An Assessment Tool for Sea Trout Fisheries Based on Life Table Approaches

Client: Natural Resources Wales

APEM Ref: P*0001193

January 2016

Dr Nigel Milner Reportv4. Final

Summary

A spreadsheet model was developed to calculate various metrics of sea trout stocks in order to support decisions on Net Limitation Orders and other forms of catch regulation. The principal feature is the use of life table approaches which allow the calculation of future life time egg production (FLE) of individual fish, age and size classes. FLE is an index of the long term reproductive value of fish and varies systematically with age through the interaction of future expectation of life (survival) and increased size and fecundity (growth). The loss of FLE resulting from fisheries catch therefore offers a measure of the impacts that fisheries exert on stock fitness. Other metrics include catch (number of fish), catch weight and annual egg deposition. While these have their advantages, they are less informative than FLE about the population dynamics outcomes of fishing. An additional supporting metric, termed gain, is introduced which reflects the component of FLE due to survival beyond the current spawning year. Key outputs are tabulated and plotted on a summary sheet. The models can be used to simulate the effect of changing regulations by changing for example size limits in the rod fishery. Models are set up for the Tywi and Teifi and example outputs are discussed to compare the metrics, illustrate sources of errors and uncertainties, sensitivity to parameters and the interpretation of results. Full life table models are also briefly outlined for both rivers, but were not explored for the purposes of this project. A number of demographic factors contribute to the uncertainty in the outputs, the most important being the accuracy of the age-weight key used to translate size distributions into age and growth, the form of the post-smolt survivorship curve, sex ratios and the timing of first maturation. In addition, fisheries-based factors, reporting and exploitation rates exert important influence on the results. While the models serve their immediate comparative purpose and improve significantly on previous methods, these uncertainties remain a constraint on the longer term application of population dynamics to sea trout assessment and management.

This report refers to models and calculations in Excel Spreadsheets: FLE.TYWI.v1, FLE.TYWI.v4, FLE.TYWI.v4. The original catch data (provided by the NRW) are found in spreadsheets: ST.Tywi.nets, ST.Tywi.rods, ST.Teifi.nets, ST.Teifi.rods.

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INTRODUCTION AND AIM

In order to implement NLO reviews and for more general purposes NRW needs to have a method for evaluating the status of sea trout stocks, the relative impact of competing fisheries and how stocks might respond to alternative catch regulations. Based on previous discussions over methods developed during the Celtic Sea Trout Project (CSTP), NRW considered that the use of life table (LT) approaches that derive future life time eggs (FLE) and various other life table outputs for stocks (here taken as synonymous with a river “population”) was a potential way forward. Such metrics link more closely with population dynamics and the actual state of populations than routine catch statistics. The LT modelling approach produces outputs ranging from simple, comparatively robust figures to complex population modelling and calculation of life history variables that are subject to large assumptions, scientific uncertainties and difficulties of practical interpretation. These boundaries need to be recognised and the more involved outputs avoided, at this stage, for the immediate practical assessment purposes. Outputs from the modelling need to be clearly understandable by stakeholders and be readily interpreted, particularly for NLO applications.

The aim of this project was to revise and enhance Excel spreadsheet life table models developed in the Celtic Sea Trout Project (CSTP, 2016) and to write guidelines for their use in order for NRW to use them as tools for estimation of FLE and basic LT parameters for NLO rivers.

BACKGROUND RATIONALE

The abundance of a fish population is determined by its population dynamics, which are tuned by evolutionary adaptations to maximise its reproductive capacity. The long term fitness of a fish is the ability to transmit genes to future generations, and the average across all the individuals of a population determines the population’s overall fitness. Fitness is considered to give stability and resilience to populations and is thus a valuable attribute to conserve (Marschall et al., 1998; Fleming et al., 2014).

In some fish species including brown trout anadromy occurs, by which part of the population migrates to sea to grow and mature. This complicates the picture because the marine and freshwater components have very different life history traits of growth, survival and maturation, reflecting their environments and selected to maximise overall fitness. In essence there are two “populations”, although they freely intermingle and breed; thus presenting the problem of which traits to use in modelling. Ideally both would be modelled simultaneously; but parameterising the freshwater stage is particularly difficult Fortunately, it has been shown that in nominal “sea trout” rivers the anadromous form, which is larger and has a higher proportion of females, dominates egg production (CSTP, 2016) and thus also the reproductive capacity. Thus, for practical purposes of this application it is considered acceptable to consider only the traits of the anadromous adults (the sea trout).

The essence of the approach is that it recognises and evaluates the long term reproductive value of each fish. The probability of a fish contributing to future generations through egg deposition (Future Lifetime Eggs, FLE) is a balance between decreasing numbers through mortality versus increasing size and fecundity through growth (Stearns, 1990; Solomon, 2006). Moreover, maturation and breeding is energetically demanding and also increases mortality Thus survival and growth rates, coupled with the onset of breeding (determined by age at first maturation) and subsequent breeding schedules drive life history features and population dynamics. The life table approach derives these so-called vital rates from stock assessment data and applies them to age-structured populations. FLE is a more realistic way of describing population impacts of fishing, because it conveys better the true long term impact on the population of fish killed by the fisheries. Complementary metrics are the Reportv4. Final simple catch numbers, catch weight and the annual number of eggs deposited each year, for the population as a whole or for its component age classes. These metrics have contrasts between them and the models will illustrate these, for two rivers the Tywi and Teifi.

OUTLINE OF LIFE TABLES

Life tables are a convenient, logical way to display the dynamics of reproduction in a population, which are controlled by two main processes: 1) The number of individuals in a population decreases with age due to mortality (or its complement, survival) 2) The average size of individuals increases with growth.

In addition, the following principles apply:

3) The number of eggs per individual female increases with size (roughly proportionally to the cube of length). 4) The proportion of mature females (i.e. those producing eggs) increases up to the time of full maturity. 5) The number of eggs per age class is therefore a function the number of females remaining alive, their size and maturity. 6) Sex ratio modifies the proportional abundance of females

Life tables give several types of outputs relating to the reproductive potential of the population and the population growth rate which, if the parameterisation of the models is correct, index a population’s fitness and potential growth rate. These include net reproductive rate (R0), the population rate of increase (ʎ), intrinsic growth rate (r) and generation time (G). These terms are explained in Appendix I, but are not used in the core outputs of this report. However, they can be used to project future population size and composition using matrix projection models. Such outputs require high quality data and although provisional indicative values are offered here, derivation of adequately robust estimates requires more detailed analysis and better data.

The primary life table result, for the comparison of competing fisheries or the evaluation of their individual impacts on reproduction, is the expected future life time eggs (FLE) that an individual at a given age produces. This can be estimated without too much difficulty and demands on other variables. If FLE per fish is known then the effect of removing that individual by fishing mortality can be estimated and summed for all fish over the fishery catch. Fortunately, the calculation of FLE does not require the parameterisation of the full life cycle population dynamics, in particular the egg to smolt survival, which is problematic because there are so few estimates of survival in this freshwater phase.

METHODS

Spreadsheets were set up for the Tywi and the Teifi. The use of life tables requires an age (or weight) specific description of the population for each river in terms of abundance (Nx) at age x (yrs) and size at age. In sea trout populations, in which egg deposition is dominated by anadromous tout, this can be conveniently derived from the adult run estimates reconstructed from rod and net catches. A number of assumptions are required which are outlined below.

The adult pre-fishery run was reconstructed by assembling weight frequency data (in 1lb classes) separately for each annual net and rod catch set (for years 2010-2015), incorporating various Reportv4. Final adjustments for reporting rate (r) and exploitation rate (U) to give an estimate of the population size structure prior to the net fishery. The size structure is then converted to an age structure using an age/weight key from the River Dee, which, because of its long history of scale reading, offers the best data available for Welsh rivers.

The outline calculations to derive the age structure are shown in Fig 1. Nx is the population abundance at age x (in years). Age can be considered as sea age (i.e. whitling are sea age 0, 1yr olds have experienced one post-smolt winter etc), or as total life time age, from year of hatching; in which case the age is about 2 yrs greater than sea age, because average age of smolts is about 2. This distinction will be made as necessary in the following.

