AN INTRODUCTION TO STOCK ASSESSMENT TECHNIQUES.

J.A. Gulland Department of Fisheries FAO, Rome, Italy

ABSTRACT

An outline is given of the purposes of ~ockassessment - to give early gfiidanke to the development of new fisheries, and to advise on management of heavily exploited stocks. The methods of assessment for the latter purpose are well established - analysis of catch and effort atatistics and of the gxwth and mortality of the fish. Methods are also being developed to pro- vide estimates of the potential yield of fish stocks before exploitation ie much advanced - by trawl surveys or with acoustic methods, etc. The estimates may be less precise than those obtained by other methods, but being ~btainableearlier, may also be more valuable, particularly for developing countries.

THE,USE OF STOCK ASSESSMENT

In any fishery advice on stock assessment is needed. The form of the advice changes as the fishery develops. In the early stages the advice needed is: what sort of fish are present, and are there enough of them to invest in vessels, shore facilities, etc.? Later the question is whether the stocks are big enough to stand further expansion in fishing - which should therefore be encouraged - or whether such an increase in effort would cause an appreciable fall in catc~lper unit effort, and result in little increase in total yield. Finally, in a heavily fished stock, the problem is whether management measures should be introduced to regulate the fishery, and if so, which.

Proc. Indo-Pacif ic Fish. Coun. , 14(11) : 24-35. The demands for accuracy vary. In the beginning a fairly rough answer can be useful - if it is known that the stock can yield between 20,000 and 100,000 tons, this is good enough for a decfsion concerning initial plans of catches sf only a few thousand tons. On the other hand, management of a fishery, e,g. by means of a catch quota, requires precise estimates, perhaps rithPn 5 or 10 perceht.

Stock wsessment, as Smet5jnw understood, is cohcerned with the 1-t: phase --the precise eatimates required for the management of heavily fished stocks. Certainly the bulk sf the scientific literature on emck assessment has been concerned with this aspect. However, the practical value of rough advacs sufficiently early in the fishery to discourage too great investment in the exploitation of a small stock may be as great, or greater. As has been pointed out by ~lv&sonand Berey~a(1969) many scientific assessments have been dona coo late, and are merely post-mortems on fisheries that have got into great difficulties.

The greateat present need Ps not so much precise and accurate assessment of a heavily exploited stock, based on long series of extensive data, but early and perhaps rather rough advice on which the fishing in- dust ry can avoid expensive mistakes (Gulld, 1970),

Stock assessment studies must, if they are to provide this early advice, include the study of all potential sources of quantitative data on fish potential, not merely the analysis of catch and effort.data, r,iortality rates, etc.

POPULATION DYNAMICS

Biscussion of stock assessment methods is best starred ~5ththe above classical methods, using the techniques of population dynamics. These have been set out in many well known papers and manuals (Ricker , 1958; Schaefer, 1954; Beverton and Holt, 1957; Gulland, 1969), and need not be discussed in detail here.

The most complex and ultimately most reliable methods, and ones which give the best understanding of what is happening to the fish stocks, are those based on a study of the growth, mortality and recruitment rates. In temperate waters these studies are faily easy - provided fads are available for collecting the necessary data - since the age of individual fish can be determined from scales or otoliths. Then the growth can be determined from quite a small sample of fish. Mortality rates require more extensive sampling; also there are theoretical difficulties in se- timating the true mortality rates of the population from samples. These samples, whether originating from catches or landings of commercial vessel6 or from research catches, are bound to be biassed. All fishing gear is selective and all information from catches must be interpreted in the light of what is known about the selectivity of the gear used. The best hope is that for the range of sizes or ages of interest the selection is not great, e.g. that as of ten assumed though not proven for trawls, there is little selection for fish above a certain size, determined by the size of the mesh of the nets.

