraction.

The major restriction of this apparently ideal market for Falkland Island crabs is

244 m 5.3. Logistic and financial aspects

that only a Japanese based company would be able to exploit the market to its full potential. Any imported goods from foreign vessels are subject to high import duties and there is a market preference for luxury products from Japanese owned vessels as these have the highest standards of quality control (Boyd & Johnson, pers com , 1990). The valuable Japanese market then, probably could not be utilised by a Falkland Island company in the same way as the UK market. If a Japanese company was to become interested in the resource, the only benefits to the islands of such an export trade would be the potential revenue to be gained by licencing the fishery.

5.3.5. Labour availability

The traditional employment in the Falkland Islands has always been sheep farming. An indigenous fishing industry has never existed and, unlike most island races, the Falkland Islanders have no real seafaring tradition. This is probably due to a variety of factors, including the strong prevailing weather, the relatively barren inshore zone and the lack of local demand for fish products from such a small and widely dispersed population. In consequence, while a factory based in Stanley could probably be locally staffed, it may still be quite difficult to obtain satisfactory local labour to crew a large, inshore fishing vessel. The problem is worsened by the general shortage of available labour in the islands, particularly in view of the many alternative opportunities recently created by the boom in development since the 1982 conflict.

The alternative use of expatriate labour, probably from the UK, would further increase the costs of exploiting this particular resource. With high current inflation of local labour rates in the Falkland Islands, the large salaries payable to expatriates are not that much greater than would presently be necessary to attract local people into a fishing industry (if suitable labour existed) (Boyd & Johnson, pers com , 1990). However, the associated costs of transporting expatriates to the islands and providing accommodation and other benefits while

245 5.3. Logistic and financial aspects under contract greatly increase the true cost of this type of labour. While a proportion of these costs could possibly be saved by using a vessel with suitable living accommodation, unless some provision was made for occasional recreational breaks, away from the boat, it is doubtful that sufficient expatriate labour could even be recruited.

5.3.6. Fishery management regulations

The final factor to consider in this section is the effect on the fishery of any management measures which are likely to be imposed. Fisheries are managed for a variety of reasons including stock conservation, processing economics and the stability and fair allocation of landings (Miller, 1976; Jamieson, 1986). In the case of a small Falkland Islands crab fishery, only the first two of these concerns are likely to be addressed as they are the only ones which can be managed with simple and reasonably enforceable regulations.

The first objective, conservation, in this case only implies preventing wasteful fishing activities and protecting the reproductive potential of the stock (Jamieson & Caddy, 1986). Such aims may be achieved by simple packages of measures including size limits, seasonal closures and gear restrictions. Suitable size limits ensure that all animals are able to breed before becoming available to the fishery. Female crabs, by virtue of their small size, are automatically excluded from many fisheries by such size limits. Separate regulations may, however, also be used toprevent the taking of females, thereby maximising the reproductive potential of the stock (Otto, 1986). Seasonal closures prevent the harvest of soft shelled and recently moulted animals during and immediately after the moulting season. Soft shelled crabs have low meat yield, poor meat quality and higher handling mortality: by delaying the fishing season, a far greater amount of meat may be obtained from a given size of recently moulted crab. Finally, restrictions on the type of gear allowed (usually traps only in crab fisheries, as for P.

246 m 5.3. Logistic and financial aspects

granulosa in Chile (CORFO, 1981)) prevent the wasteful high mortality, on returnable animals, associated with other fishing methods such as tangle nets and trawls.

The second management objective supports the economic viability of the fishery by limiting landings to those crabs of a size and quality that can be processed at a profit acceptable to the industry (Miller, 1976; Jamieson, 1986). The same basic measures are also used to achieve these objectives, with size limits ensuring economical processing (see section 5.3.4.) and closed seasons restricting the capture of poorly conditioned animals, maintaining product quality. In other crab fisheries, legal size limits have often been determined more by these economic factors than by any yield per recruit type calculations, as there is often little biological information to support any one size limit over another (Jamieson & Caddy, 1986). This is indeed the case in the Falkland Islands but, as with other lithodid crabs, the size at maturity is considerably smaller than the processable size, and the size limit adopted is fully acceptable from both the commercial and the conservation viewpoints.

This simple statement of objectives and the package of passive regulations has been referred to as the "size-sex-season" method of management (Otto, 1986) and is the basis of many invertebrate fisheries. The more commercially important species are also managed to promote both biological and economical stability, by the use of such methods as catch quotas and effort controls. However, the Falkland Islands inshore crab stock, like many other small stocks of invertebrates (Jamieson, 1986), will probably never justify the investment necessary for such active management.

The management of any future crab fishery in the Falkland Islands, is therefore likely to be limited to the following four simple and constant regulations:

1. a minimum size limit (determined by processing economics) 2. the exclusion of females from the catches

247 5.3. Logistic and financial aspects

3. gear restriction allowing the use of pots only 4. the closure of the fishery around the moulting season.

These management measures would not greatly limit the development of any new fishery. The first three conditions would probably be adopted by the industry anyway as the most economic and efficient way of exploiting the resource. Indeed, these conditions have already been integrated into the assessment as the estimated potential yields relate only to the weight of male crabs over the commercially acceptable size of 72mm. The closed season may also be adopted voluntarily to ensure product quality. However, both to minimise wastage and to reduce unnecessary handling mortality on both sexes, it is recommended that a closed season be legally enacted to cover both the male and the female moult seasons. These have been identified in section 3.2. as early October to late November and mid-November to mid-December respectively. A closed season of October to December inclusive is therefore suggested, limiting the activity of any new fishery to a fishing season of 39 weeks per year. The inclusion of December in this period (which may not be adopted voluntarily) would achieve two purposes: male crabs would be fully hardened and well-conditioned before being caught and vulnerable female crabs would not be disturbed during their moulting and mating season.

248 5.4. Exploitation scenarios

5.4. Exploitation of the resource

5.4.1. Previous exploitation

The previous commercial exploitation of this stock has been limited to the 11 months of fishing between September 1987 and August 1988 (phases 1-4 of this research) by the locally registered company, Falkland Seafoods Ltd, a subsidiary of the joint venture company SWB Holdings Ltd. After the optimistic reports of Fortoser (1986(b)) and Van Smirren (1986), the company was formed in the belief that an annual yield of between 168 and 252 tonnes could be expected and that a significant demand existed for the product on the UK market. Even at the time, the review of ERL (1986) had pointed out that financial success would be dependent on the yield being close to the upper end of this range and that such an objective would not be easy. With hindsight, it is evident that neither Fortoser, nor SWB, paid sufficient attention to the real logistical constraints of exploiting this fishery. This section briefly examines the company structure and the method of operations of Falklands Seafoods Ltd and the problems it encountered.

Structure and operation of the fishery

Falkland Seafoods Ltd owned both a fishing vessel, working in Lafonia, and a processing factory, based in Stanley. The catches were landed, on average twice a week, and transported by road from East Cove to Stanley. At the factory, the crabs were boiled and the meat extracted by hand using local labour. The final product was frozen in packs of 200 and 400 grammes for export to the U K

The vessel used was the 36ft ’Laura Jay’, a modem, GRP, purpose built crabber, previously used in the UK Channel fishery for brown crab, off Devon. Although equipped with three forward bunks, the vessel did not have sufficient space to

249 5.4. Exploitation scenarios

accommodate its crew for more than a few nights at a time. The company was therefore restricted, from the outset, to those stocks closest to East Cove and in particular to Choiseul Sound (see figure 1).

The company employed between eight and ten people during normal operations. Expatriate labour was used both for the skipper and deckhand of the vessel and for the manager of the factory: accommodation was provided for these employees in Stanley. A general factory assistant, one male processor and between three and five female processors were employed locally.

During the year, a total of 33,109 pots were hauled (at the average rate of 881 per week of fishing) resulting in a total catch of only 41,165kg, over 98% of this from Choiseul Sound alone. As noted in section 2, selectivity was very variable during this time and a considerable number of small, but certainly processable crabs were returned at times of high selectivity.

Problems encountered by the fishery

After section 5.3., it should be evident that this approach had a number of serious restrictions, largely as a result of the use of a 36ft vessel in such an undeveloped location and in such generally inclement weather. Only Choiseul Sound, less than one sixth of the potential resource, could be effectively fished by the ’Laura Jay’ and several days fishing were lost as a result of high winds (section 5.3.3.). Accommodation on board the boat was greatly enhanced by the help and generosity of the inhabitants of the local settlements but could not be imagined as a permanent solution. In addition, the use of expatriate labour and the provision of extra housing in Stanley increased the costs of the fishery and, on the marketing side, attempts to sell the processed crab meat in the UK proved difficult and the anticipated price for the product was never realised.

At the end of 1988, the company ceased activity, after a trading loss of almost

250 5.4. Exploitation scenarios

£400,000 (Falkland Seafoods limited, Annual report, 1988). The failure of the company was attributed to "the high level of costs and the uncertainty as to the volume of crab available and the market for the crab meat". While costs were undoubtedly high, the volume of crab available was, in fact, limited as much by the inability of the company to exploit the whole resource as by the smaller than anticipated size of the stock.

5.4.2. Scenario 1. Continuous fishing with shore based processing

Industry structure

This first scenario for future development is basically similar to the previous exploitation of Falkland Seafoods Ltd, again with factory processing of the catch for export to the UK market. It is reassessed here, simply to test if a more suitable size of vessel, exploiting the whole resource, could be any more successful than the ’Laura Jay’. As noted in section 5.3.6., the fishing season would probably be limited to a period of nine months per year, but apart from this short closed season, it is assumed that the fishery would operate continuously into the future. The annual yields would thus be expected to be initially high and gradually decline to the low ESY levels given in section 5.2.3.. This basic fishery structure is examined more closely as, for the reasons in section 5.3., it would appear to be the only way the resource could provide a stable and on-going source of income and employment to the Falkland Islands.

Financial viability

The various costs and benefits of this operation have been estimated during discussions with the previous directors of Falkland Seafoods Ltd and are given in table 4. Costs have been divided into two basic sections, the initial investment and the annual running costs. The running costs are further subdivided into

251 5.4. Exploitation scenarios those which are fixed (such as the wages of the crew, fuel and bait costs) and those which are proportional to the size of the catch (ie. the costs of processing, packing and delivering each tonne of crabs). A simple cost/benefit analysis, discounted over the lifetime of the vessel, had originally been intended at this point. It can, however, be quickly and simply seen that, financially, such a permanent industry, based in the Falkland Islands, would be completely unviable.

From the table (and as discussed in section 5.3.4.), the actual value of the product can be seen to be only (£1,544 - £805 =) £739 / tonne. Given the very high annual running costs of £232,650, an annual harvest of 315 tonnes would be needed just to balance these basic costs, without paying off any of the initial investment of £442,000. In view of the ESYs estimated in section 5.2.3., this cannot even be seen as a remote possibility. Furthermore, as noted earlier, the real attainable yields would probably not even be as high as given in table 2 due to the difficulties of harvesting such a widespread resource with such limited fishing effort. Not even the inclusion of a measure of density dependence (unaccounted for in the methods of section 5.2.3.) would be likely to raise the available yields by the necessary amount.

In conclusion, it appears that the only way the resource could be fully exploited by a local company would not be financially viable. At the present level of stock density and with the current value of the product on the UK market, the yields would simply be too small to support the amount of investment needed to operate both a fishing vessel and a processing factory in the Falkland Islands.

252 5.4. Exploitation scenarios

Table 4. Estimated costs and values for scenario 1 (continuous fishing)

1. Initial Investment

Purchase of boat (« 60 ft) including gear and any refitting £ 250,000 Delivery to Falkland Islands from UK £ 20,000

Purchase of processing equipment £ 160,000

Purchase of 2 landrovers and trailer £ 12,000

Total £ 442,000

Anticipated lifetime of vessel at cost quoted 10 years Anticipated lifetime of vehicles at cost quoted 5 years

2. Fixed Annual Running Costs

Labour costs:

At UK expatriate wage rates: Boat crew (skipper and two deckhands) £ 50,000 Other employees (general manager and assistant) £ 35,000

Extra costs of using UK labour: Flights to Falkland Islands (2 returns/person/year) £ 6,000 Accommodation and food allowance £ 4,500

Fuel, general running and servicing costs for boat £ 75,000 Bait costs (at 2000 pots per week) £ 1,500

Servicing costs: Vehicles £ 2,000 Factory £ 3,000 Replacement of fishing gear £ 3,000

Office costs: Telephone, telex etc £ 6,000 Rent and rates for factory £ 7,000 Insurance at 3% of fixed assets £ 12,500 Electricity, water etc £ 6,000

Contingency allowance at 10% of annual running costs £ 21,150

Total £ 232,650

253 ft 5.4. Exploitation scenarios

Table 4 (continued).