Derivation of pre-fishery run

Net catch + [Declared Rod catch (N/wt) x r] x 1/U N/wt

Derivation of Nx

Adult pre-fishery run Age/wt key (R. Dee) (=”population”) (N by wt class) x

Nx (by sea age) for Life table

Survival Modelled Nx Maturity & sex ratio (Dee; (vertical or fecundity (Solomon) horizontal)

Partial life table Population growth (R0, r)

Assessment metrics

Killed catch FLE per fish Totals Rods + nets Annual eggs per fish OUTPUTS & per In-river loss, natural ASSESSMENT Natural losses Weight per fish fishery + post-release

Fig 1 Outline stages in deriving life table outputs, using abundance at age x (Nx), derived from rod and net catches. Nx is the starting variable in life tables, other terms and definitions are given in supporting text and boxes.

Assumption 1: Sea trout populations are dominated by anadromous egg deposition. A small proportion of resident females will produce eggs, but they are much smaller than anadromous females and due to cubic relationship with fecundity and body length, have disproportionately fewer eggs. It has been shown that due the large size of sea trout adults compared with resident trout, the former dominate egg deposition in most “sea trout” rivers, such as prevail in Wales (CSTP, 2016). The implication is that it is an acceptable approximation to model stock reproduction using only the migratory egg component.

Assumption 2: Reportv4. Final

The declared net catches represent actual catches, without any adjustment for reporting rate; because no information is available on what that adjustment term might be.

Assumption 3: Rod reporting rate (r), taken to be 1.1. True catch (Ct) = declared catch (Cd) x 1.1. This has been used as the reporting rate adjustment for migratory salmonids since the introduction of the salmon conservation limit method in 1996. Very recently, a revised factor has been proposed by the EA/NRW, but the original value is used here for continuity with historical data accounts.

Assumption 4: Rod exploitation rate (U) is the proportion of the run that enters the river after the net fishery exploitation. U = True catch / run. Usually, no independent run data are available, but the River Dee Stock Assessment programme (DSAP) provides trap data for that river, which gives run estimates.

U was taken to be constant across all size/age classes, because studies in the Dee have not demonstrated any size or age-selectivity. Exploitation rates for rivers other than the Dee were derived by NRW based on an empirical relationship between extant rod exploitation rate (for salmon and sea trout from counted rivers) and angling effort and flow (Davidson et al., in prep).

Dee U = 0.034 (based on trap and rod catch data Tywi U = 0 .174 (based on NRW formula) Teifi U = 0.130 (based on NRW formula)

The net fisheries are assumed to operate before the rod catch. On the Tywi and Teifi, some rod- caught fish may be taken downstream (before) the coracle fishery, but no adjustment is made for this (assumed) small proportion of the rod catch.

Assumption 5: In-river survival had two components. (1) natural survival of uncaught fish (Sn = 0.9), based on values used for salmon; (2) post-release survival of released fish (Sr = 0.8), based on reported post-hooking rates for salmon. The true values will vary with time of river entry and capture; but no information was available to allow for this and given other sources of error this was considered acceptable. Oher values can be entered and tested via the model summary sheet

Age-Weight key

This was derived for the River Dee from data provided by the NRW (Appendix II) for the period 2005- 2014. This was the best data available, but it can be seen that the low frequency of larger / older fish introduces considerable uncertainty into the estimation of older age classes, in particular inflating the abundance of the oldest age classes, which introduce systematic errors in the fish > 7yrs. The use of one age/wt key assumes that marine growth is the same between the rivers. The CSTP study showed that sea trout in South Wales are fast growing compared with more northerly populations within the Irish Sea. However, the Dee grouped statistically with the Clwyd, Conwy, Dyfi, Teifi, Tywi and Tawe; so the potential error, due to growth variation, of applying Dee relationships to the Tywi and Teifi is thought to be small.

Run age composition

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The run abundance and size structures reconstructed for the Tywi for the years 2010-2015, using methods outlined above are given in Appendix III.

Run age structure

Run size structures were derived by multiplying the size structure by the Dee age structure. Thus the Dee age/wt key will influence the pattern of ages seen in the other rivers. This average age/wt key, combining data over 2005 -2014 (in order to have sufficient data for an acceptable accurate key), will therefore impose that average pattern on the individual years’ run structures for the other rivers, and which in turn will influence the annual survival patterns. The estimates of N at sea age for the Tywi, up to age 9 (the limit of the Dee age/wt key) show the effect of no data for sea age 8 fish being available for the Rive Dee.

Post-smolt adult survival

Two approaches to modelling annual survival were explored: (1) assuming constant survival and (2) assuming a quadratic model. They are both outlined for information, although the quadratic model was selected in the end because it fitted the data better.

Constant survival

Annual survival (S%) was estimated from loss rates based on the abundance (Nt) of sea age classes, taking whitling as year 0, using the expression:

-zt Nt = Noe (Equation 1)

Where N0 = start abundance, Nt = final abundance, t = the time period (years) and z = instantaneous mortality (loss) rate. From which annual S = 100.e-z. This linear regression approach assumes constant annual mortality through the adult phase and the slope is therefore an average of the survival over the time period of the data (this assumption requires further consideration – see below).

Using this approach there are two ways to derive annual survival from the catch data available (Table 1). 1) Vertical, static or sampling occasion-specific. This method takes data from one year (e.g. a year’s catch statistics) on fish of different ages (the vertical column in Table 1) and assumes that they represent the abundance of a population that experiences the same recruitment each year. For example in 2010, abundance of 0 sea yr fish (whitling) was 10,506, reducing to 4,276 for 1yr olds and to 21 at age 9 yr olds. 2) Horizontal, dynamic or cohort. This follows the progress of individual age classes (i.e. fish born at the same time) over time to record their long term survival (diagonal data in Table1). In practice the data in the left hand column of Table 1 refer to sea age classes; but because not all sea trout smolt at the same age, although the majority appear to emigrate at age 2, they will represent a mix of true age classes (i.e. most will have been born in the same year). However, most smolts migrate at age 2 and the classes in Table 1 do represent groups of fish that experience the same conditions after sea entry.

Horizontal approaches give the most accurate depiction of population change, the data being based on the same putative year classes; but the data are more limited by the time span of observations. If annual recruitment (= starting abundance) varies greatly that will be reflected in relative abundance of the age classes making up the notional “population” in a vertical data set and could lead to errors in the estimation of averages. For example, conceivably, abundance might be higher for older fish Reportv4. Final

(say age 4) than a younger class (sea age 3). However in most contemporary sea trout cases, the populations vary randomly and are reasonably stable, at least in comparison with the between year losses due to annual mortality; so the effect of mixing year classes is thought to be acceptably small.

A further complication with sea trout is that an unknown, but possibly substantial, proportion of the marine population remains at sea and do not return as whitling in their first post-smolt summer. Estimates of 0yr old fish, based on river runs (traps or net and rod catches) will not account for this “at sea” component. On the Dee, tagging studies have shown that 45% of 0yr olds may remain at sea to return as older maidens. Marine residence over the 2nd sea winter can also occur and influence the apparent abundance of 1yr old fish, but at a lower rate and thus is thought usually to be a much smaller source of error. Due to lack of information there was no way to adjust for this effect in this study. An option, if the data suggest it is necessary, is to omit the 0yr olds from the calculations and start at sea age1 (e.g. CSTP, 2016; Milner et al., in prep). In this project all age data were used, which is acceptable if the same procedure is used for all analyses and the proportion of marine residence does not vary greatly.

Table 1 Reconstructed pre-fishery abundance at sea age (yrs) of sea trout in the River Tywi, for years 2010 to 2015. Vertical data are in each column, horizontal data are shown for two example sea year classes 2008 (pink) and 2010 (blue). {FLE.TYWI.v4/SH8A}

YEAR OF OBSERVATION Sea age 2010 2011 2012 2013 2014 2015 0 10506 11975 7740 7211 6113 10363 1 4276 2962 2983 2794 2338 4316 2 2375 1483 1907 1486 1106 1827 3 788 558 687 477 393 581 4 351 281 285 236 216 308 5 86 85 64 56 61 81 6 34 27 30 19 25 42 7 18 15 22 12 13 25 8 1 1 0 4 2 0 9 21 11 20 26 19 24 Total 18455 17396 13737 12320 10287 17567

The vertical analysis gives more data (Table 1), but is evidently subject to errors at older ages (>7yrs) due to the low accuracy of the age/wt key at older age classes where there were few data (Appendix II). The horizontal method lacks data for oldest fish and could be slightly biased by the preponderance of values for younger ages. In the case of the Tywi the two approaches gave similar estimates of z (Fig 2), from which annual survival was calculated to be 42.9% (vertical) and 41.1% (horizontal), indicating that at face value sea survival was approximately constant. With that assumption, the sensitivity of the outputs to varying S was tested for the Tywi.

