An Ecological Approach to Fisheries Assessment

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 methodology 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 considered as the equivalent of the aggregate of individual (physiological) growth rates, and sometimes as the net population (ecological) 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 capacity, 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

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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 extrapolation. 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 efficiency, 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 infomation 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 production 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 dependence 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 example, 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

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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 exponent 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 exponent 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 organisms 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 specific 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 equation

P P B - (7) - - - x - 0

R B R

Since PlR is constant within a group and Banse and Mosher (1980) and Dickie et al. (1987) have shown that within such a group, P/B = bw" where c takes a value of about -0.4, it follows ha t BIR, which represents the biomass per unit respiration per unit m a , must be related to individual organism weight by m exponent of about 4-0.4. This value is different from the value of a b u t 0.2 which would be expected s n the basis of the well-known relationship between metabolism and body size a d appem ts reflect size-redated features of the biomass density distribution in natural populations. It may be related to the cbmging costs of predation md assirnilation in populations sf

different average body sizes. These and similar relations that have been determined from studies of territoriality in grazing populations have been reviewed by Dickie et al. (1987), and their ubiquity attests to the generality of an ecological scaling factor in relation to body size. In fact, similar considerations of scaling in relation to body size apply to all three of the dynamic components underlying the efficiency ratios in eq. (21, 4 3 , and (4).

It must be concluded from the foregoing that a primary ~ a l i n g of production is related to physiological processes reflected in the overall relation of specific production parameters to body mass, w4.20 to w ~ - ~ ~ . The secondary or ecological scaling factor which appears within groups of a limited average body size range is reflected in the within-species-group body mass exponent values of about w4.". There is reason to suppose that a tertiary scaling may exist for ranges of body size within individual species. For example, McGurk (1986) has found that over their small size range the turnover rates of fish eggs and larvae have a mass exponent of over -0.8 and that this steep slope is at least partly explained as a result of spatial aggregations in their distribution . S irnilarl y , B Arnstedt and Sk~oHdal(1980) showed that RNA concentrations within species of zooplankton and small mesopelagic fishes have mass exponents of over -0.78 whereas exponents for interspecific comparisons based on average body sizes are described by a -0.33 value, comparab8e with that found by Banse and Mosher (1980). It thus appears that a third-order scaling may be required in dealing with production changes in relation to rauges in body size that are characteristic of cohorts of individual species, or at least the ranges of size within particular food and growth stanzas of the individual species (Paloheirno and Bickie 1966; Parker and Larkin 1959).

Fitting the Parameters in Fisheries Yield Models

The foregoing relationships enable us to use data on natural populations to establish values for modelling production and yield in terns of population growth and mortality.

Natural Mortality

If the age and size composition of any natural population is stable over a period of time, the various measured values of P/B for successive size groups are a measure of the average turnover rate at these sizes. That is, the specific rate of production at each size must be the rate of increase necessary to maintain the characteristic stock structure between sizes. In the long run, it would be expected that the observed growth rate has evolved as a result of the forces acting to produce this structure. Using such an argument, it could be concluded that an observed average growth curve is itself an indication of the natural mortality pattern which applies to the particular stock.

The foregoing argument will give an index of natural mortality for a fish stock only if it is h o w n that growth rate has not changed due to fishing. However, since fishing effects seem likely to most influeaace the larger sizes, in which natural mortality is a relatively unimportant part of the total mortality, the argument might well be expected to be useful in exploring the effects sf differences in pregecmit natural mortality patterns between stocks or species.

As an illustration of the method in the calculated examples, we have used growth curves md length-weight relationships for a population of herring (Clupea hreptgus) from the Scotian

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TABLE 1 . Age- and size-depndent production parameters for populations of herring and cod. P / B = 1.05 (size)-'." (Banse and Mosher 1980) or 3 -49 (Schwinghamer et al. 1986); BIB = 0.$87 (A) Herring population h m southwest Nova Scotia afier Tibbo (1957) and the condition factor W - 0 . ~ 0 5 ~ ~ . ~ . Length at age 2 is interpolated. (B) Cod population from the North Sea after Daan (1 974); W = 0 . 0 0 7 ~ ~ I .

Body Body PIB PIB Age length size c = -4.37 c = -0.70 BIR (YH) (cm) (cm) (kcal) (kcal) BIR (rel.)