3. Running costs proportional to catch (per tonne")

Delivery of catches to Stanley (fuel cost for vehicles) £ 20

Processing costs: Labour (at 25 worker-days per tonne) £ 700 Packaging £ 40

Distribution of product (transportation to point of sale in UK) £ 45

Total £ 805

4. Benefits

Value of product: Average UK market price (per tonne of processed meat) £ 8,820

Average meat yield 17.5%

Average value of catch (per tonne fresh weight) £ 1.544

254 5.4. Exploitation scenarios

5.4.3. Scenario 2. Pulse fishing with at-sea processing

Industry structure

As suggested by the comments in section 5.3.4., this second scenario is based around the export of whole frozen crabs to the Japanese market to take advantage of the high prices available and the reduced processing costs. While such exploitation would probably be limited to a Japanese-based company (or a suitable joint venture company) and the benefits to the Falkland Islands would be much reduced, this is likely to be the only way this stock could be economically fished.

This scenario would utilise a single, large, self-contained fishing boat, probably around 90 feet in length and 100 tonnes in weight. All the necessary processing and freezing facilities would be carried on board to enable a high quality, whole product to be packed and frozen ready for market. Such a vessel would comfortably accommodate its crew and have the freedom to exploit the full range of the stock in the Lafonia area.

No shore-based development is envisaged and there would be no requirement for the industry to operate in a stable, continuous manner. The advantages of pulse fishing the stock (section 5.2.4.) could also therefore be gained, greatly increasing the catch rates by only fishing at times of high stock abundance. Unfortunately, unless access could be obtained to either the south American or the south African crab fisheries, no alternative opportunities would exist locally for this company in-between the years of exploiting the Falkland Islands. The purchase of a new 100 tonne vessel for this project, at a cost above £1 million (Boyd & Johnson, pers com , 1990) is thus inadvisable. The project has been costed instead by the charter of a suitable vessel, complete with crew, for each separate pulse of activity. The vessel would probably need to come from Japan, but even with the high costs of the return delivery to the Falkland Islands for each pulse of fishing, this industry structure could still be financially viable.

255 5.4. Exploitation scenarios

None of the crew would be Falkland Islanders, nor British, and as the operation would only last for the limited period of each pulse, the recruitment of suitable labour from Japan should be less problematic. Assuming the company would be attached to one of those already operating in the Falkland Islands, the packaged catches could be trans-shipped occasionally to the company reefer ships for transport to market.

Financial viability - methods of assessment

The costs of this type of operation have again been estimated with the help of the previous directors of Falkland Seafoods Ltd and are shown in the much simplified table 5. The cost of chartering a suitable boat to sail to the islands and fish for a single nine month legal season has been given as £540,000 (the charter fees are reduced during the inactive delivery period as the crew wages would be lower at this time).

The value and the variable costs associated with each tonne of crabs are given in the table as £4,500 and £240 respectively. Because the revenue from the project would only be received at the end of the year (after the sale of the catch), while the costs would mostly be incurred at the beginning of the year, the real net value of each tonne of crabs must be obtained by the process known as 'discounting’. Discounting takes account of the fact that a payment received now is worth more, in real terms, than the same payment received some time in the future. This is basically because the payment received immediately could be invested and earn interest over and above its initial value. In standard economics terms, the present value, PV of a benefit B , received in n years time, is obtained by discounting at the rate r, using the formula:

PV = B

(1 + r f

256 # 5.4. Exploitation scenarios

The discount rate, r is clearly central to this process: the higher the discount rate, the lower the PVs of any benefits received in the future. The discount rate actually used varies with time according to the current rates of interest which can be earned in the financial market place and also with the current rate of inflation. The true discount rate reflects what is known as "society’s rate of time preference" (Mishan, 1972) and is usually taken to be the excess of nominal interest rates over the rate of inflation (Clark, 1976). Furthermore, the discount rate actually used by government agencies at any given time will commonly be less than that used by industry at that time. This is because governments place greater value on the longer-term benefits of projects, thereby promoting economic and social stability. Private industries, on the other hand, need to be more cautious and use the higher discount rates to ensure the commercial profitability of their ventures. At the present time, the true discount rate, given current rates of interest and inflation, is close to 5 or 6 percent. In this analysis, the effect of using two different discount rates is investigated. The lower rate of 5% represents that currently used by government: the higher rate of 10% is used as a likely upper limit to the discounting used by industry and thus indicates the m inim um likely value of the project.

Applying these principles, at the higher discount rate of 10% (ie r = 0.1), the minimum PV of each tonne of crabs, sold at the end of the pulse, one year after the initial payment of costs (ie n = 1), is (£4,500 / 1.1 = ) £4,091. Including the running costs, the discounted net value of a tonne of crabs in this scenario has thus been estimated as (£4,091 - £240 = ) £3,851, over six times its equivalent value of the UK market. Given these figures, an annual landing of only (£540,000 / £3,851 = ) 140 tonnes would now be needed to break even financially. Assuming that the given costs and values would inflate at equal rates, this same yield would also be necessary to break even in any future year of activity.

The potential catches to each pulse of the fishery and the resulting changes in the size of the stock have been estimated using the dynamic yield model of

2 5 7 m 5.4. Exploitation scenarios

appendix 2. As noted in section 5.2.4., the yield to this pulse fishing scenario depends to a much greater extent on the amount of effort which can be applied during the year. Assuming a fishing season of 39 weeks, it is necessary to know the average number of pots the chosen vessel could reasonably haul every week. In the UK Channel fishery, some boats currently fish as many as 1000 pots in a single day. No time, however, is spent searching for suitable ground in this fishery as the brown crabs continually migrate across the fishing grounds into the path of the waiting traps and the gear is always relaid in more or less the same place. In the Falkland Islands, much more time would need to be spent searching for new ground as the previously fished areas became depleted. Even so, a vessel and its crew based permanently in Lafonia should still be capable of hauling considerably more gear than achieved by the Laura Jay. It is thought that at least 2000 pots could be hauled on average each week and possibly as many as 3000 with suitable incentive: these two alternative estimates have been used in this assessment. As the catchability coefficient, q, is central to this assessment procedure (appendix 2), it is necessary to assume that the new vessel would, in fact, use the same type of gear as the Laura Jay. As discussed in section 4.3.2., q could possibly be increased by using larger pots, but this would reduce the amount of gear which could be hauled each week and the overall effect on the total yield would probably be small.

The length of the interval between pulses depends on the growth or recovery rate of the stock and on the stock size necessary to make a return visit worthwhile (ie. a stock size large enough to produce a yield of at least 140 tonnes from the effort available). The recovery rate of the stock is primarily determined (in this model at least) by the mortality rate, M due to its influence over the size of the annual recruitment. The effect of K, in this respect, is fairly negligible within the range considered likely (section 5.2.3.) and is excluded from the assessment to simplify the results (the predictions have actually been made using K = 0.15).

258 5.4. Exploitation scenarios

Results

Several results are presented for this scenario, broadly divided into two sections indicating the short-term and the long-term viability of such a fishery. The short­ term, in this case, refers to the first single pulse of fishing, producing the maximum possible yield from the virgin stock. The profitability of the fishery is assessed using the methods outlined above allowing for variability in the parameters of fishing effort, natural mortality (section 5.2.2.) and the discount rate. The investigation of the longer-term viability concentrates on the likely pulse frequencies that the stock could support and the profits to be made by pulse fishing at the optimum rates. These analyses are made from the point of view of the fishing industry harvesting the stock. In a later section, the potential licence revenue to the Falkland Islands government is also calculated as a simple function of the commercial profits.

Only pulses of one years duration are considered. Given the yields available and the costs of bringing a vessel to the islands (or waiting over the closed season), fishing pulses of anything less than or greater than one year would not be economical.

Short-term viability

The short-term results are presented in table 6 and include the yields from the first year of fishing and the associated profit margins at each discount rate (ie. the discounted net value of the year’s catch minus the initial, fixed cost of chartering the vessel). These yields and profits, as taken in the first year of the fishery and hence from the virgin biomass, represent the maximum values that could be attained (using this model) and provide upper limits for these statistics in future years.

The most important comment is that, for all but one of the combinations of

259 5.4. Exploitation scenarios parameters, the first year catches always exceed the minimum viable catch, thus giving the industry a definite profit. As the charter fee is assumed to be the same at each level of effort, the greatest financial gains are obviously made by the boat which fishes the hardest in the time available. The results are also affected by the level of natural mortality: in contrast to the ESY model (of section 5.2.3. and table 3.), the greatest catches and profits are now taken at the lowest levels of M. This is due to two reasons: firstly, more crabs remain available for capture under low M and secondly, the estimated catchability coefficient, q is greatest at low M (section 2.4.) so that the given fishing effort, / corresponds to a larger fishing mortality, F (appendix 2). On average, the first- year catches from the pulse fishing model are almost seven times greater than the continuously available, ESY estimates given in table 3 (for the same Lafonia region and K = 0.15).

As shown in table 6, the amount of fishing effort applied has great significance on the results. At the higher effort level, this first "one off' pulse is potentially a very attractive venture: whatever the level of M or r, at the prices quoted, the project generates a healthy profit. The ’internal rate of return’ (IRR), also quoted in the table, is the discount rate which would result in a discounted net profit of zero over the year. The excess of the IRR over the discount rate, thus represents the discounted percentage profit of the venture. With IRRs of between 45 and 69%, a single year’s pulse of fishing at 3000 pots/week would clearly represent an excellent investment.

However, for any company or vessel which considered the lower level of fishing effort to be more realistic, the rates of return are somewhat more marginal. While still potentially profitable at most parameter values, in view of the various uncertainties and the inherent riskiness of the project, these returns may well be considered too low for any financial commitment at the present time.

260 # 5.4. Exploitation scenarios

Long-term viability

The preceding section has shown that the first pulse of fishing should be commercially viable, even attractive. The main consideration of this section is the frequency with which the stock could be fished on a regular basis thereafter. Most stocks, obviously, are big enough to be profitably exploited every year. The slow growth and small absolute size of this stock, however, mean that, even for this second, more cost-effective scenario, the ESYs available every year (table 3) are still far less than the minimum needed for economic viability. The actual frequencies at which profitable yields could be taken have been estimated using the dynamic yield model (appendix 2) by simulating the gradual recovery and the increasing potential yields of the stock in each year following a fishing pulse. Both the minimum and the optimum periods between pulses have been estimated in this way: as the former period is somewhat simpler to understand, it is considered first.

The ’minimum interpulse period’ (or minimum IP) is simply the time necessary for the stock to rebuild itself to a biomass capable of yielding a further catch of at least the minimum profitable size (eg. 140 tonnes at r = 0.1). Due to the non-equilibrium population structure in the early years of the fishery, the first IPs may be relatively short. Eventually, however, by harvesting a number of yields at a constant interval, a stable situation is reached with the IP and the resulting yields in balance with the growth rate of the stock. The minimum IP of this section is thus the shortest viable equilibrium interval between pulses. Any future visits, made after even longer periods of recovery should thus result in a profit to the fishery: the longer the IP, the greater the profit, up to a maximum level equal to that taken in the very first pulse. To illustrate these ideas, two potential developments of the fishery are shown in figure 2, depending on the achievable effort. In both cases, after the profitable catch of the first year, the minimum IPs are used so that each fishery operates at the point of zero net revenue. By generating a higher fishing mortality, it may be seen that the high-effort fishery obtains the minimum necessary catches from a smaller

261 * 5.4. Exploitation scenarios

biomass. As this more reduced stock is comprised of a greater proportion of younger and faster growing crabs, these high-/ catches are available at more than twice the frequency.

