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Approach to Fisheries Assessment

L. M. Dickie, S. R. Kerr, and P. Schwinghamer Department of Fisheries and Oceans, Biological Sciences Branch, Bedford institute of Oceanography,

Dartmouth, M.S. B2Y4A2

Dickie, b. M., S. R. Kerr, and P. Schwinghamer. 1987. An ecological approach to fisheries assessment. Can. ). Fish. Aquat. Sci. 44 (Suppl. 2): 68-74.

Deductions based on recent ecological information suggest that while current fishery assessment metho- dology has captured the main features of fishery production, it may not well anticipate the effects of early natural mortality or of major changes in fishing. We propose here a new methodology based on ecological theory related to a characteristic biomass size spectrum. Theoretical considerations coupled with empirical data on population production appear to take into account high natural mortalities at small sizes and the effects of spatial distribution on production parameters throughout the life history. The resulting models offer a somewhat modified view of the relation of fishery yield to effort and the prospect of population assessments with more modest data requirements.

Des concBusions tirees de recentes donnees ecologiques portent 3 croire que m$me si %a methsde actuelle dr6valuatican des peches ewglobe les principales caracteristiques de la produdion halieutique, elle peut ne pas bien anticiper %es incidences d'une mortalite naturelle precoce ou d'importants changements de la psche. bes auteurs presentewt une ncsuvelle methode basee sur la theorie 6coilogique relative a unegamrne caracteristique de tailles de la biomasse. Des facteurs theoriques jumel6s ii des donnees empiriques sur la production d6rnographique sernblent tenir compte de taux &!eves de mortalit6 naturelie des individus de petite taille et des incidences de la repartition spatiale sur les parametres de pr~duction pendant tout le cycle vital. Les rnodeles obtenus offrent un expose quelque peu rnodifie de la relation entre le rendement et I'effort et la possibilite d'evaluer des populations avec moins de dopenees.

Received November 13, 198.5 Accepted March 3 1,1987 (J8564)

odels underlying the assessment of potential fisheries production are intended to describe yield in tems of parameters subject to management manipulation or control. The Beverton and Holt (1957) formulation

of yield-per-recruit in relation to size and fishing rate was a landmark of clarity, built on a respectable legacy of studies by Bafmov (1918)' Thompson and Bell (1934), Ricker (1940, 1945, 1954), and Schaefer ( 1954). Differences among these models have been chiefly in the handling of the production functions. However, as pointed out by Ricker (19'75) in his discussions of Lee's phenomenon, certain obscurities have been persistent, and in general the models have not been satisfactorily comprehensive. For example, growth rate was sometimes cons- idered as the equivalent of the aggregate of individual (physiolo- gical) growth rates, and sometimes as the net population (ecolo- gical) growth which took into account size-selective mortality. Nonfishing mortality has been generally treated as a constant. Recruitment functions, where they are considered explicitly at all, have fallen into two classes, the "average carrying capacity" or yield-per-recruit approach, which has Iow predictive capac- ity, or the more analytical "stock-recmitmenB" approach, which requires much data. Fishing mortality rates have also been treated as uniform within the gear-selection range and as exoge- nous variables which vary free from interactions with the rest of the system. The full consequences of these artifices have not yet been well appreciated.

Through experience with management, there has grown a confidence that the logical analytical systems developed for

Regas le 13 novernbre 7985 Accept6 6e 31 mars 6987

these partial models often predict short-term yield changes of the right order of magnitude. However, two problems have become more serious as fishing intensities have grown. The first is that the precision with which the manipulable parameters can be estimated is generally low, so that effective control of inten- sive fisheries in real-time t ems is very demanding of costly data. The second is that the models lack an established basis either in ecology or in the socio-economic aspects of fisheries, so it is impossible to use them to extrapolate beyond the realm of present experience into suspected m a s of critical interactions, or to help redefine long-term management policy objectives.

