density-dependent habitat selection by juvenile haddock ( melanogrammus aeglefinus ...

Density~dependent habitat selection by juvenile haddock (Melanogrammus aeglefinus) on the southwestern Scotian Shelf

C. Para Marshall and Kenneth P. Frank

Abstract: Positive correlations between total abundance and indices representing distributional area bave been reported for several marine fish stocks. Different indices can produce different results for the same stock and many indices scale p~sitiveIy with total abundance. We describe an alternative approach to modelling the distributional response to variation in total abundance using data for juvenile haddock (Melanogramrnus aeglefinues) from the southwestern Scotian Shelf. Annual bsttom trawl surveys having a stratified random design were used to estimate the local density of haddock age 1 and 2 in each strata. Estimates of total abundance-at-age were obtained from sequential population analysis. The relationship between local density and total abundance-at-age was described for each strata using an exponential model with a Poisson error structure. Systematic variation among strata in the model parameters was indicative of density-dependent habitat selection and supported a previous study showing a positive correlation between distributional area and total abundance. Density-dependent habitat selection by juvenile haddock did not generate correlations between mean length-at-age and total abundance-at-age because the proportional abundance of haddock in areas of differing growth rates remained approximately constant as total abundance-at-age increased.

R6sum6 : Des corrClations positives entre l'abondance totale et les indices reprksentant l'aire de distribution owt CtC constatkes pour plusieurs stocks de poissons marins. Des indices difErents peuvent prodanire des rCsuItats diffkrents pour un meme stock et un nombre d'indices se rCvkIent proportionnels B I'abondance totale. Nous dCcrivons une autre faqon de mod$liser la rCaction de la distribution B la variation de I'abondance totale, h l'aide de donnCes sur les aiglefins juvdniles (Melanogrcsmmm aeglefinus) du sud-ouest de la plate-forme nCo-Ccossaise. Des relevks annuels au chalaat de fond, effectuCs selon une grille stratifike alCatoire, ont QtC bntilisCs pour Cvaluer la densit6 locale de l'aiglefiw d'Bge 1 et 2 B chaque strate. kes estimations de l'abondance totale par 2ge ont Ct$ obtenues au moyen de l'analyse ~Cquentielle des populations. Ee rapport entre la densit6 locale et l'abondance totale par 2ige a CtC dCcrit pour chaque strate au msyen d'un modkle exponentiel comportant une structure d'erreur fond& sur la lsi de Poisson. La variation systkmatique des paramktres du modkle, entre les strates, tradaaisant Bane sClection de l'habitat dCpendante de la densit6 et corroborait Hes rdsultats d'une Ctude antCrieure montrant une corrCIation positive entre I'aire de distribution et l'abondance totale. La s$lection de l'habitat dCpendante de la densit6 par les aiglefins juvCniles n9a pas produit de corrClations entre la longueur moyenne par 5ge et l'abondance totale par age, parce que l'abondance proportionnelle de l'aiglefin dans des zones B taux de croissance diffkrents est demeurCe B peu prks constante alors que l'abondance par 5ge augmentait.

[Traduit par la W6dactionI

lntroductien annual bottom trawl surveys to indirectly estimate the distributional area of groundfish stocks. Several of these

Direct estimation s f the area occupied by marine fish stocks studies have observed positive correlations between total that are distributed over broad spatial scales (10~-10~ km2) abundance and indices representing distributional area is not possible. Instead, recent studies have used data from (Crecco and OverhoBtz 1998; Lange 1991; Swain and Wade

Received February 11, 1994. Accepted January 4, 1995. HI2273

COTa Marshall. Department of Oceanography, Balhobasie University, Halifax, NS B3H 431, Canada. K.T. Frank. Marine Fish Division, Department of Fisheries and Oceans. Bedford Institute of Oceanography, P-8 . Box 1006, Dartmouth, NS B2Y 4A2, Canada.

Can. 9. Fish. Aquat. Sci. 52: 1007-1017 (1995). Printed in Canada / Imprim6 au Canada

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1993). However, these results are misleading if distributional indices scale positively with total abundance (Gaston 1990; Murawski and Finn 1988). For example, Crecco and Bverholtz (1998) estimated distributional area for Georges Bank haddock (Melanogrammees aeglefinus) by summing stratum areas where the mean catch-per-tow exceeded the long-term median catch-per-tow. Using this criterion to estimate distributional area inflates the degree of correlation between total abundance and distributional area (Marshall and Frank 1994; Swain and Sinclair 1994). An alternative approach to modelling the distributional respsnse to variation in abundance is to describe regional differences in the relationship between local density and total abundance.

Theoretical models describing these regional differences are well developed. Following the ideal free distribution, MacCall (1990) assumed that spatial variation in local density reflects gradients in resource availability: local density is highest where resources are abundant (optimal habitat) and lowest where resources are scarce (marginal habitat).'As abundance increases, optimal habitat becomes saturated causing the distributional area to expand and the local density of fish occupying marginal habitat to increase rapidly. This type of distributional response, referred to as density-dependent habitat selection (DDHS), is consistent with a positive correlation between abundance and distributional area. Several empirical studies have tested for DDHS in fish populations by contrasting the parmeters describing the relationship between local density and total abundance in areas where fish are abundant with values observed in areas where fish are scarce (Myers and Stokes 1989; Swain and Wade 1993; Talbot 1994).