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vertical Horizontal 10

8 Vertical y = -0.8464x + 8.8774 R² = 0.9002 6

ln(N+1) 4

Horizontal 2 y = -0.9096x + 9.0677 R² = 0.9767

0 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs)

Fig 2 Comparison of sea trout survival rates based on vertical and horizontal data analysis, illustrating error in older fish when using vertical data (see text). {FLE.TYWI/SH8A}

Both simple bivariate regression methods (vertical and horizontal) using equation 1 imply a constant loss rate (i.e. constant proportional loss each year, over a cohort’s lifetime and data from several Irish Sea rivers suggest constant loss rates at least from the second sea year (CSTP, 2016). However, on biological grounds the assumption of constant survival may not be sound. Early marine life is a time of high mortality in salmon and in sea trout probably due to small size, making them vulnerable to predation, and to poor initial adaptation of post-smolts to the new environment (Davidson et al., in prep). Variable survival has been observed for the River Dee (Davidson et al. 2006, in prep; CSTP, 2016), but good data are needed to detect such variation. For this reason it was decided to use the horizontal data, which are likely to be more realistic even if there are fewer of them, and to explore polynomial (quadratic) models that might fit better to the data.

Quadratic survival model After inspecting and trialling run data for the Teifi it was seen that a constant survival model gave anomalous results, such that the over-estimate of Nx for most of the lifetime resulted in unrealistically high egg depositions. A quadratic model gave a better fit to the data and was used subsequently for both rivers, even though the benefits in terms of statistical fit for the Tywi were marginal.

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Tywi horizontal Tywi vertical

10 y = 0.0076x2 - 0.9565x + 9.1116 10 y = 0.0409x2 - 1.2146x + 9.3682 9 R² = 0.977 9 R² = 0.9137 8 8 7 7 6 6

5 5 ln(N+1) 4 ln(N+1) 4 3 3 y = -0.9096x + 9.0677 2 2 y = -0.8464x + 8.8774 R² = 0.9767 1 1 R² = 0.9002 0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs) Sea age (yrs)

Fig 3A Comparison of survival models for the Twyi, using horizontal and vertical data and constant and quadratic survival models (shown in figures). The FLE model uses the horizontal, quadratic equation to predict abundance at age (Nx) {SH8A}

Teifi horizontal Teifi vertical 12 12 y = 0.0746x2 - 1.643x + 9.5208 y = 0.0827x2 - 1.7348x + 9.6437 10 R² = 0.9894 10 R² = 0.9662

8 8 y = -1.1805x + 9.0873 y = -0.9903x + 8.6509 R² = 0.9733

6 6 R² = 0.9249

ln(N+1) ln(N+1) 4 4

2 2

0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs) Sea age (yrs)

Fig 4 Comparison of survival models for the Teifi, using horizontal and vertical data and constant and quadratic survival models. The FLE model uses the horizontal, quadratic equation to predict abundance at age (Nx) {SH8A}

For the Teifi, the quadratic model gave an improved fit to the data (Fig 4). The mean annual survival was higher in the Tywi (41.1%) than the Teifi (29.8%) and the pattern of variations in survival over age were noticeably different in the two rivers (Fig 5), with the Teifi showing lower survival at younger ages; but this was not seen in the Tywi. The observed annual survival for year 6 (S >=1) is clearly anomalous in both cases, and is thought to result from error in the older classes.

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Tywi, horizontal Teifi, horizontal obs Px (% annual S) obs Px (% annual S) Constant S (41.1%) Constant S (29.8%) 1.2 Quadratic model 1.2 Quadratic model

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

Annual survival (S Px) or(S survival Annual Px) or(S survival Annual

0.0 0.0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Sea age (yrs) Sea age (yrs)

Fig 5 Comparison of annual survival in the Tywi and Teifi, showing the fits of different models. {FLE.TYWI.v4/SH8A}

Knowing the true survival pattern is essential to obtaining accurate reproductive outputs over age classes (annual egg deposition) and lifetimes (FLE) and thus for determining the effects of catch regulations. It is seen that the survival patterns for the Tywi and Teifi are quite different. The Twyi showed a comparatively constant rate over age, decreasing after age 6; but the Teifi showed an initial survival much lower than the Tywi that increased with age. This is the proximate result of the quadratic model fits to the data, but may also be affected by unknown errors in catch recording. The survival results affect strongly the later reproductive indices and the conclusions such as the benefits of size limits in the two fisheries, so they are very important variables in the analysis. In the time available for this project it has not been possible to explore these effects further; but they represent a crucially important feature of sea trout population dynamics and stock assessment, and present a priority research topic. For present purposes, the quadratic models and horizontal data have been used in the models, being the best available set

Growth rate

Growth rate was estimated from the Dee age-weight key. Unfortunately, due to small sample sizes, weight distributions for the older age classes were subject to error and biases. The necessary application of this key resulted in some anomalous results such as increasing abundance with age and decreasing fecundity. These problems arose in oldest age groups which only contributed small proportions of egg deposition and FLE, so the errors do not materially affect the outputs.

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Dee age/wt growth Dee age/wt data modelled (von Bertalanffy) fitted von Bertalanffy model 1000 20 900 18 800 16 700 14 600 12 500 10

400 8 Mean wt(lbs) Mean Fork lengthFork (mm) 300 6 200 4 2 100 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs) Sea age (yrs)

Fig 6 Modelled growth of sea trout based on the Dee age/wt key. Left panel: A von Bertalanffy model (solid line) was fitted to the length data (L∞ = 902mm, K = 0.244, t0 = 0.467). Right panel: the same relationship fitted to lb weight data. These fitted lines were used in the FLE estimation. {FLE.TYWI.v4/SH4}

Nevertheless, smoothing the growth data was considered necessary and this was done by fitting a von Bertalanffy growth model (e.g. King, 2007) to the Dee size data and are seen give a reasonable fit to the data (Fig 4), with parameters: K = 0.244, L∞ = 902mm, t0 = 0.467. These values are similar to those estimated for sea trout around the Irish Sea (CSTP, 2016). These modelled lengths were then converted back to weight in lbs, to make compatible with the catch data, using the relationship.

W(lbs) = 10^(-4.631221 + log10(L, mm) x 2.888346) x 0.00220462 (Equation 2)

Adapted from Evans (1994)

Fecundity was estimated from length from:

Log10(Eggs) = log10(L, mm) x 2.754 – 4.0721. (Equation 3)

From Solomon (1997, 2006).

Life Tables

Partial life tables (PLT), i.e. not, at this stage going into the estimation of R0 and r, were produced using standard nomenclature (e.g. Gotelli, 2008), with some adaptations to suit these data and application (Table 2).

Table 2 Example partial life table, data averaged for the Tywi and Teifi, 2010-2015. These use quadratic survival rates and modelled Nx and lengths. (In SH9.FLE)