The second problem relating to mortality is the separation of the total mortality (estimated, say, as the rate of decrease of successive age-groups observed in samples) into the mortality due to fishing, and that due to other causes (natural mortality). Most of the methods used depend on correlating certain changes in the stock - the mortality rate itself, or the average size of fish, the catch per unit effort, etc. - with changes in the amount of fishing. Given the normal degree of un- certainty in estimates of these quantities, reliable reparation of natural and fishing mortality requires either a long series of data, or very big changes due to fishing. Neither of these requirements is likely to be fulfilled in the early stages of a fishery, and without the separation of the two causes of mortality, and hence the determina- tion of how much fishing, in terms of weight caught, or number of vessels, corresponds to a particular level of fishing mortality, it is difficult for this form of stock assessment alone to provide early guidance about the state of the stock.

Separation of natural and fishing mortality is, of course, possible when the latter is known to be zero, i.e. in an unexploited stock. The difficulty here is not so much"in deterxiining that the maximum yield would be taken with a fishing mortality of, say, 0.45, but of determining, in absolute terms, what this yield would be, and what fishing effort (in terms for example of number of days fishing) would be required to produce this fishing mortality.

Estimation of recruitment, and more particularly the study of its possible variation, raises special problems. The critical question is whether fishing, by reducing the average population of adults, can significantly affect the average number of recruits entering the fishery. In nearly all marine fisheries this question remains unanswered. For elasmobranchs, producing only a few young per female,reduced adult stock has resulted in reduced recruitment. The same is true, though the decrease seems less shayp, for salmon, where the number of eggs produced per female is a few thousand.

Most marine fish produce many more eggs, so that the mortality in the first few months of life is very high. It only requires a small change in this to balance quite large changes in adult stock e.g. a change from 99.98% mortality to 99.96% mortality could balance a halving of adult stock. For a limited number of stocks, e.g. North Sea plaice (Beverton, 1962) it has been shown that over quite a wide range of adult stocks the average recruitment varies very little. For a few others there are sug- gestions that recruitment decreases at levels for adult stocks likely to be encountered under moderate to heavy fishing. For most, however, the available evidence is quite inconclusive, largely because of the large fluctuations in recruitment (year-class strength) due to causes other than variations in adult abundance. Failing better information it is usually most convenient and probably quite realistic to treat recruit- ment as being independent of adult stock, at least during the early stages of exploiting a fish stock.

Once estimates of growth, mortality (split between natural and fishing) and recruitment have been obtained, assessment of the state of the stocks, and the possible effects on catches of changes in the fishery (especially increases in.fishing effort) can be made directly. The actual calculations can take various arithmetical and algebraic forms, but the concepts are the same. The fate of a brood of young fish entering the fishery is examined, usually taking each successive period of life (e.g. a month or year) separately. During each period an individual fish may be caught, or die from natural causes, or it can survive until the beginning of the next period. The number dying and surviving can be calculated from the mortality rates for each period in succession. The weight caught can be calculated as the sum of the number caught in each period, multiplied by their average size (given by the growth pattern).

These calculations can be repeated for any pattern of fishing (different fishing mortalities, and ages at which fishing starts, which will be determined by the selectivity of the gear). The effects on catches, of any changes, especially increases in the amount of fishing can then be assessed.

A great merit of this approach is that it clearly separates the characteristics of the population dynamics of the fish stocks which are directly affected by fishing (the fishing mortality, and the ages over which it operates) from those which are more nearly independent of fishing (growth,natural mortality and recruitment). This can greatly assist the discrimination between fishery - dependent and fishery-independent changes in the stocks. For example an observed decline in the stocks caused by heavy fishing must, at least initially, be due to increased fishing mor- tality. If the observed total mortality has not changed, then other factors are at work, e.g. an environmentally caused decline in recruit- ment. These concepts can still be used when the ages of individual fish cannot be determined. Analysis of the length distribution can yield similar information as the analysis of age distribution. In particular the slope of the right hand limb of the length distribution will be closely related to the mortality. In fact, if the growth is linear (which it often is to a close approximation over quite a wide range, including most of the sizes taken in a moderately exploited fishery) the slope will be proportional to the mortality. It is then possible to carry out analyses similar to those outlined above, using as a unit of time not a year of a month, but the period (unknown) which a fish takes to grow 1 cm. Provided this arbitrary unit of time is used consistently in the analysis the conclusion will be correct.