(A) Hearing 0.931 0.440 0.179 0.136 0.131 0.120 0.116 0.112 0.110 0.104

(B) Cod

1.624 0.494 0.124 0.077 0.050 0.041 0.036 0.033 0.030 0.026

Shelf (Tibbo 1957) and cod (Gadus morhua) from the North Sea (Dam 19741, together with egg size and fecundity data from Blaxkr and Hunter (1982) and Oosthuizen and Daan (1974), to generate estimates sf initial size (Table 1). In Fig. 1A and lEl, we show a resulting curve of mortality at age derived using the Banse and Mosher weight exponent of -8.37 and a higher value of -0.7, in keeping with the results of Bfrmstedt and Sk~oldal (1980) and Dickie et al. (1987).

The natural mortality estimates depicted in Fig. 1 should correspond to a first approximation to equilibrium mortalities per unit area occupied by the stock. We cannot improve on them from the available data, in part because we lack information on the effects that changed fishing rates might exert on the rates of growth, through their influence on density. However, such effects should not seriously modify the difference in overall patterns of mortality for the two species, since both of them had been subjected to fishing for a number of yeas. The estimates may thus provide a first index of the sensitivity of yield changes to these important aspects of the population dynamics of types of species.

It is immediately evident from the figures that the natural mortality patterns for the cod and herring stocks are quite different from the rates typically used in current fisheries assessments, particularly for the smallest sizes. They are also different between species. However, the high levels sf early mortality derived by this method are quite consistent with preliminary results of mltispecies virtual population analysis (Gislason and Helgasow 1985) and of mortality patterns based on bioenergetics considerations (Sissenwine 1985) that have been applied to similar production systems. These and other lines of recent

evidence (e.g. Welch 1986) point to the probable importance of mortalities during postlarval and juvenile stages on the production characteristics of exploited stocks. In the present instance, the major difference between our method and that of others is that we have required relatively few data to reach similar conclusions. The approach appem to be applicable to most fisheries that have a characteristic biomass size spectrum and for which elementary size-at-age data are available.

Fishing Mortality

Current fishing theory defines the fishing mortality F = qf wherefis the number of effort units employed (number of boat days, for example) and q is the catchability coefficient, defined as the fraction of the total population removed by a unit of effort. While there is little real information on q , it is usually considered to rise rapidly in the threshold region of selection by the fishing gear and to be constant thereafter. The relationships deduced above suggest that an alternative formulation might be appropriate.

Fish are commonly found to be aggregated throughout the area of their occurrence, and a fishing vessel searches for areas of concentration within which it sweeps a given volume of water during each operation of its gear. Depending partly on the searching pattern, the search will cover a given volume sf water per unit time. The fishing success will depend jointly on the total area over which the stock is distributed and on the pmbability of encountering a school during the search and fishing phases of its operation. If we suppose, as is reasonable, that the general area of occurrence of the stock is known from a combination of historical precedent and current fleet distribution, then the prob-

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I I A. HERRING MORTALITY 2.8 B. COD MORTALITY

NATURAL AND FISHING NATURAL AND FISHING

0.8 2.4 k) W I- I- 4 4 2 E M 0.6

> > 'I + 1.6 - d -B

2 0.4 a

ia2 E 8 8 E 0.8

0.2 0*4

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

AGE (YEARS) AGE (YEARS)

PIG 1 . Comparison of natural and fishing mmlity estimates for (A) herring and (B) cod populations, described in Table 1 , prepared using the two slope values described in the text.

ability of encountering and catching fish will be a function of the average population density and its variance. That is, the catchability of the fish population, q , is appropriately defined in relation to the probability of capturing a fish per unit area, rather than per unit population abundance.

It is in this connection that the foregoing ecslogical study of productivity is of particular interest. Diekie et al. (2987) have deduced that because of the combination of the physiological and ecological scaling factors underlying production, it is possible to define the ratio of biomass (B ) to respiratory food requirements (R) in relation to the body size (tv) of the feeding population. That is, within an area of given productivity, the total biomass which can be supported on a unit area will be proportional to SJR, which is itself proportional to wo.%r wO.', depending on the size range sf population being considered.