In view of figure 2, any fishery operating at the lower effort level may now be seen to be particularly inefficient: not only is the first year yield marginal in value, but because the stock must be allowed to return almost to its carrying capacity before the next harvest, the future catches (of even lesser value than the first) could only be taken extremely infrequently. Exploitation of this stock is therefore only likely to be worthwhile at the higher level of effort and, for the remainder of this assessment, only the rate of / = 3000 pots/week is considered.

The long-term results are presented in table 7. The minimum interpulse periods vary between 5 and 14 years, being at their longest for the lowest levels of M, due to the slower recovery rates of the stock. The resulting variability, however, is not as great as the approximately four-fold effect found for M in the ESY model. As with the first year yields, this is again due to the opposing influence of the higher apparent qs at low M. As shown in table 7, the discount rate has relatively little bearing on these results (at least over the range considered). The overall effect of r is discussed later.

It has been mentioned that any pulses fished at longer IPs than the minima given in table 7 should result in a profit to the fishery. However, due to the discounting process, increasing the IP reduces the present value (PV) of a given harvest. Furthermore, while the PVs decrease continuously with increasing IP, the potential yields and hence the profits only increase asymptotically, towards the maximum yield from the population at its ’carrying capacity’. There is thus an optim um which IP produces the maximum present value of each pulse. Fishing at this optimum IP produces a continuous and stable time stream of yields and actual revenues, with the PV of each successive income being increasingly less than that of the preceding one. The sum of the PVs of all future pulses may be envisaged as the net present value (or NPV) of the whole

2 6 2 5.4. Exploitation scenarios fishery. At the discount rates used, the PVs of any pulses more than about 50 or 60 years away are almost negligible in value and do not contribute significantly to the overall NPV of the fishery. The ’Optimum IP’ of this section has thus been calculated, using the dynamic yield model, by maximising the total NPV of the fishery over a 60-year period.

This process is illustrated in figure 3 at each level of the discount rate, r and the mortality rate, M. The NPV curves can be seen to be peaked, rising from negative values at short IPs (when the cumulative losses from the future pulses cancel the profit of the first pulse) up to the maximum NPV at the optimum recovery time. At longer IPs, the NPV of the fishery decreases asymptotically towards the present value of one single pulse (when the future pulses are so far away that they are almost worthless in present terms). The peaks of the curves are most pronounced for the highest levels of Af, the future catches being more valuable as they are not so far away. Not surprisingly, both the minimum and the optimum IPs are affected by M in similar ways, the optimum period being longer by an average of just under 4 years (table 7). Except for the lowest M of 0.05 (which is probably the least likely), the optimum IPs are clustered around an average interval of 10 years duration.

The actual size of the discount rate has surprisingly little effect on the estimated interpulse periods. This, however, is partly because the IPs are necessarily rounded to the nearest year and, in fact, increasing r from 0.05 to 0.1 does have two small effects. Firstly, within each pulse, a higher discount rate means that the minimum viable yield must be larger so the minimum IP is slightly increased (this is only apparent in the table at M = 0.05). Secondly, also with higher r, the more distant catches are worth less so the optimum IP is decreased to compensate. As shown by the remaining columns in table 7, this reduction in IP decreases both the future yields and their individual values and also the total NPV of the fishery over the 60 year period.

In conclusion, these results suggest that this fishery would be best exploited with

263 * 5.4. Exploitation scenarios

a high-effort pulse of fishing approximately once every 10 years. As shown in table 7, the yields and profit margins to each stabilised pulse of this optimal strategy are considerably less than the equivalent values from the first pulse (table 6). However, due to the discounting process, in present terms, these small but reasonably frequent revenues are still more valuable than the maximal yields which could only be achieved again after much longer recovery times. Fishing at the optimal IP thus maximises the discounted long-term profits from this very low-output fishery.

In parenthesis, it may be noted that similar optimal IPs have previously been calculated using a method derived as long ago as 1849 by a German forester, M. Faustmann (see Clark, 1976). This Faustmann formula has mostly been used to optimise the 'rotation times' of forests, which are usually clear-felled and replanted with no residual from the previous plantation. Optimising rotation times to allow for the 'thinning' of forests (analogous to the partial harvesting of a crab population), however, is mathematically complex. The simpler, Leslie matrix type of approach used in the dynamic model of this section has enabled both the estimation of the first year yields and also the long-term optimisation of interpulse periods, with the added reality of the population declining gradually towards its equilibrium situation.

Potential Licence Revenue

Fishing licence fees are commonly calculated as a certain proportion of the total expected revenue of a vessel, this being estimated from the expected catch and the average price per tonne. In this assessment, however, the actual p ro fit margins of the fishery have been estimated, from which licence fees can be similarly calculated, but more consistently and fairly. Clearly, the discounted net profit margins to the fishery are much higher for the first pulse (table 6) than for the long-term, stabilised, future pulses (table 7) and higher licence fees should thus be applied at this time. (Note that the long-term figures are the

2 6 4 * 5.4. Exploitation scenarios

actual profits to the fishery at the times they occur, discounted within the year (remembering that the benefits are received after the costs are incurred) but not discounted to their present values.)

Assuming that the licence fees were to be calculated as a constant fraction of the profit margins (the actual fraction being negotiated with the exploiting industry), the fees could easily be set using the data from the tables. Using the more cautious discount rate of 10% and setting the licence fee at say 50% of industry profits, significant government revenues in the range £92,000 to £159,000 could be obtained from the first pulse. Future licence fees, however, would necessarily be much smaller, between £30,000 and £46,000 at the 50% rate. In fact, given the small actual profits, it is unlikely that a rate as high as 50% could be supported in the long run and the real potential would probably be even less.

Conclusions

In conclusion, it is suggested that this type of pulse fishing could be financially viable. The profitability of the fishery would clearly be very sensitive to the true values of the various costs and benefits (particularly the assumed high value of

the product) and also to the amount of fishing effort which could be attained by the vessel employed. The first pulse of fishing, with the stock at its maximum initial abundance, would be particularly profitable. The limited variability in the size of the first year catches arises only from the different estimation of q at each level of M. Regardless of the magnitude of M or of the discount rate, r, if a level of effort of 3000 pots/week could be achieved, the resulting profit margins should be highly attractive. At the lower fishing effort of 2000 pots/week, the project may still be financially viable, but would certainly be far less beneficial.

Given the estimated catch rates, even the single vessel employed would take as much as (223t / 542t = ) 41% of the total stock in the first nine-month season.

265 5.4. Exploitation scenarios

Due to the slow rate of turn-over or recovery of this stock, it would then be a further 5-14 years before another (even marginally) profitable catch could be taken. The greatest long-term benefit would be obtained by a company fishing (at the high effort level) at the rate of one nine-month pulse approximately every 10 years. This recommendation is relatively insensitive to both the turn­ over rates of the stock and the discount rate used. However, such infrequent pulse harvesting does mean that this Falkland Island product would only occasionally be available for sale. As a result, it may actually be very difficult to achieve the high market prices on which the long-term success of this scenario depends.

26 6 5.4. Exploitation scenarios

Table 5. Estimated costs and values for scenario 2 (pulse fishing). Charter fees have been calculated using the rate £1 = $1.8.

1. Fixed Annual Running Costs

Charter of boat (« 90 ft) with on-board processing and cold storage including costs of labour, gear, bait, insurance, servicing and running.

Delivery from Japan (return trip at $2000per day) £ 90,000 Nine months fishing (at $3000 per day) £ 450,000

Total £ 540.000

2. Running costs proportional to catch (per tonnel

Processing costs: Packaging £ 40

Distribution of product (transportation to point of sale in Japan) £ 200

Total £ 240

3. Benefits

Value of product: Average Japanese market price (per tonne whole frozen crab) £ 4,500

267 « 5.4. Exploitation scenarios

Table 6. The short-term viability of the pulse fishing scenario: the maximum yields and profit margins as taken by the first pulse of fishing, for the likely range of fishing effort and natural mortality (and for K = 0.15).

Fishing Natural Yield Discounted Net Profit Internal Effort Mortality (tonnes) Rate of (pots/week) M r = 0.05 r = 0.1 Return (%)

2000 0.05 162 £ 115,406 £ 83,847 25.9 0.1 153 £ 78,994 £ 49,189 19.4 0.15 144 £ 42,583 £ 14,531 12.8 0.2 135 £ 6,171 £ -20,127 6.1

3000 0.05 223 £ 362,194 £ 318,753 69.1 0.1 212 £ 317,691 £ 276,393 61.5 0.15 200 £ 269,143 £ 230,182 53.1 0.2 188 £ 220,594 £ 183,971 44.6

Table 7. The long-term viability of the pulse fishing scenario for the likely range of natural mortality and discount rate (for / = 3000 pots/week and K = 0.15). The table shows the minimum interpulse periods and the optimum interpulse periods (found by maximising the net present value of the fishery) and the yields and discounted net profits of the stabilised future catches taken at the optimum frequencies.

Discount Natural Interpulse Period Maximum Stabilised Discounted Rate Mortality (years) NPV over Future Net Profit r M Minimum Optimum 60 years Yields of future (tonnes) yields

0.05 0.05 13 20 £ 446,586 167 £ 135,864 0.1 8 12 £ 502,559 168 £ 139,450 0.15 6 10 £ 502,872 170 £ 147,112 0.2 5 8 £ 468,518 163 £ 120,206

0.1 0.05 14 17 £ 339,182 156 £ 61,040 0.1 8 11 £ 336,543 162 £ 86,068 0.15 6 9 £ 307,070 164 £ 93,570 0.2 5 8 £ 269,531 163 £ 88,416

268 ♦ 5.4. Exploitation scenarios

0 ID 20 3D 40 50 60

Tine (years)

Figure 2. An illustration of the scenario 2 (pulse fishing) model showing the future harvesting of the fishery at the minimum interpulse periods (see text) for fishing efforts of a) 2000 pots/week and b) 3000 pots/week, when M = 0.1 and r = 0.1 (and K = 0.15). The continuous line shows the stock size at the start of each year while the bars indicate the annual catches.

269 iue . h ifune fItrus Pro o te e Present Net the on Period Interpulse of influence The 3. Figure au o h fsey t w lvl o h dson rate, discount the of levels two at fishery the of Value

Net Present Value over 60 years (£ 000's) I n t e r p u l s e P e r i o d( y e a r s ) .. xliain scenarios Exploitation 5.4. r.

# 5.5. Summary of bioeconomics

5.5. Summary and conclusions

This section has initially examined the potential yields of the Falkland Islands’ inshore crab stock and proceeded to look at the considerable logistic and financial restraints of exploiting this resource. In view of these factors, the failure of the previous exploitation of the stock has been explained and two further scenarios for the future use of the resource have been identified and examined.

The first scenario, similar in structure to the previous industry, but using a larger vessel more capable of exploiting the whole resource, has been found to be equally unviable. Both the previous exploitation and this first scenario involve companies based in the Falkland Islands whose primary market would be in the UK. The main market demand in this country, however, is for extracted crab meat and to guarantee product quality, it would thus be necessary to have a factory located in the islands. Unfortunately, at current UK price levels, the resource is simply too small to support this amount of investment.

The second scenario would involve, probably a Japanese company, exporting whole crabs to Japan for the highest available prices and the minimum processing costs. Only a single, self-contained boat would be employed, carrying all the necessary processing facilities on board, to allow the greatest freedom of access to the resource. However, due to the small size and the low growth rate of the stock, continuous exploitation would still be financially impossible: even at the highest possible rate of fishing effort, acceptable catch rates could only be achieved by a pulse fishing approach. In this form though, given acceptable price levels for the presently unknown product in the far-eastern market, the scenario could be financially attractive, particularly the very first pulse. The long-term value of the fishery would be maximised by fishing the stock fairly infrequently, probably only one year in every ten or so. Such pulse fishing would obviously be less attractive than a permanently based industry, but as Japanese

271 5.5. Summary of bioeconomics access to the fishing grounds of the world becomes more and more restricted, smaller stocks such as this may start to be exploited. Unfortunately, apart from a possible income from licensing the fishery, this scenario would have limited benefits to the Falkland Islands. In contrast to the first scenario though, it is at least worthy of further consideration and, in particular, of better definition of the probable costs and values involved.

Finally, it has to be said that any stock which could only support the infrequent attentions of one single vessel must be regarded as a relatively unattractive proposition. At present there are still many more viable stocks elsewhere in the world and it will probably take a considerable change in circumstances before any regular crab fishery in the Falkland Islands is established.