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TYWI quadratic survival a b c 0.0075613 -0.956503 9.11159827 POPULATION(PREFISHERY) MEAN 2010- 2015 Sea age (x) Popn Nx.mod Px.obs Px.mod Wt(lbs)mod. Length(mm). Fecundity Pr Female Pr mature Fertility (mx) Eggs per (Nx).obs mod age class 0 8985 9058.76 0.36 0.387 1.02 336 770 0.6 0.55 254 2,302,311 1 3278 3506.49 0.52 0.393 2.59 459 1,808 0.72 0.8 1,042 3,652,496 2 1697 1377.62 0.34 0.399 4.57 554 3,049 0.8 1 2,439 3,360,676 3 580 549.12 0.48 0.404 6.70 629 4,327 0.95 1 4,110 2,257,049 4 280 221.86 0.26 0.409 8.76 688 5,534 0.95 1 5,258 1,166,491 5 72 90.66 0.41 0.411 10.65 734 6,617 0.95 1 6,286 569,930 6 30 37.27 0.59 0.408 12.30 771 7,554 0.95 1 7,176 267,484 7 17 15.23 0.06 0.393 13.71 799 8,344 0.95 1 7,927 120,688 8 1 5.98 18.16 0.343 14.89 821 8,999 0.95 1 8,549 51,149 9 20 2.05 0.02 0.172 15.86 839 9,534 0.95 1 9,058 18,579 10 0.35 ANNUAL TOTAL= 13,766,854 TEIFI quadratic survival a b c 0.0746085 -1.643027 9.52082166 POPULATION(PREFISHERY) MEAN 2010- 2015 Sea age (x) Popn Nx.mod Px.obs Px.mod Wt(lbs)mod. Length(mm). Fecundity Pr Female Pr mature Fertility (mx) Eggs per (Nx).obs mod age class 0 15481 13639.81 0.15 0.208 1.02 336 770 0.6 0.55 254 3,466,599 1 2395 2841.40 0.32 0.242 2.59 459 1,808 0.72 0.8 1,042 2,959,710 2 756 686.60 0.25 0.280 4.57 554 3,049 0.8 1 2,439 1,674,941 3 192 192.10 0.42 0.323 6.70 629 4,327 0.95 1 4,110 789,594 4 81 61.96 0.26 0.368 8.76 688 5,534 0.95 1 5,258 325,749 5 21 22.83 0.41 0.415 10.65 734 6,617 0.95 1 6,286 143,509 6 9 9.47 0.47 0.458 12.30 771 7,554 0.95 1 7,176 67,961 7 4 4.34 0.00 0.498 13.71 799 8,344 0.95 1 7,927 34,412 8 0 2.16 #DIV/0! 0.543 14.89 821 8,999 0.95 1 8,549 18,492 9 5 1.17 0.15 0.626 15.86 839 9,534 0.95 1 9,058 10,640 10 0.74 ANNUAL TOTAL= 9,491,607

The models estimate the average population status in the last six years (2010-2015) and indicate total potential egg deposition or the pre-fishery run (i.e. before exploitation), based on the modelled average population abundance at age, of 13.8m and 9.5m in the Tywi and Teifi respectively, and that ages contributing maximum potential eggs are 1yr olds for the Tywi and 0yr olds (whitling) on the Teifi. The model outputs include basic description of the reproductive value at each age (Fig 7), characteristic of the two stocks. The FLE values for example are used to calculate the absolute and proportional effect of the different fisheries and in-river losses and by subtraction the actual deposited eggs, and of changing size limit regulations.

Tywi, age-specific FLE & egg deposition Teifi, age-specific FLE & egg deposition

Total potential eggs / age FLE / fish Total FLE / age class Total potential eggs / age FLE / fish Total FLE / age 6 16 6 16 14 14 5 5 12 12 4 4 10 10 3 8 3 8

6 6

2 2 Annual eggs eggs (millions)Annual Annual eggs eggs Annual(millions) 4 4

1 1 FLE/ind. ('000s), FLE/ind. ('000s), FLE (millions) Total 2 2 FLE/ind. ('000s), TotalFLE (millions)

0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs) Sea age (yrs)

Fig 7 Age-specific egg deposition and FLE results for the Tywi and Teifi, based on the PLT models, shown on same scale. {FLE.TYWI.v4/FLE9}

FLE peaked at ages 7 and 6 yrs for the Tywi and Teifi respectively; and similarly contribution to total eggs was greatest at 1yr and 0yr respectively. Total potential egg plot (i.e. pre-fishery) in Fig 7 shows Reportv4. Final the same data as in the rightmost column of Table 2. Lower age-specific FLE in the Teifi is the result of lower survival rate.

SUMMARY GUIDELINES FOR USE OF THE SPREADSHEETS

Models and calculations are in Excel Spreadsheets: FLE.TYWI.v1 (constant S), FLE.TYWI.v4 (quadratic S model), FLE.TYWI.v4 (quadratic S model).

The original catch data (provided by the NRW) are found in spreadsheets: ST.Tywi.nets, ST.Tywi.rods, ST.Teifi.nets, ST.Teifi.rods.

To set up for a new fishery follow stages 1, 2, 5 and 9. The other stages are automatic calculations that are shown to illustrate the process.

Stage 1. Import lb weight class declared catch data from catch files into sheets SH2 (nets) and SH5 (rods).

Stage 2. Check that the parameter assumptions (rod catch reporting rate, exploitation rate, in-river survival of uncaught fish and of released fish) in the summary sheet (SH1) are appropriate to the river. Initially, survival rate (S, horizontal) was set here for models that assumed constant survival, but as discussed above this was dropped in favour of quadratic models, although a constant S is used in the full life table in SH11, to be compared with the quadratic model in SH12. Note that for the Twyi, a constant model was a reasonable approximation of the dynamics and was used to estimate the effect of changing survival in sensitivity analysis. This remains in model spreadsheet FLE.TYWI.v1, and can be applied there if required, but it is advised to stick with version FLE.RIVER.v4, and adapt that for constant S if required. In FLE.TYWIv1 S initially took its value from the S estimate based on horizontal data in SH8A. S can be changed at will in the summary sheet to examine effects; but if S is changed in the Summary sheet it should be set back to the SH8A cell (AS15). In spreadsheet models FLE.TYWI.v4 and FLE.TEIFI.v4 the quadratic terms for survival are set in SH8A and are not alterable via the summary sheet.

Stage 3. Convert weight classes of the total run to age classes in SH7A, these are averaged and used to estimate survival (in SH8A) and to seed the PLT in SH9 and SH10, and the full life tables in SH11 and SH12. The conversion of the weight to age classes is based on the Dee age/wt key (SH4A).

Stage 4. For FLE.TYWI.v1 only….estimate average survival (SH8A), assuming constant over the life time of the adults, and this value feeds into the PLT through the summary sheet (see above). In the .v4 models the quadratic survival equation terms are determined in SH8A, from where they are taken up automatically into the FLE sheets (SH9 and SH10).

Stage 5. Check PLT (in SH9) for the whole population, i.e. using pre-fishery age structures (done in SH7A). Terms for weight, length, fecundity and the proportion of females mature are already built in, but can be altered if required and need to be checked for appropriateness. See example in Table 2. The Popn.obs (Col C) is the actual abundance in the pre-fishery run averaged over 20101 – 2015, given here for completeness and to compare with the modelled values (see stage 5). Likewise Px.obs (proportional survival between years) is shown only for comparison with the modelled value in

Px.mod. Nx.mod is the modelled abundance on which FLE calculations are based and takes the N0 observed to which is applied the modelled survival rates (see Stage 2). Other parameters are as described above. The growth model is von Bertalanffy using Dee age wt/data and calculated in SH4B.

Stage 6. In the PLT, use the starting run size (averaged over 2010-2015) as the N0 value in Col D and Reportv4. Final

then apply the S to calculate Nx up to age 9 (or older if required, but this limit is set by the data from the Dee Age/wt data).

Stage 7. In the PLT calculate fertility (Col L, eggs/female) and apply to the Nx values to calculate eggs for age class (Col M)

Stage 8. Using observed data for total run (Rows 20:30), rod kill (Rows 35:45), coracle (Rows 50:60), seine net catches (Rows 65:75) and natural losses (Rows 80:90) calculate (1) the FLE for each fishery summed across ages, (2) total catch weight, and (3) total lost annual eggs, for each of 2010-2015 yrs. These are the principal metrics shown on the summary sheet.

Stage 9. Assemble summary statistics to compare catch impact indices using N (catches), weights, FLE and total annual egg loss, and import to the summary sheet (SH1). Carry out any further sensitivity analysis if required (an example for the Tywi is shown in SH1 of FLE.TYWI.v1). The summary sheet (SH1) has boxes (in yellow) where reporting rate and exploitation rate are set, and these can be altered to show the effect of changing them through the summary graphics and tables linked to the other worksheets, (see SH1).

CATCH REGULATION CHANGE SIMULATION

The same models can be adapted to calculate the effect on FLE, annual egg deposition or other impact metrics of changing the catch regulations by for example season, quotas or slot limits. The most streamlined way to do this is to prepare tables that show the effect of changes in proportions of each fishery’s catch in each weight class (see SH10). For example a complete closure, or imposition of 100% C&R (allowing no post-release mortality) of a fishery would simply modify catches in all wt classes by -1.0; or perhaps 0.5 is regarded as more appropriate. A slot limit might allow no catch in the 2-4 lb band. A quota could be set by simulating a fixed catch rate across all the size classes. Season changes could be applied by characterising the monthly catches size distributions and adjusting the catch factors by that amount.