Within a population on a given area, the abundance sf a cohort at various sizes or ages is determined by a number of factors of recruitment and mortality. The relationship of BJR to w suggests that, given the relationships between size, food requirements, and biomass, as body size increases a higher proportion of the total biomass at that size can be supported on a given area. It follows that q defined in relation to population density should be proportional to BJR or to wU.4 or w' .~ .

In Table 1 we have used an estimate of BJR to derive a relative value of q at different body sizes for the cod and herring populations. In the calculations, we have standardized q at age 3 for herring and age 4 for cod, based partly on the assumption that cod are on average recruited to fishing at a later age than are herring. The resulting yield curves are shown in Fig. 2 and m discussed in more detail below.

Recruitment

It is clear from eq. (4) that a period of relative stability of the population dynamics parameters corresponds to a period in which the biomass spectrum maintains a more or less constant fom. In fact, we suppose with Borgmann (1982) and Platt and Denman (1977) that the populations being analyzed are char- acterized by such a size spectrum and that the populations which can be supported on a given food supply will be a function of that spectrum. While it is thus clear that considerable refinement may be possible, based on knowledge of the reproductive capacity of size elements in the stocks (Ware 1980), and the balance of stock and environmental influences on recruitment (Welch

1986), in the model considered here we make only the simple assumption that an upper limit of reproduction will be established by the living space made available by the growth and mortality of the stock. Such a reproduction function is compara- ble with a simple yield-per-recruit model and is reasonable for stocks in an equilibrium state. It may poorly approximate situa- tions during periods of change in fishing or in intense fisheries. The possibility of delay-times in recruitment response, due to either stock or environmental influences, will then be of the utmost practical importance and require special consideration. It would appear from the foregoing that a study of the stability of the biomass spectrum for a region, both in total and by species, is likely to offer more direct and useful information than will any other data source. We do not consider such complications here, preferring to first examine sensitivity to the mortality fomu- lations.

Relative Yield

It is evident from an explicit comparison sf eq. (2) and (4) that conversion of the biomass spectrum to an ecological efficiency offers infomation only on relative yield changes, unless this is accompanied by information on the f d supply and its uptake. It is sften considered in population models that this is more or less constant, which is the same as assuming that K in eq. (21, (3), and (4) is a constant. Cdow ( 1 977) pointed out that within a given population this cannot be true for individuals on either theoretical or empirical grounds, although Borgmann ( 1982, 1983) has calculated an overall particle size conversion efficiency which suggests that it may be related to body size in a predictable fashion.

The nature of the population utilization of food by fishes was described by Paloheirno and Dickie (1966) in the form sf what was termed the K-line. Ken (11971) showed that it could be applied to natural populations by taking into account the size distribution of the prey population. Ow use of observed growth data m&es the relationship implicit, but it is reasonable to assume that the fish populations modelled here pass through two or more food stanzas, each c terized by a K-line applicable for the range of food particles taken in each stanza. This suggests that in addition to the initial recruitment to the first age group of the stock, there will be subsequent "recmitment" of the growing stocks from one stanza to another, depending on the availability of food as the population grows through its various

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A. HERRING YIELD VARIABLE F SCALED TO AGE 3

SLOPE = 0.37

1 - B. COD YIELD

0 6.2 0.4 0.6 0.8 I 1.2 FISHING MORTALITY (F)

VARIABLE F SCALED TO AGE 4 M = 0.

SLOPE= 0.37

0.4 0.6 0.8 I 1.2 FISHING MORTALITY bF1

FIG. 2. Fishing yield per recruit estimates for (A) hening and (B) cod populations resulting from the mortality patterns shown in Fig. 1 , assuming constant egg production, compared with yield estimated for constant natural mortality.

phases. Relevant observations on the prey resources of the populations analysed in Fig. 1 and 2 would provide a means for converting relative yield into terms of total population production.

Results of the Models

Examples of application of these "ecological" models with varying parameters to populations of hewing and cod are given in Fig. 2A and 2B, respectively. The figures show predicted relative yield in relation to fishing intensity. For comparison, also shown are the results for constant parameter models, com- parable with those used in current assessment techniques. The outstanding feature in both examples is the somewhat slower response of the yield to changes in fishing mortality for the varying parameter models, especially in the range of intemedi- ate fishing intensities at F between 0.2 and 0.6. The difference is more marked for the cod example than for the herring.