272 Chapter 6

273 m 6.1. Commercial potential

6. Discussion

In the introduction to this thesis, the main research objectives were specified in two broad categories: the clarification of the commercial potential of the stock and the provision of a suitable management strategy for the new fishery (section 1.2.). All of the four main chapters make some contribution to each of these subjects. In this final chapter, the various results are summarised and discussed in two separate sections to draw the final conclusions on the two issues.

6.1. The commercial potential of the stock

Prior to this research, the realistic maximum potential yield of the fishery had already been predicted by Fortoser (1986(b)) at between 168 and 252 tonnes per year. The estimates were made by the well known equation, Yield = 0.5 M B 0 of Gulland (1970) and are thus completely dependent on the accuracy of the two parameters, natural mortality, M and initial biomass, B 0. In this thesis, the potential yield is re-estimated, using similar but more sophisticated methods with better-estimated parameters and the original figures are shown to be highly optimistic.

Fortoser’s estimate of B 0 was derived from a single, simple tagging experiment done in one small part of Choiseul Sound, which has been criticised in section 5.2.1.. In this assessment, the biomass has been estimated from the decline in catch rates observed in the whole of Choiseul Sound as a single stock unit. The extensive time series of catch and effort data has been standardised for variability in crew selectivity and differences between pot types and also for the effect of soaktime on apparent fishing effort. Analysis of these data with a variant of the 'Leslie removal method’ discounted for natural mortality has produced more reliable biomass estimates about three times lower than the originals.

274 6.1. Commercial potential

For natural mortality, the second parameter in Gulland’s equation, Fortoser used a range between 0.2 and 0.3, although virtually no justification was given for this choice. During this research, a number of attempts have been made to clarify both growth and mortality rates. The true rates for P. granulosa still remain unknown, as indeed they do for many similar species, and these uncertainties continue to form the weakest link in this stock assessment. Several advances have, however, been made, suggesting that M is also probably somewhat less than assumed by Fortoser (see sections 3.2.4., 4.3.3. and 5.2.2.). In brief, the analysis of size-specific moult frequencies has shown that P. granulosa is one of the slower-growing lithodids, probably moulting biennially, not annually, as legal­ sized adults. Further theoretical considerations on the shape of the length composition of the stock suggest that the mortality rate is also likely to be low, at least among the older animals (as may also be expected from the low moult frequency). Such comparative information and published data on the growth of other lithodids suggest that neither K nor M are likely to be above 0.2 at least among the adults of this relatively unproductive species.

In using these results to estimate the potential yield from the initial biomass, the more exact approach of Beddington & Cooke (1983) has been used. The basic method has been further modified in this case to account for the fact that individual P. granulosa do not moult or grow during the fishing season and that the biomass estimate relates to the stock at the start of the year and not the seasonal average. With such improved methods, the most likely potential yields for the Falkland Islands stock have been found to be in the disappointing range of only 14-60 tonnes per year.

This thesis then greatly extends the work of Fortoser by considering the logistic aspects of any future fishery and the special problems associated with processing the catch and distributing and marketing the product. Two fishing strategies in particular are examined, the first being the permanent industry intended by both Fortoser and SWB with a local fishing boat delivering regular catches to shore based processing facilities within the Falkland Islands. In the light of the new,

275 6.1. Commercial potential lower estimate of potential yield and the very high costs necessitated by this undeveloped location so remote from its potential markets, such a fishery is shown to be completely uneconomic.

The second strategy examined involves a non-permanent, pulse fishing approach with no shore-based development and only a single, self-contained vessel exporting whole frozen crabs to the more valuable Japanese market. By only fishing the stock at its highest levels of abundance, this approach is shown to be far more viable. Given certain criteria on the amount of fishing effort achievable (which would need to be considerably greater than managed by SWB) and on the value of the presently unknown product, a single, intensive, nine- month harvest of the stock could give very attractive discounted financial returns of between 50 and 60%. For any company capable of such a one-off venture, better clarification of the exact costs involved and the marketability of the product would seem to be worthwhile. In the longer term, however, further pulses of fishing could only be made economically by leaving the stock to recover for periods of at least around 6-8 years. It has also finally been shown that the maximum discounted value of the fishery would be obtained by only fishing at the very slow rate of around one such nine-month pulse in every ten years.

Such results must be seen as fairly disappointing and it may be questioned why the potential for a Falkland Islands crab fishery should be so low. The reasons would appear to be mainly two-fold, associated firstly with the stock itself and secondly with the location. In the first case, comparisons with the other commercially profitable lithodid stocks both in Alaska and Chile have shown the Falkland Islands stock to be particularly small, mostly limited by the area of suitable habitat. In addition, the individual crabs are also small and unproductive both in comparison to the other species and even to the same species in Chile, suggesting that the Falkland Islands is a relatively poor environment for P. granulosa. Secondly, the development of an inshore fishery in the Falkland Islands is severely hindered by the almost complete lack of onshore facilities and the negligible local demand for any crab product. Thus, although

276 6.1. Commercial potential the Fortoser report was misleadingly optimistic, the failure of the resulting SWB joint venture was due not only to the low catch rates but also to the ’Laura Jay”s inability to fish any further afield than Choiseul Sound. In a more developed location, the available stock probably could have supported a low technology industry supplying local markets for small profits. In the Falkland Islands, however, a large vessel would be needed for logistic reasons, but simply could not be supported by the catches available. Although both Fortoser and ERL did address such problems, the unfortunate, short history of this fishery must highlight the common problem of inadequate communication between fishery biologists and the fishing industry.

277 6.2. Management o f the fishery

6.2. Management of the fishery

In view of the comments of the previous section and the recent collapse of the SWB joint venture, no further crab fishing activity is expected, at least in the near future. Should further exploitation be proposed, however, a number of regulations could be recommended to ensure both the efficiency of the industry and the conservation of the stock (see section 5.3.6.). Given the small potential size of the fishery, the proposals, as listed below, are simple and should be reasonably enforceable:

1. A minimum size limit 2. Restriction of the landings to male crabs only 3. Restriction of the gear to pots only 4. Closure of the fishery during the moulting and mating season.

For reasons of efficiency such measures would probably be adopted voluntarily by the industry. Thus, the labour-intensive extraction of crab meat necessitates a certain minimum size and automatically excludes the naturally smaller females. In addition, correctly designed crab pots are easier to work than either trawls or tangle nets, particularly for such small crabs and fishing would probably be suspended around the moulting season to avoid the reduced meat yield and poor meat quality of soft-shelled crabs. Legal enactment of such measures would simply prevent any other more wasteful fishing activities and ensure that the stock is exploited in the most efficient way.

Luckily for this fishery, the same regulations should also protect the reproductive capacity of the stock. Thus, any size limit likely to be acceptable to industry has been shown to be well above the newly-estimated size at male maturity allowing all crabs a period of reproductive activity before becoming vulnerable to capture. The live return of all female crabs to the sea would further maintain the maximum spawning stock and the use of non-destructive gear at only the least vulnerable times would minimise unnecessary mortality. Avoiding the need to

278 * 6.2. Management o f the fishery

set quotas, these measures should at least ensure that the yield and the value of the fishery are close to the maximum possible from the naturally occurring level of recruitment. The safety of the stock should also be protected by its wide and low-density distribution such that any fishing activity would be expected to cease long before the population became dangerously depleted. Indeed, it has been shown that it would not be economic to reduce this stock to any less than around half its initial size which would not usually be considered an excessive threat to recruitment. Of course, according to the common surplus yield models, such harvesting should give the maximum growth and production from the stock. Unlike the usual situation, therefore, both the economic and the biological viewpoints are surprisingly compatible with the conservation of the stock.

This thesis has provided many of the results needed for the exact specification of regulations 1 and 4. In the case of the latter, the extensive research on the life history of the stock has indicated that the closed season should ideally include the period October to December leaving a nine-month fishing season. This would cover both the male moult season (identified as early October to late November) and the later female moult season with its associated mating activity (mid-November to mid-December). Delaying the closed season into December, which possibly would not be adopted voluntarily, would ensure males were fully hardened before capture and allow the mating season to take place without disturbance.

Choosing the ideal size limit (regulation 1) is more complicated. Thankfully, with this fishery, it can be argued that the choice can safely be left to the fishing industry. If the stock was exploited for the UK market, the industry’s own size limit of approximately 72mm CL (enabling viable hand-processing) would be acceptable from a conservation point of view, being about 20mm above the average size at male maturity. If, on the other hand, the Japanese market for whole crabs was exploited, there would possibly be no need for such a high size limit, but it is proposed as follows that this approximate limit would probably still be adopted voluntarily.

279 6.2. Management o f the fishery

In a joint comparison of the biology and the management strategies of the various lithodid stocks (section 4.3.), it has been shown that the group as a whole has a fairly characteristic pattern of growth and maturation. Although the absolute sizes are highly variable within the family, both the sizes at maturity and the minimum legal sizes of the different stocks form a relatively constant 56% and 70% respectively of the maximum size of each species. The minimum legal sizes are consistent because each of the stocks are managed in broadly the same way, such sizes being set to allow a certain amount of time after maturity purely for breeding purposes. To set size limits in this way, reasonable information is needed about annual growth rates, most of which remains unknown for P. granulosa.

However, the industry’s usual acceptance of such size limits may well be due, not so much to the perceived wisdom of this approach, as to the general allometric characteristics of the lithodid family. Both P. granulosa and the other lithodids do not change shape significantly at maturity but only change the relative rates at which the different parts are growing. From the industry point of view, adult crabs may only become ’processable’ after a few moults at the adult allometiy pattern have increased the relative sizes of the legs and claws. It is only at this time that both the aesthetic appearance of the crab and the available meat yield are noticeably improved. Thus, according to both management and industry, both the minimum legal size and the minimum ’processable’ size of the Alaskan red king crab are much higher than the equivalent sizes for P. granulosa.

It is therefore suggested that even an industry exporting whole crabs to Japan or elsewhere would probably also choose its own size limit reasonably close to the approximate 70% criteria used in this assessment and in the management of the other species. If the size-specific growth and mortality rates of P. granulosa were more fully understood, it would have been useful and interesting to integrate the allometry data with a yield-per-recruit type of analysis to optimise the minimum legal size to give the maximum ’meat yield-per-recruit’. It seems likely that the optimum size would be fairly close to the industry’s perceived

280 6.2. Management of the fishery

’processable’ size and still safely higher than the size at maturity.

Finally, although overcapitalisation does not seem very probable in this fishery and effort limitation is not specifically included as a management tool, it is obvious that the stock could only support a very limited amount of fishing effort. Although, as shown above, the stock itself should be able to survive virtually any feasible exploitation, the profitability of the fishery is far more uncertain. At the price levels used, only a single vessel could be economically supported, and then only in short pulses: two boats may be possible if they could share the available catches and substantially reduce their costs in some way. The fishery should thus be licensed, as much for the sake of industry as for conservation and almost certainly not more than two licences should be issued, for any one season. Assuming that the stock is safeguarded by its own wide distribution and low abundance, future requests for licences could be issued when applied for without undue concern. The likely profit margins have been calculated so that suitable licence fees could be simply estimated depending on acceptable licensing criteria agreed between management and industry. Both the profits and the supportable licence fee should be greatest for the very first pulse. The profits to any future pulses are not likely to be large and licence fees probably should not exceed around £30,000 for each future season. Both the catches and the effort should obviously be monitored in the future to update both this assessment and the licensing criteria.

This thesis has thus shown the Falkland Islands inshore crab stock to be of far less commercial interest than previously supposed. Simple guidelines have been given for the efficient management of any future fishery which should be acceptable to the fishing industry. The greatest restriction to such development lies with the small and very infrequent profits to be gained from this stock. Quite simply, the individual crabs in the Falkland Islands are too small, the stock as a whole is too small and the locality is both too undeveloped and too far from its potential markets.