Another,approach to population dynamics is to treat the population as a simple unit, ignoring its structure (age composition etc.). The population may then be considered as subject to simple laws of growth i.e. assuming that the natural rate of growth - the increase in population per unir time in the absence of fishing - is a simple single-valued function of the population abundance. The growth will be small at small population sizes, and again small at population sizes, when the abundance is approaching the maximum. The rnaxfmum growth will then occur at some moderate population abundance. If the catch is equal to the natural growth then the population size will remain constant - the sustainable yield is being taken.

This method can be applied by assuming some form for the population growth e.g. the logistic (Schaefer, 1954). In this the general relation

when y = natural papulation increase sustainable yield

B = population abundance, or biomass, is assumed to be of the form

when a = constant

Bo = maximum, unexploited biomass.

One method of fitting has been described by Schaefer (1954), in which the equilibrium catch Y is estimated for each year as the observed catch plus the (positive or negative) change in the population.

Alternatively the biomass may be estimated as being proportional to the catch per unit effort, i.e. in the steady state situation, we can write Y B=bif where f = fishing effort, b = constant bY end hence Y = B(B*- /f)bTf B where c = ~/b

That is, if the catch per unit effort is blotted against the fishing effort, the result should be a straight line. This can be readily fitted to the observed data, and hence the relation between effort, catch per unit effort, and also catch, can be determined.

Often, if this is done for a fishery in which the fishing effort has varied over a wide range, it has been found that a straight line does not fit well. A better fit is generally a line concave upwards. It may therefore be preferable to obtain a purely empirical relation between fi~hing~effort,and catch per unit effort (and hence catch) by drawing a curve by eye through the observed points.

One disadvantage of this procedure, using simply the pairs of values of effort and catch per unit in the same period, occurs when the fish are fairly long lived. Then, in any one year, there will be fish of several year-classes present in the fishery. The abundance of the older fish will be determined as much by the events in previous years as by the fishing effort in the current year. The catch per unit effort in one year should, therefore, be related to the average fishing effort over some longer period, extending back from the current year. k sug- gested duration is equal to the average duration of life in the fish in the fishery.

MULTI-SPECIES FISHERIES

The above analyses are directly applicable only to single species. In tropical areas, and increasingly in other areas, fisheries are based on a whole range of species. Even when a fishery may be species-selective, other fisheries in the same area may be exploiting other species which interact to a greater or lesser extent. For instance in the Gulf of Thailand the trawlers catch very many species, while the mackerel fishery in the same area, using a variety of gears, catches almost entirely Ras&rcZZ

where Mo, No are the mortality rate and predator abundance in the unfished state.

Almost certainly, presently available data are not sufficient to apply these ideas in a quantitative manner, but they provide a guide to the sorts of interactions that might occur, and how they might be detected in the data, e.g. fishing on predators of the young may appear as im- proved recruitment, fishing on competitors as better growth, etc.

The more urgent problem of multi-species analysis concerns a fishery on several species. In principle this could be handled by analysing the data separately for each species, taking into account any interactions, and adding the results together, for any combination of fishing effort and (for trawls) mesh size, to give the total catch. This has been dane, for example, for the combined cod, haddock and plaice fisheries in the North Sea by Beverton and Holt (1957). For more than a handful of species this approach becomes impossibly complicated, even without taking into account possible interactions. For the Gulf of Thailand trawl fisheries, and similar fisheries based on a very large number of spdcies, the only practicable analysis at present is one that treate the species complex as a whole, to examine the overall catch per unit effort, and to relate this to the total effort and hence determine empirically (as done above for a single species) the relation between total effort and the combined catch of all species.

Though the main reason for doing this is the immediate practical one that this is the only method presently available, this may also have theoretical advantages over a species by species analysis. In the latter, all the interactions have to be estimated and then incorporated into the calculations, dut in the former the interactions, or at least the short- term interactions, are taken into account, That is, the observations are of the final effect of fishing, ooth direct and indirect. Also if a number of species, or groups of species are caught in the same gear and sold in the same market, there may be no important practical need for assessing each species separately. The interactions between species, and the possibly rather un- expected effects tfiese may have on the apecies composition of the catch, should not be ignored. In many areas studies on changes in species com- pasition are made difffcult through the absence of good data on the real species composition of the stocks. Typically, fisheries are selective, not only in such obvious ways as the release of small fish through the meshes of trawl, but also amall differences in the way the gear 9s rigged, or in the grounds being workedo The preferred species are, therefore, averrepresented in the catches, As the initially preferred species are reduced by fishing, the preference may shift to a second group of species. This causes a change in the tactics of the fishermen - amall shifts in the grounds fished, or in adjustments to the gear - which will cause the catches sf the second group of species to rise, and those of the first group to fall. Thus changes in the sea are likely to be exaggerated in the commercial 'catches.