It should be recognized that despite the superficial similarity in the results, there is a fundamental difference in the presenta- tion which may eventually prove to have some practical importance. That is, the yield calculation for the more conventional constant parameter model implies that there is some whole population that is being exploited. The predicted steep drop in yield may thus be artificially exaggerated because of the im- plication that the population remains spread throughout its original area, even with large changes in equilibrium abundance. The variable parameter model involves a relative yield calculation which, because of the manner in which the PIB and BIB relationships are derived, is indexed on a per-unit-area basis. That is, the calculation of F in the variable model case takes into account changes in both the proportion of the original area occupied by the stocks and the efficiency of fishing.

The differences in yield are not, however, completely attrib- utable to features of the fishing mortality description. This is evident at low fishing mortalities where the maximum yield and its rate of change in relation to fishing are different for the two species. Differences in these lower regions of the yield curves are more likely to reflect the differences in net population growth and mortality with fish size. Thus, for example, the highest yield of herring occurs at lower fishing intensities, and the rate of decline with increased fishing appears to be notably more gradual than with cod.

The level of relative yield, given in the figures in millions of kilocalories, is a direct result of the observed growth patterns, interacting with the fecundity and caloric determination data available in the literature. There are major apparent differences in the predicted level of yield for the two species which are suggestive of possible differences in unit area productivity. However, at the present primitive level of our calculation system, we are not in a position to evaluate their actual significance. The differences are related to the growth potentials of the species and the reproductive potentials of the environments, which are in turn expressed in features of the recruitment functions. The apparent yield differences result simply from inser- tion of different growth pattems in similar model systems. The usefulness of this approach is a subject for future specific study.

Discussion

It should not be surprising that the short-term changes in yield in relation to various fishing parameters deduced from these models do not differ substantially from the deductions of the simpler yield models which f o m the basis for current assessment of productive potential. Over the years the models in use have been successively calibrated and fine tuned by observing the results of management actions. The results show that current calculation systems have captured the main features of fish population production, and it is apprent that our calculations are in relative general agreement with them.

The main advantage which might accrue to practical mnage- ment from model revisions remains, therefore, in the area of reliability of extrapolation from existing conditions and reduc- tion in the high costs consequent on present dependence on large amounts of sample data. In the former area, it is evident from Fig. 1 that deductions based on recent ecological information imply that major changes in fishing practices may not be well anticipated by constant parameters, and this is verified in our model results. In the second area, our results support the im- plications of the even more general models of Borgmann (1982, 19831, and before him of Platt and Denman (1 977) or Silvert and Platt (1 980), which suggest that quite readily accessible information on the biomass - body size spectrum can provide practical and useful infomation. Our models have the possible advantage over these more general approaches in showing that by the addition of more explicit information on body size in

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relation to V&OUS of the underlying production parameters, it may be possible to predict results at the level of individual species or the individual populations of species on which current fishery practice is based. The basic distinction is that our approach to mortality schedules is founded in ecological observation.

At this stage of analysis, the values of the weight exponents sf the production parameters are still open to question. The values used in the paper are for illustration only. The reference material reviewed by both Humphreys and by Banse and Mssher has been assembled by them to provide comparisons between species, not within them, and the different exponents found by these authors may in fact reflect differences in the index of average species size that they adopted. Refinement of the models for application within species, such as we have undertaken here, is based on preliminary data and requires further studies of particular life histories. We do not yet know the extent to which this may vary between species having different life history energy strategies.

References

ALLEN, P.. AND 9. R ~ c G L ~ E . 1986. Dynamics of discovery and exploitation: the case of the Scotia Shelf groundfish fisheries. Can. 9. Fish. Aquat, Sci. 43: 1187-1200.

BKMSTEDT, U., AND H. R. SKJOLDAL. 1980. RNA concentration of zooplankton: relationship with size and growth. Limnol. Ckeanogr. 25: 304-316.

BANSB, K., AND S. MOSHER. 1980. Adult $s8y mass and annual productio~tl biomass relationships of field populations. Ecol. Monogr. 58(3): 355-379.

BARANOV, F. I. 1918. On the question of the biological basis of fisheries. Nauch. Issl. Mtiol. Inst. Izvest. l(1): 81-128. Transl. Natalie Notkin (1934).