281 6.2. Management o f the fishery

This overall conclusion will no doubt be disappointing both for the fishing industry and for the population of the Falkland Islands. On a more positive note, the real contribution of this thesis lies with the many smaller conclusions which have been drawn on the life history and biology of P. granulosa. The most important discoveries concern the intermoult periods of this species and the spatial organisation of its moulting and mating cycles. In the first case, the biennial moulting of most adult crabs and the unusually long incubation period within this stock suggest that the Falkland Islands are a sub-optimal environment for P. granulosa and have interesting implications on both growth and mortality rates. Secondly, with non-moulting males mating with females in a central, deep­ water location while recently moulted males migrate on to shallower feeding grounds, the migratory behaviour of P. granulosa is very uncharacteristic of the lithodid group. Further useful discoveries include the timing of the moulting and mating cycles, the precise sizes at male and female maturity and the effects of the parasite B. callosus on this host. Considered together, these results will make a significant contribution to the understanding of both P. granulosa and the lithodid crabs in general.

282 Appendices

283 A l. Linear equation for numbers at length

Al. Derivation of a simple linear equation for steady-state numbers at length and its potential use for the simultaneous estimation of Z/K and

Al.l. Estimation of Z from ape-based data

For a year-class or cohort of animals with a constant instantaneous rate of total mortality Z, the stock size at time t may be predicted from the equation for exponential decline in numbers

N, = N0 o z ‘ (1)

where N t and N q are the numbers of animals alive at times t and 0 respectively (Beverton & Holt, 1957). Taking natural logarithms, the relation is seen to have a linear form

InN, = InN0 -Zt (2) from which Z can be estimated by plotting or regressing log Nt against t. In practice, it is not necessary to follow the decline of a single cohort, year after year. The procedure may easily be approximated by sampling the numbers of all the cohorts comprising the stock at just one point in time. Under conditions of reasonably constant recruitment, the relative numbers of the different age classes in such a sample will be proportional to the relative numbers of the single cohort after each succeeding year of mortality.

A1.2. Estimation of Z/K from length-based data

However, for animals which are not readily aged, these ’catch curve’ methods for the estimation of mortality need to be modified to use data on length rather than time. Such ’length-converted catch curves’ have been developed in a

284 ♦ A h Linear equation for numbers at length

variety of ways (Jones, 1984; Pauly, 1984), as functions of the underlying growth and mortality rates within the stock. When used to estimate mortality, all such methods imply some previously obtained knowledge of the growth parameters.

In the present case, it is assumed that these growth parameters are not available prior to the analysis. A simple formula has been developed from equation (1) which explicitly gives the relative numbers at length, rather than time: exactly the data which are collected as the size composition of the catch. In a linear form the relationship enables the estimation of the ratio of the growth and mortality rates, Z/K and of the asymptotic length, L^. Like other similar methods, it assumes that the growth and mortality parameters, in addition to recruitment, remain reasonably constant over the period in consideration.

To enable length data to be used, the derivation begins by recasting the N^_ of equation (1) as N^, the number of animals alive at a length 1, equivalent to time t. This is achieved by the relationship

N = Nx dl/dt (3)

where dl/dt is the rate of change of length with time (ie. the growth

rate) evaluated at time t. It may appear surprising that N and are not equal. In explanation, note that the number of animals between the ages t and t+1 is exactly equal to the number between the equivalent lengths 1 and 1 Such numbers may be seen as the areas (or

integrals) under the two curves representing N and N^; the numbers of animals against time and length respectively. Then, if, 1 ^ exceeds 1 by, say 5 units of length, for the two areas to remain

equal, the curve must be only a fifth of the height of the N curve. Equation (3) thus represents the instantaneous relationship

between and and reflects the fact that animals grow through age classes and length classes at different rates.

Now, growth in length is modelled by the von Bertalanffy growth function whereby animals grow asymptotically towards a theoretical maximum length L^

285 Al. Linear equation for numbers at length at a rate K. The relationship between length, / and time, t is given by

/ = Z-oo (1 - e-*(' - 'o)) (4)

where t0 is the age at which the animal would have had zero length if it had been growing according to the same pattern for all of its life (von Bertalanffy, 1938). The growth rate, dl/dt is obtained by differentiating equation (4) which gives

dl/dt = K (5).

Combining equations (1), (3) and (5) we obtain the following expression for as a function of time:

Nj = N0 eZt

K Lm e K)

= N 0 - z)r (6).

K L ^ e P o

Now, the von Bertalanffy growth function in equation (4) can be rearranged to give the time, t at which the animal reaches length, l as

t = In( L n / / K + t0 (7).

Finally, it is possible to replace the time, t in equation (6) with the expression for t, composed only of length and the growth parameters, given above in equation (7). The numbers in the stock N[ at length / are thus expressed without reference to either time or age as:

286 # Al. Linear equation for numbers at length

— N q g (K - Z) {r0 + ln(L0 / (L a - [)) / K}

K L m

= N q e " ^ o - Z/K) ln(Loj / (La> - /)) (gjt

K L ^

Like equation (1), this explicit equation giving the steady-state numbers at length also has a linear form, again obtained by taking logarithms:

InNt = ln(Af0 / KLX) - Zt„ + (1 - Z/K) \n(Lm I (Lm - 1)) (9).

The above formula does not enable the estimation of Z given by the age-based version in equation (2). However, given a previously obtained estimate of Lw, it does permit the estimation of Z/K from the regression of InAfy on the length- based variable / (L^ - /)). The remaining two terms of equation (9) sum to give the intercept of the regression line. Note that the slope of the regression line may be either positive or negative depending on the value of Z/K. In order to obtain a correct estimate of Z/K, the actual value of the slope (including its sign) should be equated with the quantity (1 - Z/K).

In practice, if real length frequency data are used with equation (9), the relationship becomes approximate. Such data always take the form of the number of animals in defined length classes (say between lengths / and /+1), and not at single specific lengths (such as Nj). However, with small length intervals, the error caused by using equation (9) in its instantaneous form, with such integrated data is less than 1% and can be neglected.

287 Al. Linear equation for numbers at length

A1.3. Simultaneous estimation of and Z/K

Several other length-based methods are available to estimate the parameter Z/K, most of which also rely on a previously obtained estimate of L^. Such methods include the analogous length-converted catch curves (Jones, 1984; Pauly, 1984), similar methods based on cumulative catches (Jones, 1981; Sparre, MS (cited in Pauly, 1984)) and the original technique of Beverton & Holt (1956) based on the mean size of animals in the catch above a certain length.

However, it is useful to note that the linearity of both equation (9) and the other linear models noted above is, in fact, conditional on the use of the true value of ^ in various formulae. Thus, when L*, is not previously known, this property can be utilised to allow for the simultaneous estimation of both Z/K and Lqo as follows.

In the case of equation (9), when an incorrect value of L^ is used in the formulation of ln(Loo / (Lqq - /)), the model is not linear but curved. When L^, is underestimated, equation (9) takes on a convex form; with overestimation, it becomes increasingly concave. L00 itself may therefore be estimated as the value which gives the most linear pattern to the data, Z/K being subsequently obtained as the slope of this optimum model. Similar approaches have been suggested by Pauly (1984) and Sanders (1987) for the estimation of L*, from age-based data.

Various criteria could be used for such a ’maximisation of linearity’. Maximising the R2 of the model (Pauly, 1984) or minimising the residual sum of squares around the line are obvious possibilities. Alternatively, a quadratic equation could be fitted to the data: an exact solution would then be possible as that value of Lqq giving zero as the coefficient of the squared term. In practice whatever method is used, it should be weighted to account for the fact that the variance around the dependent variable Inincreases as numbers at length are reduced towards zero. This happens as a result of the logarithmic transformation of the variable as will now be shown.

28 8 Al. Linear equation for numbers at length

When statistical data consist of integers, such as the number of occurrences of a certain situation, the variability of such data often follows a Poisson distribution (Feller, 1968). In this distribution, the variance of the data is exactly equal to their mean (Bartlett, 1947). In the present case, the numbers of animals recorded at each length, N[ may be expected to follow Poisson distributions. Thus, for any total sample size, the expected frequencies (or means) in each size class are determined from the true underlying ’shape’ of the length frequency. This expected pattern is due to the relative abundance and selection characteristics of each size of animal in the population. When sampling, the true shape is approximated, with the obtained value of each frequency being distributed as a Poisson variable, and the variances of relatively common length classes being proportionately greater than those of rare ones.

Examination of some fairly typical length frequencies (see for example those in figures 1 & 2, section 3.2.2.) show that the random fluctuations in numbers from one length to the next are far greater for the abundant sizes classes in the middle of the distributions than they are for the rarer sizes at the edges. Note that as the variance is equal to the mean, the standard deviation is equal to the square root of the mean and the coefficient of variation decreases with increasing sample size. This is the reason why length frequency data become smoother for larger samples.

Now, let N represent a random variable (such as the sampled frequency of length /) with mean N and variance V(N). If N is distributed as a Poisson variable

V(N) = N.

In equation (9), such a variable is log-transformed. This process may be viewed as taking the function g(N) of the variable where g(N) = InN. The variance of such a function may be closely approximated by the Delta method whereby:

2 89 Al. Linear equation for numbers at length

V(g(H)) « 0m ) Z V(N).

Since the derivative of In N is 1/N,

v{g(N)) = V(lnN) ~ 1/N.

Thus, in this case, the variance of liiiV is approximately equal to 1/N, becoming larger, not for the commonly occurring size classes, but as N approaches zero.

For the present application, this means that the relatively uncommon sizes usually found at the upper end of the length distribution have a large variance, and hence an inflated contribution to any goodness-of-fit criteria for the model. To balance this tendency, the regression should be made using the method of weighted least squares with the weights set equal to the mean number N (ie the inverse of the relative variance) at each length. In fact, these weights are not known absolutely. However, given a reasonable sample size the raw data could be used as the weights for a first attempt at maximising the linearity of the model. Then, the predicted values of N, taken from the best fitting line could be entered as more accurate weights and the parameters of the model re-estimated (van Houwelingen, 1988).

A1.4. Discussion

It is emphasized that this technique, and the others mentioned, are only suitable for use with length frequency data which include several different cohorts of animals. This implies stocks with relatively slow growth rates and smooth size compositions. Those fast growing species showing discernible modes in length frequency data are not likely to give reliable results with these methods.

When applying the above technique, only the points in the linear portion of the

290 » A l. Linear equation for numbers at length

catch curve should be used in the estimation procedure. Such points represent lengths at which the animals are fully selected and retained by the gear used for sampling.

Even with suitable species and good data, the interpretation of the curve may

sometimes be difficult. When Z / K > 1, as would be expected in most cases,

equation (9) should result in a smooth and declining curve. However, when Z/K < 1, the animals grow faster than they die and accumulate in the larger size classes, resulting in a positive slope in equation (9). With variation in between individuals, as may be expected in nature, the curve may increase initially for the above reason, and decrease eventually as the largest animals finally die off (Powell, 1979). Fitting equation (9) to the declining portion of

such a curve would result in a completely incorrect estimate of Z/K. Data with such patterns must be treated with caution, particularly when the recruitment and selection ogives of the stock are poorly understood.

One further problem with the use of equation (9) may be mentioned. The method assumes that the data are taken from a stable population, such that the

values of Z, K and so on have been constant, at least for the age classes presently comprising the stock. When there have been trends in one or more of these parameters, it is possible that the non-linearity of the model resulting from such trends may be mistaken for non-linearity caused by the use of an incorrect

value of Lqq.

All such methods for estimating these parameters from length frequency data undoubtedly share similar problems. Little is known on the relative reliability of

the various methods when used on ’difficult’ data (Majkowski e t a l, 1987;

Wetherall e t a l, 1987). The method most commonly used at the present time is

probably that due to Wetherall (1986; see also Pauly, 1986; Wetherall e t a l, 1987) as implemented in the ELEFAN suite of programs (Morgan & Pauly, 1987). In this method, the successive mean lengths of animals from a length frequency sample are plotted against the cutoff lengths used in their

291 A l. Linear equation for numbers at length computation. As with the related cumulative methods, this technique is also likely to be "extremely sensitive to the values of the catches in the largest size groups" (Pauly, 1984). In addition, the use of mean values instead of the raw data must result in serial correlation within the dependent variable, thereby invalidating the basic regression assumptions.

The procedure detailed here, and tentatively recommended for use, no doubt also has its pros and cons. It, at least, avoids the serial correlation of the Wetherall method by using only the individual numbers at length in the independent variable. The comparative performance of these and other methods for estimating L <*> and Z/fiT, when used on realistic data, remains to be investigated.