As an example, this is done in SH10 where (at E67:G90) the proportions of the rod killed and net catches are altered from a default of 1.00. In practice it is not likely that upper size limits would be set for the net fisheries (although lower limits might be via mesh sizes), but the option is there. Thus, to set “no kill” of fish smaller than 2lbs for the rods one sets the values to 0 in E67:68. The spreadsheet calculates the revised metrics and the difference (the savings incurred by the regulation) from the current state. This allows the benefits of setting different size limits to be compared directly (Fig 8). Note that instead of calculating this for each of the years 2010 – 2015 individually, in SH10 average values for this period were used.

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Tywi, savings at various size (lbs) limits Teifi, savings at various size (lbs) limits

Annual deposited eggs Total FLE % ann. egg deposition Annual deposited eggs Total FLE % ann. egg deposition 3.0 8 3.0 8

2.5 2.5

6 6 2.0 2.0

1.5 4 1.5 4 Total savings (m) savings Total

1.0 (m) savings Total 1.0 % of annual egg egg deposition % annual of 2 2 egg deposition % annual of 0.5 0.5

0.0 0 0.0 0

Size limit (lbs) Size limit (lbs)

Fig 8 The savings incurred in annual egg deposition and FLE by different size limits on the rod fisheries: <2lbs and cumulative savings at increasing lb limits from 2lbs upwards. The black line / open circle plots show the % saving on the annual egg deposition. {SH10}

The differences between the rivers in absolute savings result from the catch differences and the survival patterns (Fig 8). FLE savings are considerably more (about x2 over much of the size range) than annual egg deposition on both rivers. The % of annual egg deposition saved by no-rod kill on <2lbs fish is <1% on the Tywi, but 1.4% on the Teifi. No-kill above 5lbs would save 2.6% eggs on the Tywi and 0.6% on the Teifi. These are small values because rod-kill accounts for only 6.4% and 3.6% of the total annual eggs on the Tywi and Teifi respectively. In-river losses, due to natural mortality and post-release mortality combined, are comparatively high at 9.5% and 10.1% on Tywi and Teifi respectively. The effects of progressively increasing the size limit reduce with size according to the pattern established by the interaction between growth and survival. Thus on the Tywi, the FLE saving by not killing any fish <2lbs is approximately equivalent to not killing fish larger than about 8.5lbs.

SENSITIVITY

The sensitivity of outputs can be tested by altering key parameters and comparing the changed outputs. For reasons to do with the optimal survival model (see above) this could only be done for survival for the Tywi (in FLE.TYWI.v1); but in principle all the parameters can be adjusted for any model within each spreadsheet. This example (Fig 9) is shown in the summary sheet worksheet (FLE.TYWI.v1/SH1), for the default setting for that Tywi model (reporting rate = 1.1, rod exploitation rate = 0.174; annual survival = 42.9%).

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y=x report rate Survival rate Report. rate Survival rate y=x

2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5 Proportionalchangein total run FLE

Proportionalchange in FLE % lost rodsto 0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 proportional change in rate (from default) proportional change in rate (from default)

Fig 9 Sensitivity of FLE to changes in values of reporting rate and annual survival rate parameters, using default Tywi model. Left panel shows proportional change in FLE attributable to rods and right hand panel shows the change in total FLE, both for proportional changes in the two parameters.{FLE.TWY.v1/SH1}

A parameter such as reporting rate, which is a multiplier in the rod component of the run estimate, exerts an almost directly proportional effect on FLE attributable to rods. Thus a -10% and +10% change causes a -6% and +8% change respectively in the FLE loss to rods. The S rate is more influential in the estimates of total FLE, exerting a curvilinear response (Fig 9, RHS) reflecting the power function in equation 1; as discussed above it is very influential on the PLT model outputs. Total FLE is a summation of all the fisheries and S affects all their estimates. Reporting rate exerts a proportional influence on FLE. Similarly for escapement (expressed as total deposited eggs), a +/- 20% change in reporting rate is directly transferred to the escapement egg estimates (Table 3). In- river natural survival rate (for which +11.1% not 20%, because S =<1) causes 20.5% change in escapement; post release S has smaller effect because it applies to only part of the run. An exploitation rate exerts asymmetric effects on escapement simply because it operates as a divisor in the run estimate.

Table 3 Example responses of actual deposited eggs estimates to 20% change in rod reporting rate, exploitation, natural survival and post-release survival.

FLE.TYWIv4 default -20% +20% Eggs-20% Eggs+20% %change,-20% %change,+20% report rate 1.1 0.88 1.32 8.108 12.162 -20.0 20.0 Utywi 17.4 13.92 20.88 12.941 8.265 27.7 -18.5 inriver S 0.9 0.72 1 8.059 11.289 -20.5 11.4 post-release S 0.8 0.64 0.96 9.937 10.333 -2.0 2.0 Escapement 10.135

FLE.TEIFIv4 default -20% +20% Eggs-20% Eggs+20% %change,-20% %change,+20% report rate 1.1 0.88 1.32 5.881 8.822 -20.0 20.0 Utywi 13.3 10.64 15.96 9.096 5.9 23.7 -19.7 inriver S 0.9 0.72 1 5.85 8.186 -20.4 11.3 post-release S 0.8 0.64 0.96 7.227 7.476 -1.7 1.7 Escapement 7.352

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Other variables such as fecundity, sex ratio and proportions mature at age can also be altered in SH9 to test their impact on the outputs of interest.

SUMMARY SHEET, COMPARISON AND INTERPRETATION OF METRICS

The Summary sheet (SH1, examples in Appendices V & VI)) displays the basic fisheries characteristics and key outputs from the PLT. Summary tables show (top) the average values of the principal four metrics of impact namely: catch (total and killed in the case of rods), weight of catch annual deposited eggs and FLE. The 2nd table summarises the model outputs and their error (approximately 95% confidence intervals) over the period 2010-2015. ) and partitions the annual potential eggs amongst the fisheries, in-river losses and total actual deposited eggs (cell L16). Total actual is the migrant sea trout nearest equivalent to the annual salmon egg deposition reported in the Cefas/EA/NRW reports to ICES.

The summary graphics show the fishery catch size distributions (Summary Fig 1) and the % contribution of the individual fishery to each size class (Summary Fig 2). Summary Fig 3 compares the FLE loss estimates of the four main sources of loss (rods, seines, coracles and in-river natural loss). Fig 4 compares the four main impact metrics (catch number, weight, annual eggs and FLE) for the three fisheries as % contribution to the loss (the killed fish only); which can be compared with the contribution to the total. For example, the rods contribute 30% of the eggs lost to the fisheries, but only 6.4 % of the annual total eggs deposited (and 34% and 6% of the FLE respectively). These numbers are on the summary sheet. Age-specific PTL outputs, including the individual fish FLE values are shown in Summary Fig 5. The fit of the quadratic survival models (calibrated on horizontal data) to the vertical data (used to calculate the by year values in SH9 and SH10), is shown in Summary Fig 6. As illustrated here (Fig 10) they fit well over most of the age range where the majority of egg deposition arises, but less so at sea ages >7yrs, for the age/wt key error reasons outlined above.

Tywi survival model Teifi survival model Obs (vertical) Nx Nx.mod Obs (vertical) Nx Nx.mod 100000 100000

10000 10000

1000 1000 100 100 10

10

1

Abundance at age (Nx) age at Abundance (Nx) age at Abundance

1 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

Fig 10. The fit of the quadratic models to the vertical data for mean (2010-2015) abundance at sea age (Nx), for the Tywi and Teifi. {FLE.TYWI.v4/FLE9}

Of the four loss metrics (catch, weight, annual eggs and FLE), the one relating to catch number is obviously different (Fig 10). In both rivers the rod fishery gave highest impacts according to numbers killed (and even higher for total rod catch), due to the numerical domination of the rod catch by small fish (more so in the Teifi). In contrast, the coracles scored highest for the reproduction-based Reportv4. Final metrics because of the high proportion of larger sea trout in that fishery. Weight was a reasonable surrogate for annual eggs and FLE due to its close correlation with fecundity.