In response to these problems, there has been a renewed interest in the study of the properties of existing models, both to find relief from their insatiable data demands (e.g. Shepherd 1982a, B982b) and to identify system properties which might support extrapolation (Allen and McGlade 1986). At the same time, information on ecological systems has been growing rapidly (Sheldon et al. 197'7; Spmles 1980; Schwinghamer et al. 19861, leading to the speculative development of new prduc- tisn models (Blatt and Denmm 1977, 19'78; Bsrgman 1982, 1983, 1987) in relation t s certain properties of the component organisms. In this paper we offer an ecological rationale for assessment models, based on new infomation on the relation of body size in marine organisms to physiological and ecological scaling factors that underlie the rate of production. W i l e the models we suggest we still in quite elementary form, the general ecological infomation on which they are based permits the development of exemplary production functions that depend

68 Can. .I. Fish. Aqucmb. Sci., Vol. 44, 6987

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explicitly on life history aspects of growth and mortality of particular groups of species. We describe fish population yield models based on these relationships. The results provide a measure of the sensitivity of predicted yield to known ecological interactions and offer the prospect of more reliable extrapola- tion. If they can be verified, the generalizations would carry the supplementary benefit of reductions in data requirements.

Formulation of the Models

Earlier biological production models were constructed on the trophic level principle outlined explicitly in Lindeman (1942). Over a specified time period the yield C, to a predator at trophic level rt + 1, from the average biomass B of a prey population at trophic level n, is expressed as

where C,+ is the catch or yield to the predator, F,+ is the fishing mortality rate generated by that predator, and B, is the average biomass of the prey. The specific rate of production of the population (production per unit time per unit biomass) is defined as Pn/Bn, which in a stable population is equal to the total mortality rate, Z, = Pn/Bn = (F, + + Mn), where Mn represents population deaths that lead directly to the biological decomposition cycle. In addition, we define P, = KnCn where Cn is the food intake (catch) by the prey organisms from their own food supply at trophic level n - 1 and K, is the gross production efficiency of fosd use by the population. Equation (1) can then be written in the form

As pointed out by Dickie (19721, the ratio C,+ l/C, is precisely the "eco~ogical efficiency" as defined by Slobodkin (1963). Hence, by substitution and transposition, we define

or comparably

That is, ecological efficiency or its related production efficien- cy, defined as the ratio of yields or productions in successive trophic levels, is a function of three parameters on which there is a growing body of infomation. Of equal importance is the fact that we may write in parallel with q. (2) and (3) (Dickie 1976).

B, (4) --- =F. ( f ) Kn.

Bn- 1 n

That is, factors underlying ecologicd and production efficiency may be expressed in terns which are the equivalent of the ratio of the average biomass at two successive trophic levels. Ex- pressing these important ecological ratios in terms of equivalent biomasses has the added advantage that the underlying variables are referable to a single trophic level, avoiding many of the difficulties and dangers of ambiguity in sampling and inteqreta- tion which arise in attempts to measure ecological efficiency directly. As pointed out by Dickie et al. (1987), the equations in this form make it possible to use current and growing infoma- tion on the biomass size spectrum of bodies of water to deduce

effects on yield in relation to specified features of the dynamics sf the populations. In what follows, we describe features of the biological dynamics of populations which permit the fitting of these ratios as yield equations, leading to the assessment of yield potential, using accessible data.

Evaluating Parameters of the Biomass Spectrum

Application sf the ecological equations to actual populations requires that there be stability in the observed stocks sufficient to permit estimation of parameter values from sampling. Stable population abundance appears to be a rarity in most fished stocks. However, Humphreys (1979) has shown that when species are considered in groups classified according to average body size, their production to respiration ratio per unit area of habitat is remarkably constant, and Banse and Mosher (1980) have shown that within similar groups the specific rate of pro- duction per unit area is significantly related to body size. Ear- lier, Ricker (1975) showed that, despite abundance fluctuations, when successive cohorts of fish are followed throughout their fishery history, catch curves of characteristic slopes can be constructed, and recent data suggest that survival rates of natural marine populations are under overall genetic control (Dickie et al. 1984; Doyle and Hunte 1981; Mallet et al. 1986). These findings, together with the more generally recognized stability of fishery yield despite fluctuations in the component species (Sutcliffe et al. 1977; Regier 1973; Pauly 1979; HoHden 1978), give reason to suppose that realistically stable values sf dynamic production parameters can be derived from stock data averaged over specified time periods.