292 A2. Pulse fishing model

A2. An age structured model for the prediction of future yields under variable fishing effort

This model is used in section 5. to investigate the potential yields from the inshore crab stocks of Lafonia, under variable levels of fishing effort, particularly in the form of ’pulses’ of activity. The method takes account of the whole history of exploitation, starting from a virgin stock, and does not assume the fishery to be in a state of equilibrium. Growth and mortality are modelled in the same way as used to estimate the continuously sustainable, equilibrium yields of section 5.2.3. and the results of the two models are fully comparable.

A2.1. Basic structure of the model

The model takes the basic form of a two dimensional matrix of the biomasses of crabs of each age a, at the start of each year, t, as illustrated in figure 1. As in the equilibrium model of section 5.2.3., the biomasses at the start of each year are used (rather than the yearly means), as the Leslie estimate of the starting biomass is, itself, in an instantaneous form. Only those age classes over the age at first capture, a c, are included and the total biomass in each year is given as the sum of all such ages. A simple equation then gives the yield from this total biomass, depending on the amount of fishing effort applied during the year.

The total biomass in the first year, B t = 0 , is assumed to be the average size of the stock under no previous exploitation, as calculated in section 5.2.1.. The biomasses of the individual age classes in this year are estimated by decomposing the total weight according to a simple model for the biomass at age of a theoretical cohort, depending on K and M. As the reproductive capacity of the stock is unlikely to be affected by the fishery, the predicted biomass of the youngest age class, as it was in the first year, prior to exploitation, is used as the estimate of annual recruitment in all future years. The biomasses of the

293 A2. Pulse fishing model remaining age classes are finally calculated following the direction of the diagonal arrows in figure 1. Each cohort is thus followed individually from its recruitment or its size at time zero and any pattern of fishing mortality can be modelled, as the structure of the stock is always known exactly.

The main difference between this method and that of section 5.2.3. lies in the assumption of stability. In the simpler equilibrium model, F is assumed to have been constant in all previous years allowing the yields and biomasses to be modelled with single integrated equations. In the age structured model of this appendix, F is allowed to vary between years (although assumed equal in all ages), causing continuous change in the composition of the stock. In consequence, the biomass must be estimated separately in every year by the summation of each age class present.

294 A2. Pulse fishing model

Fishing mortality daring year t

T

Time, t (years) t=0

a=a

\4 \4 V Age, a Biomasses of crabs of age, a, (years) at start of year, t

1

a=a max

Sum of biomasses at start of year t,

Yield during year t. Y t

Figure 1. An illustration of the matrix format of the age- structured model for prediction of future yields under variable fishing mortality.

295 A2. Pulse fishing model A2.2. Decomposition of starting biomass into contribution of each age class

The initial biomasses in the first column of the time by age matrix (figure 1) are filled by splitting up the total biomass estimate according to specified patterns of growth and mortality. First of all, however, the age at first capture, a c, must be determined as follows. As noted in section 5.2.3., only the s iz e at first capture is known for P. granulosa. Expressing this size as a fraction of the asymptotic length La, results in the parameter c which is close to 0.7 for all lithodids (section 4.3.3.). Now, by rearranging the von Bertalanffy equation for growth in length, the age at first capture, equivalent to length c, may be found by:

- In (1 - c) ac = ------K

(Beverton & Holt, 1964). Thus, although it is always the upper 30% of the size range which is exploited, the actual age at first capture is variable and depends on the value of K used in the model.

For this age, ac, and all greater ages up to the maximum a m ax (at which the stock size becomes negligibly small), the virgin biomasses at time t = 0 are estimated from the following, commonly used models (eg. Beddington & Cooke, 1983). Assuming only natural mortality, M, prior to the fishery and at a constant level at all ages, the numbers in a theoretical cohort at age a are given by:

Na = R e Ma

where R is the number of recruits at age zero.

Further assuming that growth follows an isometric von Bertalanffy format with zero weight at zero age, the weight at age a is:

wa = Wx (l- e - ^ ) 3

296 A2. Pulse fishing model

where is the asymptotic weight equivalent to L ^.

Therefore, the biomass at age a is the product:

Ba = R Wm erMa ( l - e Ka' f (I).

Under these patterns of mortality and growth and under constant recruitment, the total recruited biomass of a stock containing all age classes over age a c, at the beginning of any year, may be calculated as:

00 3 n n e r n K a c

2 B, R erMac S ------(2 ) a—af n = 0 1 - G< M + nK) where n is the summation constant of Beverton & Holt (1957) which assumes the values n0 = +1,^1 = -3, n2 = +3 and n3 = -1.

Equations (1) and (2) give the biomass at age and the total biomass of the recruited stock for a theoretical population with arbitrary levels of R and W^. Thus, by using the ratio of these equations and the real, recruited biomass at time zero, Bt=G, the initial biomasses of all age classes over age ac can be estimated. The first column of the matrix is thus obtained by:

B , Ba,t =0 Bt t_=0 oo 2 B, a=ar

It may be noted that, as (1 - c) = e"^c, the age-based equation (2) is exactly equivalent to the length-based equation used for the unexploited, recruited biomass, B0 in section 5.2.3.

297 « A2. Pulse fishing model

A2.3. Estimation of recruitment

As the mean size at male maturity of P. granulosa is considerably less than the processable size and because the females are not exploited, the reproductive potential of this stock is unlikely to be greatly affected by exploitation. Therefore, assuming that the presently observed stock is close to its mean long­ term abundance, it may be expected that the annual recruitment would continue at an average level given by the biomass Ba=a^ =0 in the top, left corner of the matrix (figure 1). The annual recruitment (the top row of the matrix) is thus assumed to be equal in all years. The magnitude of this recruitment is dependent on the levels of K and M. At least for the higher levels of M, the recruitment is actually the same as the potential yields given in section 5.2.3. (tables 2 and 3). This is because the maximum yields, in this case, are obtained at F = oo, by catching the whole years recruitment as it enters the fishery.

A2.4. Estimation of future biomasses conditional on fishing mortality

The left column and the top row of the matrix are now specified. The remaining cells in the matrix depend on the variable level of fishing mortality, Ft in each year. With the same assumptions as before about growth and natural mortality, the future biomasses at age are calculated by the expression:

d _ p fzGfl-M-Ft Ba+U+1 ~ Ba,t e

where the growth rate, Ga is simply modelled as the log difference of weight at age (Mohn, 1986):

G a = ln K + l / w a) ■

298 A2. Pulse fishing model

A2.5. Use of fishing effort data

For modelling the economics of a fishery, it is more useful if the fishing mortality can be expressed in terms of the amount of effort applied as only the effort can be assigned a cost. The relationship between fishing mortality and fishing effort, f t may be defined as:

F t = «/<•

The catchability coefficient, q represents the proportion of the stock taken by a single, standardised unit of gear (in the present case, a single pot corrected to a soaktime of one day). This parameter has been estimated (conditional on M) in section 2.4. by the Leslie method for the stock of crabs in Choiseul Sound. The yield estimations of section 5., however, are made for the whole stock of the much larger area of Lafonia. A single pot fished in Lafonia, for the same catch rate, obviously takes a much smaller proportion of this larger stock. Assuming that the density of crabs is equal in all areas, the catchability coefficient for Lafonia is thus related to that of Choiseul Sound simply by the ratio of their areas (section 5.2.1.):

^Lafonia = #Ch. Sound ^ reaCh. Sound *

Lafonia

c In applying the model, the effort, f t in year t, is therfore specified as the corrected number of pots, spread over the whole Lafonia grounds and the fishing mortality rate for the year is calculated as:

“ ^Lafonia ft *

299 * A 1 Pulse fishing model

A2.6. Summation of biomasses and estimation of annual yields

As indicated in figure 1, the final steps of the procedure are the summation of the yearly biomass over all age classes and the prediction of the annual yield. The yield is simply obtained by the catch equation:

Y t = FA

where Bt is the mean total biomass during the year. As noted in section 5.2.3., for these annually moulting crustaceans, there is no growth of individual crabs during the whole fishing season: the only change in the weight of the cohort in this time is due to the exponential decline in numbers, which is assumed to be equal in all ages. The average biomass over the year may therefore be simply obtained by summing all the starting weights and then applying an overall correction giving the mean value of an exponential function:

( 1 - e) B, = ------S B ait. Ft + M a=ac

If growth does occur during the year, as in most species, estimation of Bt is somewhat more complicated as the correction producing the mean weight from the initial weight varies with age. In such a situation, both the corrections for growth and mortality must be made before the summation of the age classes.

300 References *

References

Austin, C.B., 1977. Incorporating soak time into measurement of fishing effort in trap fisheries. Fish. Bull. U.S. 75: 213-218

Bailey, R.F.J. & R.W. Elner, 1989. Northwest Atlantic Snow Crab Fisheries: Lessons in Research and Management, pp. 261-280 In Caddy, J.F. [ed.] Marine Invertebrate Fisheries: their Assessment and Management. John Wiley & Sons.

Bain, L.J. & M. Engelhardt, 1989. Introduction to Probability and Mathematical Statistics. PWS Kent Publ. Co. 565pp.

Bannister, R.C.A., 1986. Assessment and population dynamics of commercially exploited shellfish in England and Wales, pp. 182-194 In G. Jamieson & N. Bourne [ed.] North Pacific Workshop on stock assessment and management of invertebrates. Can. Spec. Publ. Fish. Aquat. Sci. 92.

Bartlett, M.S., 1947. The use of transformations. Biometrics 3: 39-52

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312 Reprinted from: CRUSTACEANA 5 9 , 2

' I 6 8 "i

LEIDEN E.J. BRILL 19 9 0 Crustaceana 59 (2) 1990, E. J. Brill, Leiden

THE EFFECTS OF PARASITISM BY THE RHIZOCEPHALAN, BRIAROSACCUS CALLOSUS BOSCHMA ON THE LITHODID CRAB, PARALOMIS GRANULOSA (JACQUINOT) IN THE FALKLAND ISLANDS

BY

DANIEL D. HOGGARTH Renewable Resources Assessment Group, Imperial College, University of London, 8 Princes Gardens, London SW7 1NA, U.K.

RESUME Le Rhizocephale parasite Briarosaccus callosus a ete observe, infestant un stock du Lithodidae Paralomisgranulosa provenant des lies Falkland avec une frequence inferieure a 1 %. L’infestation a ete decelee exterieurement par la presence du sac reproductif ou “externa” du parasite. Des crabes marques d’une cicatrice ont aussi ete trouves, chez lesquels l’externa aurait ete perdu apres la mort presumee naturelle du parasite. Les crabes avec externae sont plus frequents, et de fagon significative, lorsqu’ils sont de petite taille, particulierement parmi les males. Cepen- dant, la frequence des crabes cicatrises augmente avec la taille de l’hote chez les femelles, tandis que Ton n’observe pas une tendance concordante chez les males. II est possible que ces particu- larites resultent de l’effet du parasite sur le taux de croissance de l’hote. Des crabes des deux sexes, avec des externae ou des cicatrices, ont ete trouves alors qu’ils avaient recemment mues. B. callosus n’empeche done pas completement la mue chez P. granulosa. La castration d’hotes des deux sexes par le parasite a ete observee aussi bien pendant qu’apres la periode d’infestation. Toutes les femelles parasitees, avec des exernae ou des cicatrices, sont non-ovigeres. Les males infestes n’atteignent pas la maturite morphologique denotee par la taille relative des pinces. A une taille donnee, les males qui portent des externae ont des pinces plus petites que meme les males juveniles. Au vu de la feminisation parasitaire sou vent observee chez d’autres hotes de Rhizocephales, il est probable que les dimensions relatives des pinces des males parasites sont les memes que chez les femelles indemnes. Les males a cicatrices, apres la perte du parasite, retrouvent les dimensions relatives des pinces des males juveniles, meme aux tailles ou ils seraient normalement a maturite.