Tywi fishery contribution to losses Teifi fishery contribution to losses

Rods Coracles Seines Rods Coracles Seines 60 80

60 40

40 Percentage Percentage 20 20

0 0 Catch.killed Weight killed Annual eggs FLE Catch.killed Weight killed Annual eggs FLE

Metric Metric

Fig 10. Examples of Summary sheet Fig 3 (left, Tywi; right, Teifi) comparing the metrics of losses attributable to the three fisheries. {FLE.TYWI/SH1}

The three reproduction-based metrics gave similar indices of the relative impacts of the fisheries (Fig 10), thus the ranking of impact was coracles > rods > seines, which reflects the catch level and size compositions. The coracles took high proportions of the heavier fish in both rivers (see Summary fig 2). Regulations involving size selectivity (gear, season or size limits) will incur varying effects due to the difference in survival rates between the rivers and the fishery-specific catch levels and can be tested through the simulation routine in SH10 (see Fig 8). Total weight gives an easily gathered index, which correlates well with egg production because of the mass-fecundity relationship, but does not inform greatly about the reproductive state.

How should the various metrics be interpreted and what might be the benefits of considering FLE over annual egg deposition and of those two metrics over total catch weight, particularly as they appear to indicate relatively similar impacts between the fisheries (Fig 10)? The answer depends on the fishery and regulatory aims. Firstly, it is clear that the catch levels alone, historically used to set controls through NLOs and other regulations, are imprecise measures of impact and are not recommended. Salmonid fisheries management recognises that sustainable fisheries should be guided by the population dynamics that control breeding success and thus sustainable levels of catch (e.g. Hilborn and Walters, 1992; NASCO, 1988). Therefore expressing the impact of fishing as measured by effects on annual egg deposition should be a minimum level of assessment. But fisheries are size-selective (e.g. mesh size effects), or can be made so by size limits, and thus portioning eggs by fish size or age classes is also necessary. The reproductive value of individual fish then becomes an important issue. It is obvious that small, young fish will contribute fewer eggs than larger fish in any one year; but it is less obvious what their long term contribution would be if they were not killed and that is the measure which determines the population’s overall fitness. The PTL analysis demonstrated that FLE peaked at age 7 in both rivers, but at quite different levels: 12,513 eggs and 14,695 eggs on the Twyi and Teifi respectively (Fig 11).

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A. FLE and fertility by age B. "Gain" in FLE by age Tywi FLE Teifi FLE Fertility Tywi Teifi weight 16000 8,000 16 15 14000 7,000 14 13 12000 6,000 12 11 10000 5,000 10 9 8000 4,000 8

7 Eggs fish Eggs / Eggs Eggs fish / 3,000 6 6000 Weight (lbs) 5 4000 2,000 4 3 2000 1,000 2 1 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Sea age (yrs) Sea age (yrs)

Fig 11. Comparison of Tywi and Teifi to show the variation in (A) FLE and (B) gain with age. Gain is the additional eggs incurred by allowing a fish to live beyond its current spawning season. {Comparisons/SH1}

These can be compared with the eggs potentially deposited by an individual of that age in that spawning year (fertility in Fig 11A) and the difference (here termed gain) between the FLE and the fertility is a measure of the additional future egg potential of fish if they were allowed to live beyond the current spawning year. Thus fertility gives the immediate benefit (i.e. in that year), FLE gives the total reproductive benefit and gain is the additional benefit due to the survival pattern of fish after the current spawning year. Gain peaked at age 6-7 on the Tywi and at 5-6yrs on the Teifi (Fig 11B), earlier than FLE. The notion of gain illustrated in Fig 11, shows why FLE is a useful tool, providing information on reproductive value that is not conveyed by annual egg deposition (which is the product of fertility and abundance only).

A. FLE and fertility by size B. "Gain" in FLE by size Tywi Teifi Fertility Tywi Teifi 16000 8,000 14000 7,000 12000 6,000 10000 5,000

8000 4,000 Eggs Eggs fish / 6000 Eggs/fish 3,000

4000 2,000

2000 1,000

0 0 0 1 2 3 4 5 6 7 8 9 1011121314151617 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Mean weight (lbs) Mean weight (lbs)

Fig 12. Comparison of Tywi and Teifi to show the variation in (A) FLE and fertility, and (B) gain with size.

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The modelled growth curve (same for both rivers) is shown in Fig 11B, and it is useful also to consider FLE, fertility and gain in terms of weight (Fig 12A & B), which demonstrates a steady increase in reproductive value at FLE and gain up to about 14lbs and 12lbs respectively, after which fish rapidly decrease in reproductive value as their expectation of future life diminishes. Fig 12 offers a useful index of benefit that would accrue by saving fish of different sizes and also illustrates quantitatively the intuitively obvious point that individual whitling (<2lbs) have low reproductive value. This does NOT imply that the 0yr age group as a whole is unimportant and therefore could be heavily exploited; but it does mean that a higher numerical quota could be set for 0yr olds than for older fish and have the same conservation effect. This information is valuable if alternative size- based quotas are to be considered.

In the case of net fisheries size limits are impracticable, apart from lower limits through mesh size change, but an option is to change effort or season. Effort could be simulated by changing the factors in SH10 uniformly; thus, halving the effort would involve changing all the weight-specific factors for that fishery to 0.5 (the simplest way to show the effect, on deposited eggs for example, is just to halve the recorded values in cells U33:V33 of SH10, or in the case of a complete closure to simply take the egg contributions of the fisheries). Seasonal changes would require examination of the size structure of seasonal runs and appropriately changing the SH10 factors. An alternative way to simulate catch change would be to modify the original rod and or net catches in SH5A and SH2 respectively, BUT note that this would also alter the survival rates and FLE/fish values. This might be preferred, but would impose different survival and FLE values for each regulations scenario which would make comparisons difficult, so is not recommended.

The analyses summarised in Figs 11 and 12 are for individual fish; but the overall population scale effects need to take all fish into account, which is done by the total egg deposition and total FLE numbers (Fig 8). However, even FLE cannot predict what population changes will occur in the long term given changes on fishing pressure, or other factors that affect survival. That requires full life cycle modelling, preceded by life table analysis and taking into account other population regulatory factors such as density dependence, or developmental switching between anadromy and residency, for which this project did not have time, although draft life tables are shown. This is potentially possible now for sea trout (it is common for salmon); but the data quality demands are high in order to accurately parameterise such models.

The technical issues of concern that have arisen in this project and which apply equally to life cycle models are: catch data quality as affected by recording and reporting efficiencies, weight recording, the age/ wt key (which requires intensive scale reading, a practice that warrants development given recent advances in methods and analysis), the understanding of the proportions of fish that remain at sea in their first and second post-smolt years, survival in post-smolt year and in old fish (i.e. incidence of senescence), post-release mortality, fecundity, age-specific maturation rates and sex ratios. Every opportunity should be made to collect such data, through directed research, index rivers, or opportunistically as fish kills or major poaching incidents arise. This reprises a recommendation made by Solomon (1997).

CONCLUSIONS

Pragmatically, annual egg deposition (fertility x abundance) is the most easily understandable metric and gives a useful relative index of immediate fishery impact and total escapement weight also gives also a useful, closely related index. Total egg deposition also offers a directly relevant level of annual mitigation or compensation, if that is appropriate to the particular evaluation context. However it does not give the full reproductive value of fish which is better expressed by FLE and which provides a more informative measure of the benefits of size-selective regulations; so the use of both indices is Reportv4. Final advisable. This analysis of simple reproductive benefits offers improved methods for enumerating and comparing fisheries impact and estimating the benefits of alternative catch controls. It is also a starting point for population models that would offer more options for impact assessment generally.

REFERENCES

Caswell. H. (2001) Matrix population models, 2nd Edition. Sinuaer Associates, Massachussets.

Celtic sea Trout Project (2016). Celtic Sea Trout Project: Technical Report to Ireland Wales Territorial Co-operation Programme 2007-2013 (INTERREG 4A). (Milner, N., McGinnity, P. & Roche, W. Eds.) [Online] Dublin, Inland Fisheries Ireland. Available at: http://celticseatrout.com/downloads/technical-report/

Davidson, I.C., Cover, R.J., Hillman, R.J., Elsmere, P.S., Cook, N. and Croft, A. (in prep) Observations on sea trout stock performance in the rivers Dee, Tamar, Lune & Tyne (1991-2014): The contribution of ‘Index River’ monitoring programmes in England & Wales to fisheries management. In: Sea Trout: Science and Management. (Graeme Harris. Ed.). Proceedings of the 2nd International Sea Trout Symposium. October 2015, Dundalk, Ireland.