.In complex multi-species fisheries regular routine surveys by research vessels, using standard gear, can be invaluable in monitoring the real changes in the fish stocks. Surveys are particularly valuable when they are made before large-scale ffshfng starts, as was done in the Gulf af Thailand (Tiews --et al. 196%)

All the above methods depend on observing changes in the fish population (reduced catch per unit effort, increased mortality, etc. ) as a result: of exploitation. They are' suitable for an analysis of past meats, and for predictions of the reeult of increased fishing in a developed fishery, but are not useful for predicting future conditions in a new fishery, However, the aeeuracy and reliability of laterbassessments, after the stock has been completed for a period, depends critically dn the existence of good data from the early period of light fishing on such things as cat& per unit effort, and size compositdLon, Therefore one im- portant function of the fishery scientitits, from the beginning of any f iehery, is to ensure the collection of adequate data, even though most of it ~$11not be used for m'inking assessmehts for some timeo

As already pointed out, another and equally important function of a fishery scientist is to give early, even if rather rough, assessments of the potential yield and desirable level sf fishing effort 9n a new fishery. This requires--a different approach. One method is ,to esthate potential yield by comparison with other areas ; another is t& estimate the standing stock and from this estimate the potential yield..

Relations between standing crop, or yield, and vartious readily measurable characteristics of the body of water concerned have been established in an approximate manner for some types of fresh' water laices and reservoirs (Ryder 1965, Jenkins 1968). So far, no similar relations have been proposed in any detail for marine fisheries. In a general review of the fish resources of the world (Gulland, 1.97Oa) , it appeared that, over broad areas of the oceans, the potential yield of demersal fish per unit area varied only within fairly narrow limits (between about 1.0 and 3.5 tons per km2 of water less than 200 m deep). There is a greater range of values if particuLarly smaller areas within the broad regions are con- sidered (e.g. up to 5 tons per km2 in the Gulf of Thailand and in the North Sea). On the other hand, much of the variation can be accounted for in at least a qualitative way by observed differences in hydrographic and similar conditions (existence of upwelling, etc.). Estimates of pelagic stocks vary more, though some of this variation may be due to difficulties in estimation.

Further studies of this matter are clearly needed, but it does appear that a figure of around 2 tons per km2, adjusted upwards or down- wards in the light of what is known of the physical or biological con- ditions in the area, will give a useful first approximation to the po- tential annual catch of demtrsal fish in an area.

This approach of course does not provide any information on the species of fish that might be caught. Such information must come from some form of direct survey. Methods of surveying fish stocks have been recently reviewed in the FA0 Manual of methods?for'fi2heries resource survey shortly to be published.

The methods described in that manual will not be repeated in detail here. 1'wo methods appear to be particularly useful, and are dis- cussed extensively. Trawl surveys are good for fish on or near the bot- tom. However, they include an element of uncertainty in determining absolute abundance (numbers or weight per unit area) from the data of catch per unit fishing time. The area of bottom covered by the trawl in unit time can be measured, and hence the catch expressed as numbers per unit area, if a value is assumed for the percentage of fish in the area covered by the trawl which are caught by it. If the fish concerned are truly bottom fish, i.e. are mostly no further off the bottom than the headline of the trawl, this percentage is likely to be fairly high (perhaps 75-90%). The other method of surveying - by acoustic methods - is parti- cularly suited to fish off the bottom. Qualitative acoustic surveys, which show the presence or absence of echo-traces, have been used for a long time. More quantitative techniques and equipment are now being developed which will enable the number of targets of different strength, i.e. fish of different sizes, in a known volume of water to be counted. Jith the addition of occasional fishing on traces for species identifi- cation, these counts can be easily converted to estimates of absolute numbers or biomass of each major species in the area. The accuracy of both types of survey can be improved by the use of the usual statistical techniques, for example by stratified sampling, in which the region to be surveyed is divided into fairly homogeneous subareas on a basis of depth, bottom type6 etc., and each sub-area is sampled and analysed separately.