INTRODUCTION During a stock assessment of the presently unexploited Falkland Island false king crab, Paralomis granulosa (Jacquinot, 1852), a number of captured specimens were found to be parasitized by the rhizocephalan, Briarosaccus callosus. Low prevalence levels are apparent in the Falkland Islands and the relationship is thought to be of little concern in this locality, as is the case for the same species in nearby Chile (Campodonico et ah, 1983). In the north Pacific, however, B. callosus is a locally prevalent parasite of the commercially important red, blue and golden king crab stocks (Kurochkin, 1972; Sloan, 1985; Hawkes, Meyers, Shirley & Koeneman, 1986). As a result, much recent BRIAROSACCUS AND PARALOMIS 157 work has concentrated on the effect of B. callosus on its various hosts in this area. It may therefore be of use to report the effect of parasitism of Falkland Island P. granulosa primarily as a contribution to the biological knowledge of B. callosus.

A GENERAL LIFE HISTORY OF THE RHIZOCEPHALA The Rhizocephala are the most important of the three orders of naked bar­ nacles, parasitic primarily on decapod crustaceans (Barnes, 1980). As adults they have neither mouth, gut nor segmented appendages. Parasitisation begins with the attachment of a female cyprid larva to the base of a hair on a vulnerable host (O’Brien & Van Wyk, 1984). The larva injects a mass of em­ bryonic cells which grow along the intestine, spreading out via connective tissue (Sparks & Morado, 1986) into a network of rootlets that penetrate many major organs and absorb nutrients directly from the host’s hepatopancreas and other tissues. This stage is known as the interna. Sexual development involves the eruption of an ‘externa’, usually through the soft tissue lining the abdomen, to lie in the position normally occupied by the egg mass of the host (Hartnoll, 1967; O ’Brien & Van Wyk, 1984). The externa remains small until the subsequent injection of primordial sperm cells from a male cyprid larva, which are stored within the externa, making the female into a hermaphrodite (Barnes, 1980). Clutches of eggs hatch within the externa and are later extruded, usually at the nauplius stage, by muscular con­ tractions of the mantle wall (Bower & Sloan, 1985). Considering the wide variety of lifestyles adopted by the various decapods, it is not surprising that there is much variation in the effect of individual rhizocephalan parasites on their hosts. In general, however, these animals affect not only the growth but, more importantly to stock management, the reproductive capability of the host (Hartnoll, 1967; O ’Brien & Van Wyk, 1984; Rubiliani, 1983).

CURRENT KNOWLEDGE OF THE BIOLOGY OF B. CALLOSUS

Briarosaccus callosus is a large peltogastrid rhizocephalan. It was first reported from a museum specimen found parasitising a Neolithodes agassizii (Smith, 1882) caught off the Atlantic coast of the U.S.A. (Boschma, 1930). It has since been reported worldwide from all the large, commercially important, lithodid crabs.

Prevalence Prevalence is used in the sense of Margolis et al. (1982) to mean the percen­ tage of the total number of crabs examined which were parasitised. Overall prevalences of B. callosus within host populations are highly variable both 158 DANIEL D. HOGGARTH between host species and between separate substocks of the same species. In the north Pacific, prevalence in the red king crab, Paralithodes camtschatica (Tilesius, 1815), is rarely above 1-2% irrespective of locality (Boschma & Haynes, 1969; Sloan, 1984, 1985; Hawkes, Meyers, Shirley & Koeneman, 1986; Sparks & Morado, 1986). Populations of Lithodes couesi Benedict, 1895, resident on deep seamounts also have been reported with prevalences of less than 1% (Somerton, 1981). The blue king crab, Paralithodes platypus (Brandt, 1850), is unparasitised by B. callosus over certain large areas of open sea in the north Pacific (Sparks & Morado, 1986). A stock inhabiting an Alaskan fjord system, however, has been recorded with a parasite prevalence of 76% (Hawkes et al., 1985; Hawkes, Meyers, Shirley & Koeneman, 1986). Lithodes aequispina Benedict, 1895, the golden king crab, suffers moderately high levels of infection in both Alaskan (20%, Hawkes, Meyers, Shirley & Koeneman, 1986) and Canadian fjord systems (40%, Sloan, 1984). A prevalence of 17 % has also been reported for the western Gulf of Alaska/ Bering Sea, by Sparks & Morado (1986) who note that this figure may be an overestimate. In partial explanation of this species variability in prevalence levels, it has been suggested that fjord-dwelling blue king crabs may be less resistant to the parasite than either red or golden king crabs, due to their reduced haemolymph immune response (Shirley et al., 1986; Hawkes, Meyers, Shirley & Koeneman, 1986). Between locations, the highest prevalences are found in the most isolated arms of fjords. In such environments, both host and parasite larvae are released simultaneously at great depths in the oceanographically enclosed fjords leading to confinement of the stock and heavy self-infection (Sloan, 1984). High parasite prevalences have also been attributed to the tur­ bidity associated with glacial run-off in fjord systems (Hawkes, Meyers, Shirley & Koeneman, 1986). It has been proposed that the efficiency of clean­ ing mechanisms may be impeded in such water, thus favouring attachment of the parasite larva. In the clear, high-circulation waters of the open ocean, much lower infestation rates are found. Elsewhere in the world, Arnaud & Do-Chi (1977) found B. callosus parasitis­ ing 3% of a stock of Lithodes murrayi Henderson, 1888, in the Crozet Islands (SW Indian Ocean). In Chilean waters Campodonico et al. (1983) found infestation rates up to 2 % for localised stocks of Paralomis granulosa.

Pattern of mutual growth Bower & Sloan (1985) found that the majority of parasitised golden king crabs were in recently moulted condition, and that the size of the externa was related to the size of the host. No difference in externa size was detected between host moult stages. In the laboratory, blue, red and golden king crabs BRIAROSACCUS AND PARALOMIS 159 were all observed to moult while parasitised by B. callosus (cf. Hawkes et al., 1987). As with other peltogastrid-anomuran relationships (O’Brien & Van Wyk, 1984), B. callosus does not inhibit moulting of its host and both parasite and host grow together. While the parasite remains healthy, there is little immunological response by the host. Upon loss of the externa, however, the internal rootlets degenerate and the host reacts with the normal crustacean foreign body response (Sparks & Morado, 1986). Crabs are frequently reported with the scars of B. callosus infections, where the externa has been lost (Sloan, 1984). Limited attention, however, has been paid to the biology of such post- parasitised crabs, most authors classifying them simply as ‘parasitised’.

Growth rates Parasite prevalence has been found to decrease with increasing size for males of both blue and golden king crabs (Sloan, 1984; Hawkes, Meyers, Shirley & Koeneman, 1986). The naturally smaller females showed no such relationship. In golden king crabs, both parasitised males and females are similar in size to uninfected females (Bower & Sloan, 1985). Such results may be caused by many factors including behavioural effects leading to sampling bias and dif­ ferences in mortalities or growth rates associated with parasitism. Both blue and golden male king crabs, however, have a lower weight at length when infected (Hawkes et al., 1986). Hawkes et al., 1986, believed that this reduc­ tion in weight at length implied that growth rate of the host was specifically affected by the parasite. Hawkes et al., 1987, later found that parasitised blue king crabs maintained in the laboratory, ate significantly less food than the unparasitised controls. Infected males, consequently had a reduced growth rate expressed as moult increment, both in terms of length and weight. Growth increment of females did not differ significantly, neither did moult frequency for either sex. In terms of relative growth rates, parasitised golden king crab males have been found to have significantly smaller chelae than healthy crabs of similar sizes (Sloan, 1984).

Parasitic castration

Of the many mature sized females found parasitised by B. callosus, none have been found in ovigerous condition (Somerton, 1981; Sloan, 1985; Hawkes et al., 1985; Campodonico et al., 1983). There seems little doubt that this rhizocephalan is responsible for the castration of female lithodids. Histologically, the marked degeneration of the ovary has been shown to be independent of actual penetration of the organ by the rootlets of the interna (Sparks & Morado, 1986). 160 DANIEL D. HOGGARTH

The effect of B. callosus parasitism on male maturation is less clear. In red, blue and golden king crabs, the testes of infected specimens are atrophied or apparently absent in some cases (Hawkes et ah, 1985; Sparks & Morado, 1986). Such crabs, however, have also been shown to possess spermatophores with sperm of normal appearance (Sparks & Morado, 1986). It is possible that these findings are the result of gonad activity, prior to infection by B. callosus.

MATERIALS AND METHODS

Specimens of Paralomis granulosa were sampled from the catches of a single fishing vessel, employed by the Falkland Island Development Corporation, for the joint purposes of commercial exploitation and research. All catches were taken between September 1987 and December 1988, by potting from the waters of Choiseul Sound in the south-west of the Falkland Islands. A variety of pot types were used during the survey, including a limited number of fine- meshed pots, specifically intended for sampling the widest range of animals. In this analysis, only the data from the smallest meshed of the commercial pot types, and the special sampling pots has been utilised. In most cases the whole catch was sampled, including females and undersize crabs. The sex of each crab was determined from the shape of the abdomen. Carapace length (CL) was measured to the nearest m m below, from the eye socket to the central posterior margin of the carapace. Moult stages were divided into two classes: recently moulted crabs having bright, clean shells (including the small number of crabs captured, still soft after ecdysis) and intermoult animals with abraded shells and resident epifauna. Moult stage was not recorded for a small proportion of the males. Four stages of female maturity were recognisable macroscopically: 1) non-ovigerous, 2) carrying uneyed eggs, 3) carrying eyed eggs and 4) with empty egg cases attached to the pleopods. All parasitised females, including scarred crabs, were non- ovigerous. The relative size of the chelae may often be used as an indicator of sexual maturity in male crabs, mature specimens having large claws as an adaptation for courtship and mating behaviour. Maximum length of the major chela was thus measured to the nearest m m below to examine the effect of parasitism on the relative growth and maturation of male P. granulosa. A subsample of nor­ mal males were measured in this regard, in addition to all parasitised males. Finally, infestation by B. callosus was recorded by the presence of an externa, and crabs with the scars of past parasite infections were noted as such. A very small number of crabs were found with double infections (i.e. two externae). Such occurrences were not recorded, however, beyond the usual note of parasite presence. Parasites at the interna stage of development only, were not detected, and prevalences are underestimated, as they are in all studies in the absence of internal examination. BRIAROSACCUS AND PARALOMIS 161

RESULTS

The effect of parasitisation on the growth of male and female crabs

The size distributions of the crabs sampled have been subdivided by sex, moult stage and infection status and aggregated by 5 m m classes of carapace length (table I). It should be noted that crabs have been captured in recently moulted condition at all combinations of sex and infection status. B. callosus, therefore, does not entirely prevent moulting in P. granulosa. Although parasite lengths were not measured, a gross correlation between the size of each parasite and that of its host was observed. The smallest crab carrying an externa was a recently moulted male of 30 m m CL. For infected and uninfected crabs of both sexes, intermoult crabs were larger, on average, than recently moulted crabs (table I). This observation is consistent with the usual assumption of decreasing moult frequency with increasing size in Crustacea. Parasitism, it may be concluded, does not greatly affect moulting in this relationship. Ignoring the effect of moulting, it was possible to increase the data set to include the extra male crabs measured for all characters except moult stage (table II). In fig. 1(a), the underlying sample distributions are plotted, along

T a b l e I Carapace length distributions by sex, moult stage and infection status (absence (N), presence (Y) of parasite externa(e) and presence of post-infection scarring (S)). The lengths given are the lower boundaries of each 5 m m class

Sex Female M ale Moult stage Recent Intermoult R ecent Intermoult Infection N Y S N Y S N Y S N Y S

Length 20 2 1 Class 25 11 3 5 (m m ): 30 62 7 43 4 6 35 130 3 22 126 7 28 40 202 62 2 240 3 59 2 45 247 1 548 1 343 1 2 168 1 50 409 3 4580 3 2 970 4 792 4 55 188 2 1 4990 8 3 1190 5 1248 5 1 60 44 1347 3 8 1284 2 1 1841 9 1 65 8 148 3 1272 2 2 2745 3 3 70 16 1072 1 2 2120 2 1 75 1 583 1 1 967 1 80 247 333 2 85 81 119 90 10 36 95 3 6 'total 1302 9 1 11725 17 16 7470 30 8 10468 26 10 162 DANIEL D. HOGGARTH

T a b l e II Carapace length distributions by sex and infection status (absence (N), presence (Y) of parasite externa(e) and presence of post-infection scarring (S)). The lengths given are the lower boundaries of each 5 m m class