Evans, D (1994) Sea trout (Salmo trutta L.): studies of the River Tywi, south Wales. PhD Thesis, University of Cardiff.

Fleming, I.A., Bottom, D.L., Jones, K.K., Simenstad, C.A. and Craig, J.F. (2014) Resilience of anadromous and resident salmonid populations. Journal of Fish Biology 85, 1-7.

Gotelli, N.J. (2008) A Primer of Ecology. Sinauer Associates Inc. Sunderland, Massachusetts.

Hilborn, R., Walters, C.J., 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman & Hall, New York, 70 pp.

King (2007) Fisheries Biology Assessment and Management. Blackwell, Oxford.

Marschall, E.A., Quinn, T.P., Roff, D.A., Hutchings, J.A., Metcalfe, N.B., Bakke, T.A., Saunders, R.L. & Poff, N.L. (1998). A framework for understanding Atlantic salmon (Salmo salar) life history. Canadian Journal of Fisheries and Aquatic Sciences, 55 (Suppl.), 48-58.

Milner, N.J., Potter, E.C.E, Roche, Tysklind, N., Davidson, I.C.D. King, J., Coyne, J. and Davies, C. (2017, in press) Variation in sea trout (Salmon trutta) abundance and life histories in the Irish Sea. In Harris, G.H. (Ed) Science and Management of Sea Trout. Proceedings of 2nd International Sea Trout symposium Dundalk, Sept 2015.

NASCO, 1998. Agreement on the adoption of a precautionary approach. Report of the Fifteenth Annual Meeting of the Council. NASCO, Edinburgh, pp. 167–172.

Solomon, D.J. (1997) Review of Sea Trout Fecundity. Environment Agency R&D Report W60.

Solomon, D.J. (2006) Migration as a life history strategy. In: Harris, G.S and Milner, N.J. (Eds) Sea Trout Biology, Conservation and management. Blackwell, Oxford. Reportv4. Final

Stearns, S.C. (1990) The Evolution of Life Histories. Oxford University Press. 249pp

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APPENDICES

APPENDIX I Outline definition of the terms r, introduced in the life table section (from CSTP 2016)

Population abundance can be described by a simple differential equation. A basic outline of a differential equation is that that over a year the population size (푁) changes by a combination of annual birth rate (푏) and death rate (푑), such that 푑푁⁄푑푡 = (푏 − 푑)푁. Let (푏 − 푑) = 푟, 푟 being a constant called the instantaneous rate of increase or intrinsic rate of increase, then 푟푡 푑푁/푑푡 = 푟푁. This is normally written as 푁푡 = 푁0 푒 , where t = time. If 푟 = 0 the population will remain constant, if 푟 > 0 it will increase to infinity, if 푟 < 0 it will decline to extinction.

For discrete time steps, 푁푡+1 = 푁푡 + 푟푁푡, which rearranged gives 푁푡+1 = 푁푡(1 + 푟).

Let ʎ = (1 + 푟), the population rate of increase, then 푁푡+1 = ʎ푁푡.

ʎ is a positive dimensionless (because it is a ratio) number that measures the proportional change in population size from one time step to the next (frequently measured in years).

Thus, to find the population size in the following year (푁푡+1) from that of the current year (푁푡), simply multiply 푁푡 by ʎ. It can be seen that if ʎ = 1.0 the population remains constant, if ʎ < 0 it will decrease and if ʎ > 0 the population will increase. For completeness, note that ʎ and 푟 are related by 푒푟 = ʎ.

A further important variable of population dynamics is R0, the net reproductive rate, which can be interpreted as the mean number of female offspring by which a female will be replaced by the end of its life. Its units are number of offspring and intuitively if 푅0 = 1.0 there is no population growth, because it exactly replaced itself, if 푅0 < 1.0 the population 퐺푒푛.푇 decreases, and if 푅0 > 1.0 then it increases. R0 is positively related to ʎ, (휆 = 푅0, where 퐺푒푛. 푇 is generation time), but they are intrinsically different: 휆 indicates the population growth per year, while R0 the population growth per generation. 푅0, and ʎ are often used as indices of population “fitness”, the ability of the population to recover from perturbations and in turn related to population features of stability and resilience (Caswell 2001).

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APPENDIX II River Dee age weight key for 2005-2014 Source I. Davidson, NRW, (“Dee Sea trout_age_weight key_ ICD1”). lb values are the class upper boundaries. Shading shows where data were available, thus, no fish in the sea age 8yr category. {FLE.TYWIv4/SH4A}

SEA AGE (raised by Returning Stock Estimates) mid.wt Wt Class (lb) 0 1 2 3 4 5 6 7 8 9 0.5 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.5 2 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.5 3 0.10 0.86 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.5 4 0.00 0.70 0.29 0.01 0.00 0.00 0.00 0.00 0.00 0.00 4.5 5 0.00 0.40 0.54 0.06 0.00 0.00 0.00 0.00 0.00 0.00 5.5 6 0.00 0.10 0.61 0.23 0.05 0.00 0.01 0.00 0.00 0.00 6.5 7 0.00 0.01 0.55 0.37 0.05 0.01 0.00 0.00 0.00 0.00 7.5 8 0.00 0.02 0.34 0.37 0.22 0.03 0.00 0.01 0.00 0.00 8.5 9 0.00 0.00 0.22 0.43 0.24 0.08 0.03 0.00 0.00 0.00 9.5 10 0.00 0.00 0.10 0.38 0.38 0.10 0.02 0.02 0.00 0.00 10.5 11 0.00 0.00 0.11 0.14 0.43 0.27 0.03 0.03 0.00 0.00 11.5 12 0.00 0.00 0.10 0.20 0.40 0.15 0.10 0.05 0.00 0.00 12.5 13 0.00 0.00 0.00 0.17 0.33 0.17 0.17 0.08 0.00 0.08 13.5 14 0.00 0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.50 14.5 15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.5 16 0.00 0.00 0.00 0.00 0.50 0.00 0.50 0.00 0.00 0.00 16.5 17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 17.5 18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 18.5 19 0.00 0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.50 0.00 19.5 20 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 mean wt (lbs) 1.06 3.40 6.26 8.42 12.47 10.62 16.91 15.67 18.50 15.97 mean wt (kg) 0.48 1.54 2.84 3.82 5.66 4.82 7.67 7.11 8.39 7.25

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APPENDIX III Illustrating conversion of Tywi declared rod catches to post net fishery run {FLE.TYWI.v4/SH5} declared TOTAL catches, from {ST.rod.Tywi.Dee/SH2B} catches adjusted for reporting rate post-net RUN = catches adjusted for exploitation rate NB add in lb classes (red) if not represented in original pivot extract NB "no date records are omitted here, not used in further analysis wt.class(lbs) 2010 2011 2012 2013 2014 2015 2010 2011 2012 2013 2014 2015 wt.class 2010 2011 2012 2013 2014 2015 1 1232 1496 869 843 594 1077 1355 1646 956 927 653 1185 1 7789 9457 5494 5329 3755 6809 2 395 371 333 270 348 519 435 408 366 297 383 571 2 2497 2345 2105 1707 2200 3281 3 353 269 227 225 215 406 388 296 250 248 237 447 3 2232 1701 1435 1422 1359 2567 4 308 161 187 162 118 232 339 177 206 178 130 255 4 1947 1018 1182 1024 746 1467 5 177 101 138 116 64 138 195 111 152 128 70 152 5 1119 639 872 733 405 872 6 124 63 108 68 55 64 136 69 119 75 61 70 6 784 398 683 430 348 405 7 59 47 67 31 21 42 65 52 74 34 23 46 7 373 297 424 196 133 266 8 54 31 42 24 15 26 59 34 46 26 17 29 8 341 196 266 152 95 164 9 22 26 23 15 15 15 24 29 25 17 17 17 9 139 164 145 95 95 95 10 16 14 17 14 6 14 18 15 19 15 7 15 10 101 89 107 89 38 89 11 9 15 6 7 10 9 10 17 7 8 11 10 11 57 95 38 44 63 57 12 11 7 6 7 7 7 12 8 7 8 8 8 12 70 44 38 44 44 44 13 5 4 1 1 4 6 6 4 1 1 4 7 13 32 25 6 6 25 38 14 4 1 2 7 4 3 4 1 2 8 4 3 14 25 6 13 44 25 19 15 3 3 3 4 0 3 3 0 3 4 15 0 19 19 0 19 25 16 1 2 3 1 0 2 0 0 3 16 6 0 13 0 0 19 17 1 1 0 0 1 0 0 1 17 0 0 6 0 0 6 18 1 0 0 1 0 0 0 18 0 0 6 0 0 0 19 1 0 0 0 1 0 0 19 0 0 0 6 0 0 20 0 0 0 0 0 0 20 0 0 0 0 0 0 21 1 1 0 0 0 1 0 1 21 0 0 0 6 0 6 22 0 0 0 0 0 0 22 0 0 0 0 0 0 23 0 0 0 0 0 0 23 0 0 0 0 0 0 24 1 0 0 1 0 0 0 24 0 0 6 0 0 0 Grand Total 2770 2609 2034 1792 1479 2567 3047 2870 2237 1971 1627 2824 17511 16494 12859 11329 9350 16228

APPENDIX IV Age distributions for the Afon Tywi sea trout pre-fishery runs, 2010 – 2015. Nx is the abundance of each age class at sea age x. Percentages show the low occurrence (0.2%) of fish older than 7yrs.