Dickie et al. (1987) have reviewed the evidence for depen- dence of the parameters of the biomass spectrum (eq. 4) on body sizes of the component organisms rather than on trophic level. This evidence consists of a number of studies of the production efficiency, K, the specific rate of production, P IB , and the rate of mortality, F , on a unit area basis. Data compiled on many different natural populations of aquatic and terrestrial organisms have demonstrated a remarkable stability of these relationships with body size over many different environments and types of organisms, despite fluctuations in total abundance. For exam- ple, Humphreys' (1979) study of populations of 235 species of organisms established that when the species were classified into seven quasi-taxonomic (functional) groupings (three groups of poikilothems and four of homeotherms), the net production efficiency was constant within groups. That is

where P is the rate of production and R is the rate of respiration per unit area. The parameter a takes different values for the different groups, but within groups is independent of body size, habitat, or the size of the production or respiration. In the data examined, all fish species fell within a single group.

In a parallel but independent study, Banse and Mosher (1980) found that when the various species were classified into groups, there was a remarkable constancy in the relation of the specific rate sf production per unit area to the average body size of the component species. Their equation could be expressed in the form

where w is body mass and the fitted expontial term, e, was constant at -0.37 within groups. The value of b differed among

Can. 9. Fish. Aqwt. Sci., V06. 44, 1987

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groups, but again all fish species examined fell within a single group.

Schwinghamer et. al. (1 986) studied additional groups of luge and small species of invertebrates from the marine benthos and found that within two ecological groups, one a rneiofauna group living in relation to the sand grains and the other a macrofauna group living in s r on the substrate, the weight exponent of the PlB relation was approximately the same as that determined by Banse and Mosher (1980). However, if the ecological groupings were disregarded, the overall weight expo- nent was different, of the order of -0.2. Dickie et. al. (1987) pointed out that this is also true of the overall weight exponent derived from Banse and Mosher's data when the groupings are disregarded. They also pointed out that the overall weight expo- nent is not different from that derived by Hernrningsen ( 1 9601, which is accepted as reflecting the well-known physiological metabolic rate to body size relationship.

In a later study, Humphreys (198 1) described the relationship between production and an index of prey utilization, within the same functional animal groupings studied earlier. These data amplify the Banse and Mosher findings and verify that within the groupings the weight exponent of specific production per unit area of natural habitat has a steeper negative slope than would be expected from a consideration only of physiological properties reflected in the rate of metabolism of the component animals, and may in fact have a somewhat steeper negative slope than was found by Banse and Mosher.

Taken together, these new considerations of the productivity of natural populations (i .e . per unit area of environment) suggest two important conclusions for the rnode$ling of fisheries produc- &on. The first is that by specifying the body size of the orga- nisms and the general functional grouping to which they belong, it is possible to evaluate the principal dynamic components of population production without the need to specify the trophic level. It appears in this connection that the general grouping to which an organism belongs is also specified by its body size.

The second major conclusion emerging from these studies is that the body size scaling of production is not a simple function of the physiologically determined metabolic rate in relation to body size. That is, the steeper negative slopes of the weight exponent within groupings of organisms apparently reflect spe- cific features of the distribution of the living biomass in the environment (see also McGurk 1986). This distributional effect may well be termed an ecological scaling factor of production.

The interpretation and significance of the ecological scaling may be more readily appreciated if we juxtapose the Humphreys (1979) and Banse and Mosher (1980) conclusions in the identity...