BEVERTON, R. H. J., AND S. J. HOLT. 1957. On the dynamics of exploited fish populations. U.K. Minist. Agric. Fish. Fish Invest. (Ser. 2) 19: 533 p.

BEAXTER, 9. H. S., AND J. R. HUNTER. 1982. The biology d the Ciupeoid Bishes. Adv. Mar. Biol. 20: 3-223.

BOHPGMANN, U. 1982. Pmicle-size-convenion efficiency and total animal @uction in pelagic ecosystems. Can. J. Fish. Aquat- Sci. 39: 648-674.

1983. Effect of somatic growth and reproduction on biomass transfer up pelagic food webs as calculated from particle-size-conversion efficiency. Can. J. Fish. Aquat. Sci. 40: 0210-2018.

1987. Models on the shape of, and biomass flow up, the biomass size spectrum. Can. J. Fish. Aquat. Sci. 44(Suppl. 2): 136-140.

CALOW, P. 1977. Conversion efficiencies in heterotrophic organisms. Bioi. Rev. 52: 385-409.

DAAN, N. 1974. Growth of North Sea cod, Gadus morhwa. Neth. J. Sea Wes. $(I): 27-48.

DICKHE, L. M. 1972. Food chains and fish production. Int. Comm. Northwest Atl. Fish. Spec. h b l . No. 8: 201-219.

1976. Predation, yield, and ecological efficiency in aquatic food chains. 9. Fish. Res. BoardCan. 33: 313-316.

B a m ~ , L. M., P. R. BBBUDREAU, AND K. R. FREEMAN. 1984. Influences of stock and site on growth and mortality in the blue mussel (My~ilus edula's). Can. J. Fish. Aquat. Sci. 41: 134-140.

D~CKIE, L. kf., S. R. K E ~ , AND P. a. BOUDREAU. 1987. Size-dependent processes underlying regularities in ecosystem structure. Ecol. Monogr. 57(3): 233-258.

DOYLE, R. W., AND W. He HUNTE. 198 1. Genetic changes in '%tness" and yield of a crustacean population in a controlled environment. I. Exp. Mar. Biol. Ecol. 52: 147- 156.

H IS LA SON, H., AND THE. HELGASON. 1985. Species interaction in assessment of fish stocks with special application to the North Sea. Dana 5: 1-44.

HEMWINGSEN, A. M. 1960. Energy metabolism as related to body size and respiratory surfaces. and its evolution. Reports s f the Steno Memorid Hospital md the Nordisk Insulinlabratorium 9 (Part HI): 1-1 18. Copenhagen.

HOLDEN, M. J. 1978. Long-ternchanges in landings of fish from the North Sea. Rapp. P.-V. Reun. Cons. Hnt. Explor. Mer 172: 1 1-26.

H u ~ m m ~ s , W. F. 1979. Production and respiration in animal populations. J. Awim. ko1.48: 427-453.

1981. Towards a simple index based on live-weight and biomass to predict assimilation in animal populations. J. Anim. Ecol. 48: 427-453.

K E ~ , S. R. 1971. A simulation model of lake trout growth. J. Fish. Res. Board Can. 28: 815-819.

LBNDEMAN, R. L. 1942. The trophic dynamic aspect of ecology. Ecology 23: 399-4 1 8.

MALLET, A. L., K. R. FREEMAN, AND L. M. DICKIE. 1986. The g ~ ~ ~ c s of production characters in the blue mussel, Mytilus du1is. I. A pmliminq analysis. Aquaculture 57: 133- 140.

MCGURK, M. D. 1986. The natural mortality of marine pelagic fish eggs and larvae: the role of spatial patchiness. Mar. Ecol. hog . Ser. 34: 227-242.

O~STHUIZEN, E., AND N. DAAN. 1974. Egg fecundity and maturity of North Sea cod, Gadus morhuca. Neth. J. Sea Wes. 8: 378-397.

PALQHEIMO, J. E., AND L. M. BICKIE. 1966. Food and growth of fishes. III. Relations among food, body size, and growth efficiency. 9. Fish. Res. Board Can. 23: 12Q9- 1248.

PARKER, R. R.. AND P. A. LARKIN. 1959. A concept of growth in fishes. J. Fish. Wes. Board Can. 16: 721-745.