RUN AGE STRUCTURE(Nx) PERCENTAGE Sea age 2010 2011 2012 2013 2014 2015 2010 2011 2012 2013 2014 2015 0 10506 11975 7740 7211 6113 10363 56.9 68.8 56.3 58.5 59.4 59.0 1 4276 2962 2983 2794 2338 4316 23.2 17.0 21.7 22.7 22.7 24.6 2 2375 1483 1907 1486 1106 1827 12.9 8.5 13.9 12.1 10.8 10.4 3 788 558 687 477 393 581 4.3 3.2 5.0 3.9 3.8 3.3 4 351 281 285 236 216 308 1.9 1.6 2.1 1.9 2.1 1.8 5 86 85 64 56 61 81 0.5 0.5 0.5 0.5 0.6 0.5 6 34 27 30 19 25 42 0.2 0.2 0.2 0.2 0.2 0.2 7 18 15 22 12 13 25 0.1 0.1 0.2 0.1 0.1 0.1 8 1 1 0 4 2 0 0.0 0.0 0.0 0.0 0.0 0.0 9 21 11 20 26 19 24 0.1 0.1 0.1 0.2 0.2 0.1 Total 18455 17396 13737 12320 10287 17567 100.0 100.0 100.0 100.0 100.0 100.0

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APPENDIX V Summary sheets for Tywi (in (FLE.TYWI.v2/SH1)

FLE.TYWI.v4 SUMMARY ASSUMPTIONS Factor Source RIVER NAME: TYWI rod catch reporting rate 1.1 NRW/EA AREA: SW rod exploitation rate 0.174 NRW/EA model inriver survival, uncaught fish (Sn) 0.9 NRW/EA model inriver survival, released fish (Sr) 0.8 guess, based on salmon

TABLE 1 FISHERIES (2010-2015) IMPACT mean total % mean total % mean total % mean annual eggs % mean FLE lost % METRICS catch (adj catch killed weight killed lost to fisheries to fisheries (m) for (N) (N) (m) reporting) ROD FISHERY 2,429 70 806 44 2047 33 0.933 30 2.602 34 NET FISHERY 1 (coracle a) 659 19 659 36 2984 47 1.590 50 3.540 46 NET FISHERY 2 (seines) 362 10 362 20 1260 20 0.630 20 1.535 20 NET FISHERY 3 TOTAL 3,451 1,827 6,291 3.153 7.676

14.690 TABLE 2 MODEL OUTPUTS Run ("population") Rod fishery nets1 nets2 (seines) In-river losses Actual (killed) (coracles) deposited eggs (m) Variable mean CL (SEx2) mean %of Run mean % of Run mean % of mean % of Run mean % of Run Run Annual survival rate (constant) 41.1 3.9 Potential annual egg deposition (m) 14.690 2.55 0.933 6.4 1.590 10.8 0.630 4.3 1.401 9.5 10.135 69.0 Future Life Time Eggs (m) 43.06 7.49 2.602 6.0 3.540 8.2 1.535 3.6 4.340 10.1 Net Reproductuve rate (R0) 0.87 Intrinsic population growth rate (r) -0.0325

Generation time (yrs) 4.18

Fig 1 Size distribution of killed catch Fig 2 Contribution to killed fish

Rod.kill Coracles Seines Rod.kill Coracles Seines 200 100 80 150 60 100 40

50 20

% to each each to%fishery Mean Mean catch(N) 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Wt class, lbs upper boundary Wt class, lbs upper boundary

FIg 3 Contribution to FLE loss by sea age Fig 4 Fishery contribution to losses 80 Rods Coracles Seines In-river Rods Coracles Seines 60 60 40 40

20

20 Percentage % for each component for % each 0 0 1 2 3 4 5 6 7 8 9 10 Catch.killed Weight killed Annual eggs FLE Sea age (yrs) Metric

Fig 5 Age-specific FLE and egg deposition Fig 6 Tywi quadratic survival model Obs (vertical) Nx Nx.mod Total eggs/run FLE/ind. Total FLE 100000 6.0 16 5.0 14 10000 12 4.0 10 1000 3.0 8 100 2.0 6 4 10 1.0

2 (Nx) Abundanceage at

Annual eggs (millions) Annualeggs 0.0 0 1 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 (millions) FLE Total ('000s), FLE/ind. Sea age (yrs) Sea age (yrs)

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APPENDIX VI Summary sheet for Teifi (in FLE.TEIFI.v2/SH1)

FLE.TEIFI.v4 SUMMARY ASSUMPTIONS Factor Source RIVER NAME: TEIFI rod catch reporting rate 1.1 NRW/EA AREA: SW rod exploitation rate 0.13 NRW/EA model inriver survival, uncaught fish (Sn) 0.9 NRW/EA model inriver survival, released fish (Sr) 0.8 guess, based on salmon

TABLE 1 FISHERIES (2010-2015) IMPACT mean total % mean total % mean total % mean annual eggs % mean FLE lost % METRICS catch (adj for catch killed weight killed lost to fisheries to fisheries (m) reporting) (N) (N) (m)

ROD FISHERY 2,374 77 640 48 989 31 0.354 25 0.783 28 NET FISHERY 1 (coracle a) 555 18 555 42 1823 57 0.883 62 1.691 60 NET FISHERY 2 (seines) 134 4 134 10 393 12 0.182 13 0.354 13 NET FISHERY 3 TOTAL 3,064 1,330 3,204 1.420 2.828

TABLE 2 MODEL OUTPUTS Run ("population") Rod fishery nets1 nets2 (seines) In-river losses Actual (killed) (coracles) deposited eggs (m) Variable mean CL (SEx2) mean %of Run mean % of Run mean % of mean % of Run mean % of Run Run Annual survival rate (constant) 29.8 3.1 Potential annual egg deposition (m) 9.761 1.31 0.354 3.6 0.883 9.1 0.182 1.9 0.989 10.1 7.352 75.3 Future Life Time Eggs (m) 21.88 3.12 0.783 3.6 1.691 7.7 0.354 1.6 2.264 10.3 Net Reproductuve rate (R0) 0.50 Intrinsic population growth rate (r) -0.1925

Generation time (yrs) 3.78

Fig 1 Size distribution of killed catch Fig 2 Contribution to killed fish

Rod.kill Coracles Seines Rod.kill Coracles Seines 200 100 80 150 60 100 40

50 20

% to each each fishery to% Mean Mean catch(N) 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Wt class, lbs upper boundary Wt class, lbs upper boundary

FIg 3 Contribution to FLE loss by sea age Fig 4 Fishery contribution to losses 80 Rods Coracles Seines In-river Rods Coracles Seines 80 60 60

40 40

20 Percentage 20 % for each component for % each 0 0 1 2 3 4 5 6 7 8 9 10 Catch.killed Weight killed Annual eggs FLE Sea age (yrs) Metric

Fig 5 Age-specific FLE and egg deposition Fig 6 Quadratic survival model Obs (vertical) Nx Nx.mod Total eggs/run FLE/ind. Total FLE 100000 6.0 16 5.0 14 10000 12 4.0 10 1000 3.0 8 100 2.0 6 4 10 1.0

2 (Nx) Abundanceage at

Annual eggs (millions) Annualeggs 0.0 0 1 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 (millions) FLE Total ('000s), FLE/ind. Sea age (yrs) Sea age (yrs)

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