Certain other methods, e.g. surveys of egg or larvae, can be used to estimate abundance, but they are less direct that the above methods. The techniques involved, e.g. estimating the numbers of adult females as the numbers of eggs laid divided by the average fecundity, are likely to be most useful when much of the field work has been already done, or is carried out partly for other purposes. For instance, there exists numerous collections of egg and larval data which could usefully be analyzed for fishery purposes, but ship's time used specifically for egg surveys would probably be better used for acoustic or fishing surveys.

Whatever method is used, survey techniques will, at best, 2roduce an estimate of. biomass, or standing stock, with greater or less detail on the species concerned, and the size and age composition. The biomass is clearly related to the more important quantity, which is the potential annual yield. The ratio of the two will depend on the average life span, and replacement rate, of the fish. A long-lived species will have a large biomass (the contribution from many year-classes) compared with a short lived species with the same annual production and potential yield. That is, the potential annual yield Y is likely to be proportional to both the unf ished biomass Bo and the turn-over rate. The latter might be measured by the natural mortality rate M. Mathematically, we can write

where

a = constant

Some theoretical studies (Gulland 1970a) suggest that the value of a is around 0.4-0.5, so that a first estimatk of the annual yield can be obtained as

and M can be estiglated as the total mortality rate of the unexploited stock, as found, for example, in survey catches.

It should be noted that if a fishery develops rapidly, and the fish concerned are long-lived, the catches in the initial years can be higher than can be sustained even under optimum management. l'llis is because the early catches will include a contribution from the removal of the accumulated productiori of many years, in addition to the ncl: production (growth plus recruitment) during the year of harvest. A fall in total catch is a clear sign that management measures are required, but it may be impossible for any measure to restore the catch to the level of the peak year.

REFERENCES

Alverson, P.L. and W.T. Pereyra (1969). Demersal fish exploration in the Northeast Pacific Ocean: an evaluation of exploratory fishing methods and analytical approaches to stock size and yield forecasts. J. Fish. Res.-. Bd. Can.,- 26(8): 1985-2001. Beverton, R.J.H. (1962). Long-term dynamics of certain North Sea fish populations. In The exploitation of natural animal populations, edited by E. ~.xeerenand M.W. Koldgate, Oxford, Blackwell, Scientific Publications, pp. 242-259.

and S.J. Holt (1957). On the dynamics of exploited fish populations. Fishery Invest., Lond. (11) , (19) : 533? , , YP Gulland, J.ri. (1969). Manual of methods of fish stock assessment. Pt . 1. Fish population analysis. FA0 Man. Fish. Sci ., (4) : 154 pp ,

(1970). Science and fishery management. J. Cons. Int. Explor. Mer., 33 (3). ------(1970a). (~omp.)(Ed.). The fish resources of the ocean. FA0 Fish. Tech. Pap., 97: 425 pp.

Jenkins, R.M. (1967). The influence of some environmental factors on standing crop and harvest of fishes in U.S. reservoirs. In Reservoir Fishery Resources Symposium, American ~isheries- Society, Reservoir Committee Southern Division, Athens, Georgia, pp. 298-321.

Ricker, W.E. (1958). Handbook of computations for biological statistics of fish populations. Bull. Fish. Res. Bd. Can., 119: 300 pp.

Ryder, R.A. (1965). A method for estimating the potential fish production of north temperate lakes. Trans. Am. Fish. Soc., 34(3): 214-218. Schaefer, MOB. (1954). ' Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull. Inter-Am. Trop, Tuna Commn., l(2) : 26-56.

Tiews, K., P. Sucondhamarn and A. Isarankura (1967). On the changes in the abundance of demersal fish stocks in the Gulf of Thailand from 1963/64 to 1966 as a consequence of trawl fishery develop- ment. Csntr. Mar. Fish. Lab. Dept. Fish,, Bangkok, 8: 38 PP*