Sex Female M ale Infection N Y S N Y S

Length class (mm) 20 2 1 25 14 5 30 69 49 4 35 152 3 154 7 40 264 2 301 5 45 795 2 537 2 2 50 4989 6 2 2019 10 2 55 5178 10 4 2807 10 1 60 1391 3 8 3587 14 2 65 156 3 4419 5 5 70 16 3462 3 4 75 1 1634 1 3 80 600 2 85 206 90 46 95 9 Total 13027 26 17 19836 61 21

with the prevalence per size interval, of (b) crabs with externa(e), and (c) scar­ red crabs. The null hypotheses that presence of externae and scarring are independent of size have been tested by the chi-square method. In each test, classes on the edges of the distributions with small sample sizes have been aggregated until the expected frequency in each cell exceeds unity (Snedecor & Cochran, 1980). For both sexes, crabs with externae are more prevalent at smaller sizes (for males: X27df= 148.86, P <0.00005; for females: X24df= 17.54, P = 0.0015). The decrease in prevalence is more pronounced for male than for female crabs. Prevalence of scarred females, however, increases with host size {X22df = 44.86, P < 0.00005) while scarred males show no consistent trend (x26df= 5.04, P = 0.539). Such size prevalence data have previously been used as an indication of the effect of the parasite on the growth of the host (see O ’Brien & Van Wyk, 1984, for a review). Trends in the pattern of prevalence by size can, however, be caused by several factors, each of which must be considered in turn. In the parasitism of Lithodes aequispina, the size of B. callosus externae have been found to increase with the size of the host (Bower & Sloan, 1985). Although parasite lengths were not measured in the present study, a similar broad correlation has been observed between the relative sizes of host and parasite. Small externae were not seen on large crabs. It is therefore assumed BRIAROSACCUS AND PARALOMIS 163

u G ^3cn CD CO PS Pcn CD &o Pm

CD O g QJ _ to E c 1 1 Males a>> p-i Fenales z

...... -1 n n n .— .— ^ 20 40 60 80 100 Carapace Length (mm)

Fig. 1. (a) The size compositions of sampled male and female crabs in 5 mm classes of carapace length (scale in thousands); and the prevalence (%) of crabs with externae (b), and scars (c). that P. granulosa, like L. aequispina, is infected with the parasite early in life. If parasitisation had no effect at all on the biology of the crab, such an infection pattern would lead to a constant prevalence of the parasite at sizes over and above the size at First infection. The clearly observed decreasing prevalent of infected crabs in both sexs (fig. lb) suggests that B. callosus does have some effect on the biology of its host. The observed patterns may be due to: 1) the loss of infected crabs into the scarred class on loss of the externa, or 2) increased mortality, 3) decreased catchability or 4) decreased growth rate, of infected crabs relatively to the healthy population. The first effect must be at least partly responsible for the observed trends in prevalence. It can not, however, be the full explanation, as the combined prevalence of crabs with either externae or scars would then be constant with host size, which clearly is not the case. There is little evidence on the relative likelihood of any of the three remaining possibilities. The limited laboratory studies of Hawkes et al. (1987) indicated no additional parasite-induced mor­ tality during intermoult but recommended further studies on the effect of 164 DANIEL D. HOGGARTH

parasitism on mortality during ecdysis. Considering the large numbers of crabs with scars, some in recently moulted condition (table I), it is evident that P. granulosa is at least capable of outliving its parasite. Little else, however, can be concluded from the present data set. Host mortality may not be greatly affected in this relationship, yet a small parasite-induced increase in mortality rate remains equally possible. O n the third factor, rhizocephalans have been reported to cause lethargy in their hosts (Shirley et al., 1986) which may result in under-representation of parasitised crabs. Although lethargy has not been reported in P. granulosa to date, it must remain a possible cause of the observed patterns. Finally, the energetic cost of supporting a parasite may be responsi­ ble for reductions to the growth rate of the host (O’Brien & Van Wyk, 1984; Hawkes et al., 1986, 1987; Hawkes, Meyers, Shirley & Koeneman, 1986). This is perhaps the most likely explanation of the patterns seen in fig. lb, but it would be incorrect to draw any more positive conclusions from these data. Similar arguments apply to the interpretation of the prevalence patterns seen for scarred crabs (fig. lc). Again there is no real evidence either way for changes in mortality or catchability, resulting from parasitisation. The data therefore suggest that females have an increased post-infection growth rate, while the growth of males, after the loss of the parasite reverts to the normal male pattern.

The effect of parasitism on the relative growth of male crabs In male crabs, and other crustaceans, the sizes of the chelae or claws change in relation to the overall size of the body at maturity. On a plot of the relative size of these two variables, the point of inflection, indicating an increase in the relative growth of this secondary sexual characteristic, has long been used as an estimate of the size at maturity of male crabs (see e.g. Hartnoll, 1963; Somerton, 1980; Somerton & Macintosh, 1983). The pattern of maturation in infected male crabs, has therefore been examined by comparing the relative growth of the chelae between healthy and parasitised individuals. The raw data? on the growth of the chelae relative to carapace length, for unparasitised and parasitised male crabs have been plotted on logarithmic scales (fig. 2). Such a transformation produces a linear fit to the data over sizes at which growth of the variable follows a constant allometric relationship (Hartnoll, 1982). The size at male maturity of P. granulosa has been estimated as 52 m m from the data for unparasitised crabs only (fig. 2a), by the technique of Somerton & Macintosh (1983). The method chooses the point on the abscissa (log 52 m m = 3.95) which minimises the total residual variance around two regression lines fitted to the data, above and below the selected point of inflection. The data for parasitised crabs, however, show only single linear trends (fig. 2b & 2c). Regression equations have been fitted to the log transformed data for ‘adults’ (carapace length greater than or equal to 52 BRIAROSACCUS AND PARALOMIS 165

Log Carapace Length Cam)

Fig. 2. Relative growth of male chelae length against carapace length, plotted as log transformed variables for crabs without (a) and with externae of B. callosus (b), and with the scar of a previous infection (c).

T able III Equations fitted to the chelae allometry data illustrated in fig. 2, for healthy and parasitised crabs

Crab type Intercept Slope n Residual MS Adult -2.4471 1.5159 1817 0.0027 Juvenile -1.2395 1.2097 466 0.0018 With externac -1.2171 1.1882 65 0.0021 Scarred -0.9750 1.1460 24 0.0065

mm), ‘juveniles’ (carapace length less than 52 mm), and parasitised crabs (table III). In figure 3, the four fitted lines are plotted over the ranges observed in the samples, for each class of crab. The residual mean squares around the four fitted regression lines (also given in table III) have been found to be heterogeneous (P < 0.005, Bartlett’s test (Snedecor & Cochran, 1980)). The assumption of homogeneity of variance in analysis of covariance is thus violated and the slopes and intercepts of the four equations should not be com- 166 DANIEL D. HOGGARTH

Log Carapace Length (mm)

Fig. 3. Regression lines fitted to the chelae allometry data illustrated in fig. 2 for healthy and infected crabs. pared by the normal AN C O V A methods. The data have instead been analysed as a multiple regression, weighted by the inverse of the variances around the fitted line, for each crab type. Du m m y variables have been used to represent contrasts between the various slopes and intercepts, in a manner analogous to a weighted analysis of covariance, with subsequent LSD tests between coeffi­ cients. All significant contrasts had probabilities below P = 0.001, while for all non-significant ones the probability exceeded 0.4. Regarding the slopes of the regression lines, adult crabs have been found to be significantly different to all other classes. No significant differences exist between the slopes of the other categories. Infected male P. granulosa, therefore, do not attain the large chelae sizes of mature crabs. Secondly, the intercepts of the juvenile and parasitised crabs have been compared, assuming a common slope (b = 1.2039) for these three classes. In this case, no significant difference BRIAROSACCUS AND PARALOMIS 167

has been found between juveniles and scarred crabs, while crabs carrying externae have significantly smaller intercepts than both other classes. At a given carapace length, recently infected crabs, therefore, have smaller chelae than either juvenile or scarred crabs.

DISCUSSION B. callosus does not inhibit the normal moulting of P. granulosa, neither does the parasite always cause the death of the host. Beyond these generally applicable results, also found for other host species, there are significant dif­ ferences in the effect of B. callosus between male and female P. granulosa. Crabs carrying externae have been shown to be smaller on average than healthy crabs, particularly in the case of males. These results have been tentatively attributed to reductions in the growth rates of infected crabs. Parasitised males, also have smaller chelae than either juvenile or adult males. As with other hosts of B. callosus, all parasitised females, both with externae and scar­ red, were non-ovigerous. Female hosts are thus changed little by parasitisation except for the replace­ ment of the eggs by the externa. The small reduction in the growth rate of females is believed due to the energetic cost of the parasite, which may be only slightly greater than the normal energetic investment on a clutch of eggs. The effects seen in infected male crabs are more severe, yet all results are compati­ ble with the parasitic feminisation frequently observed in other hosts of rhizocephalans (Hartnoll, 1982; O ’Brien & Van Wyk, 1984). In evolutionary terms, feminisation of the male is necessary to provide a safe accommodation for the externa, beneath the enlarged abdomen. The observed decreases in mean body size and relative chelae size in infected males may simply be a reflection of this feminisation. Furthermore, the reduced weight at length of infected males found by Hawkes et al. (1986), is also better explained by the feminised, (i.e. short-legged and lighter) state of such crabs, than by a reduc­ tion in growth rate. It is unfortunate that the chelae dimensions were not measured for a small sample of female crabs. In view of the feminisation generally observed in male hosts of rhizocephalans, it is likely that this is the relative size to which parasitised male chelae are reduced. Neither is it statistically valid to compare the mean sizes of female unparasitised crabs with infected male crabs, as the contrast involves more than a single factor, in a non-additive design. However, in support of feminisation, although abdomen width was not measured for either males or females, infected male crabs were always recognisable in the field by virtue of their wide abdomens, even before the externa was revealed. Abdomen width is thus undoubtedly increased in parasitised males, to at least the approximate width of females. 168 DANIEL D. HOGGARTH

Secondly, modifications to the growth of scarred, post-parasitisation crabs also differed between the sexes. Scarred females, all of which were non- ovigerous, were significantly larger than normal females. Such an increase in size may reflect the extra energy available for somatic growth, in the absence of the energetic demands of both the parasite and normal reproductive activity. After loss of the externae, scarred males above the average size of maturity returned to the relative chelae size of uninfected, juvenile crabs. Thus, even after the presumed death of the parasite, males still do not achieve (mor­ phometric) maturity and are probably sterilised permanently. The increased variability observed around the scarred allometry phase may reflect the delay in recently liberated crabs returning from the parasitised to the juvenile male allometry pattern. Post-parasitisation males, however, were not significantly larger than normal males. Male crabs normally invest less energy in reproduc­ tion than female crabs so that little extra energy is available to a scarred but sterile male (Hartnoll, 1984). The suppression of growth in male hosts of B. callosus has been reported to be a unique feature among peltogastrid rhizocephalans (Hawkes et al., 1987). However, at least four other paguroidean hosts also show reductions in the average size of males parasitised by peltogastrids (O’Brien & Van Wyk, 1984). In all these host species, males are normally larger than females, so that the adjustment to male growth caused by the parasite can be reasonably inter­ preted as an effect of parasitic feminisation. This study indicates the importance of considering both parasitised and post-parasitised crabs, and male and female crabs separately, particularly in the case of pronounced sexual dimorphism. With further investigations of this type, the reduced growth seen in hosts of B. callosus, and certain other peltogastrids, may be shown to be less unusual than is at present supposed.

ACKNOWLEDGEMENTS This research was supported by a grant from Stanley Fisheries Ltd, the com­ mercial arm of the Falkland Islands Development Corporation. I am also particularly grateful to M r T. Boyd and M r A. Johnson of Witte Boyd Holdings Ltd for their continued support of the project and for the patience and cooperation of the four skippers and crews of the fishing vessel Laura Jay. Dr R. W. Ingle of the British Museum (Natural History) kindly confirmed the identity of specimens of B. callosus. Finally I wish to thank the following staff of the Renewable Resources Assessment Group, Imperial College, University of London, for their help. Drs S. Des Clers, A. Rosenberg and G. Tingley gave useful comments on earlier versions of the manuscript and Mr M. V. Bravington assisted with the statistical analysis. BRIAROSACCUS AND PARALOMIS 169

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Received for publication 6 September 1989.