PAULY, D. 1979. Theory and management of tropical multispecies stocks: a review with emphasis on the Southeast Asian demersal fisheries. Int. Cent. Living Aquat. Res. Manage. (ICLAWM) Stud. md Rev. No. 1: 35 p.

PLATT, T., AND K. BENMAN. 1977. Organization in the pelagic ecosystem. HelgoI. Wiss. Meeresunten. 30: 575-581.

1978. The structure of pelagic muine ecosystems. Rapp. P.-V. Reun. Cons. Int. Explor. Mer 173: 60-65.

REGHER, H. A. 1973. Sequence of exploitation of stocks in multispcies fisheries in the Laearentian Great Lakes. J. Fish. Wes. Boxd Can. 30: 1992- 19-99.

RICKER, W. E. 1948. Relation of "catch per unit effort" to abundance and rate of exploitation. J. Fish. Res. Board Can. 5: 43-70.

1945. A method of estimating maximum size limits for obtaining maximum yield. Copeia 1945(2): 84-94.

1954. Stock and recruitment. J. Fish. Res. Board Can. 1 1: 559-623. 1975. Computation and interpretation of biological statistics of fish

populations. Bull. Fish. Res. Board Can. 191 : 382 p. S C H A E ~ R , M. B. 1954. Some aspects of the dynamics of populations important

t the management of the commercial marine fisheries. Bull. Inter-Am. Trop. Tuna Comm. l(2): 27-56.

SCHWGHAMER, P., B. HARGRAVE, B. PEER, AND C. M. HAWKINS. 1986. Partitioning of production and respiration among size groups of ogmisms in an intertidal benthic community. Mar. Ecol. hog . Ser. 3 1: 13 1- 142.

SHELDON, R. W., W. H, SUTCEIFPE, JR., AND M. A. PARANJAPE. 1977. Structure of pelagic food chain and relationship between plankton and fish production. J. Fish. Res. Board Can. 34: 2344-2353.

SHEPHERD, J. G. 1982a. A family of general production curves for exploited populations. Math. Biosci. 59: 77-93.

1982b. A versatile new stock-recruitment relationship for fisheries, and the construction of sustainable yield curves. J . Cons. Int. Explor. Mer 4w1): 67-75.

SILVEWT, W., AND T. PLATT. 1980. Bynmic energy-flow model of the particle size distribution in pelagic ecosystmes, p. 754-763. In W. C. Kerfoot [ed.] Evolution and ecology of zooplankton communities. University Press of New England, Hmover, NH.

SISSENWNE, M. P. 1985. Perturbation of a predator-controlled continental shelf ecosystem, p. 55-86. I n K. Sherman and %. M. Alexander red.]. Variabil- ity and management of large marine ecosystems. AAAS Selected Sympo- sium 99.

SLQBQDKIN, L. B. 1963. Growth and regulation of animal populations. Holt, R inehd and Winston, New York, NY. 194 p.

SPRULES, W. G. 1980. Zoogeogaphic patterns in the size-structure of zooplankton communities with possible application to lake ecosystem modelling and management, p. 642-656. In W. C. Kerfoot [ed.] Evolution and ecology of zooplankton communities. University Press of New England, Hansver, NH.

SUTCLIWE, W. H, JR., K. DRINKWATER, ANEBB. S. MUHR. 1977. Cowelation of fish catch and environmental factors in the Gulf of Maine. J. Fish. Res. Board Can. 34: 19-30.

THOMBON, W. F., slnd F. H. BELL. 1934. Biological statistics of the Pacific halibut fishery. 2. Effect of changes in intensity upon total yield and yield per unit of gear. Rep. k t . Pac. Halibut Comm. 8: 49 p.

THBBCP, S. N. 2957. Contribution to the biology of herring (CIupea haaengus, L.) on the Atlantic coast of Nova Scotia. Bull. Rsh. Res. Board Can. 11 1: 239-151.

WARE, B. M. 1980. Bioenergetics of stock and recruitment. Can. J. Fish. Aquat. Sci. 37: 1812-1024.

W E L ~ , D. W. 1985. Identifying the stsck-recruitment relationship for age- structured populations using time-variant matched linear filters. Cam. J . Fish. Aquat. Sci. 43: 108- 123.

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An Ecological Approach to Fisheries Assessment