Density-dependent habitat selection has important implications for the analysis of interannual variation in size-at- age. For example, if habitat that is marginal in a distributional sense is also associated with low growth rates then inverse correlations between abundance and mean size-at- age (density-dependent growth) could result from fish expanding into habitat that is suboptimal for growth when abundance is high and contracting into habitat that is optimal for growth when abundance is low (Baan et al. 1990; Toreson 1990). Juvenile haddock on the southwestern Scotian Shelf (Fig. 1) exhibit a positive correlation between total abundance and distributional area (Marshall and Frank 1994). Juvenile haddock also exhibit a distinct spatial gradient in length: ages 1 and 2 haddock caught in the Bay of Fundy are distinctly larger than haddock caught in areas east of Browns Bank (Fig. 2). Browns Bank is the geographic centre of distribution for juvenile haddock md it has been shown that the frequency of occurrence (i.e., cap- ture) of age 2 haddock increases more rapidly in areas lying to the east of Browns Bank relative to the Bay of Fundy as abundance increases (see Fig. 6 in Marshall and Frank 1994). Inverse correlations between abundance and mean size-at-age could potentially result from an increase in the proportional abundance of slow growing juveniles in areas east of Browns Bank as the total abundance of juveniles increases.

The specific objectives of this paper were to (i) develop a statistical model describing the relationship between local density and total abundance-at-age for subareas within

the stock range of juvenile haddock on the southwestern Scotian Shelf (NAFO Division 4x1; ( i k ) test whether regional differences in the relationship are consistent with the definition of DDHS; and (iii) investigate whether the distributional response of juvenile haddock to increasing abundance, in csnjunction with a spatial gradient in growth rates, could potentially generate density-dependent growth. The analysis was confined to haddock ages 1 and 2 because growth rates are higher and the contrast in abundance-at- age among cohorts is greater for juvenile fish. Further- more, these two age classes do not exhibit the diurnal variation in catch rates that is characteristic of older haddock (Marshall and Frank 1994).

Bottom trawl surveys Bottom trawl surveys of the southwestern Scotian Shelf have been conducted every suiaamer since 1970 by the Canadian Department of Fisheries and Oceans (Halliday and Koeller 1981). The surveys use a stratified random design and depth is the major stratifying variable (Fig. 1). At each sampling station, groundfish are collected using a Yankee 36 (1970-1981) or a Western IIA (1982-present) trawl equipped with a 19 mm cod end liner and towed at a constant speed for 30 min or approximately 3.2 km. Catch rates for surveys conducted using the Yankee 36 trawl were corrected for differences in catchability by multi- plying by 1.2 (Farming 1985). The age-specific mean number of haddock caught per tow (yi,jt) is estimated for each stratum and year by

where yhUt is the number of age j haddock caught in set h for stratum E' in year t and Hi is the total number s f sets collected in stratum i (Smith 1988). Further details of the surveys are contained in Marshall and Frank (1994).

Testing for density-dependent habitat selection If the entire population of haddock could be censused with- out error, then the total number of age j haddock in stratum i and year P (nij,) and the total abundance of age j haddock in the entire stock range for year t (Njt) would be known such that:

1

121 Nj , = nut i=l

If immigration and emigration are negligible then the relationship between nijt and Njt must be positive for some, if not all, strata. Therefore, the relationship between nijt and N, can be expressed for each stratum as a power function:

Equation 3 satisfies the boundary condition that when Njt equals zero, nijt equals zero for all i. Two forms of DDHS are possible: in respsnse to increasing abundance, haddock can either expand or contract their distributional area. In both cases, the value of Pij would vary systematically among strata. If haddock expand their distributional area as

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Fig. 1. Stratification scheme used for annual bottom trawl surveys of the southwestern Scotian Shelf. Individual strata are identified by number.

total abundance increases then values of Po would be less than one in optimal habitat where haddock are consistently very abundant but finite resources limit the rate of increase in stratum abundance (Fig. 3). Values of Pi, would be greater than one in marginal habitat where haddock are absent or scarce until increasing total abundance causes the distribution of the stock to expand into these areas. Consequently, the proportional abundance of haddock occupying marginal habitat (n,jNjt) would increase relative to optimal habitat with increasing N,. If haddock contract their distributional area as total abundance increases then values of p, would be higher in optimal habitat relative to marginal habitat and the proportional abundance of haddock occupying marginal habitat would decrease relative to optimal habitat with increasing Mjt (Fig. 3).

Alternatively, distributional area could remain constant as total abundance increased and n,, increase linearly with N,, in all strata that are occupied by haddock (Fig. 3). Therefore, Po would be equal to one and a, would equal the proportional abundance of age j haddock in stratum i (i.e., n,/N,,). Optimal habitat would be associated with high values of a,, whereas, marginal habitat would be associated with low values of a,.. Therefore, as total abundance increases, both the proportional abundance of haddock in each stratum and the distributional area remain constant. Given that this type of distributional response is independent of spatial variation in local density it can be termed density-independent habitat selection (DIMS). DIMS is equivalent to the site invariant response described in Myers and Stokes (1989), the proportional density model described

Fig. 2. Mean length-at-age by staturn for 1970-1990. Each observation represents the arithmetic average for a given survey for a11 observations for which age and length are known. (A) age 1 haddock. (B) age 2 haddock. See Fig. 1 for strata Bocations.

26

Stratum

in Hilborn and Walters (1992), and the spatially uniform model described in Swain and Sinclair (1994).

In practice, the total number of haddock occupying each strata (nut! is unknown. Values of yijt estimate the mean local density of age j haddock in a unit of area corresponding to the area swept by a trawl (approximately 0.04 kmz for a 30 min. tow). Consequently, Yij , differs from not by a scaling factor that is proportional to the area sf stratum i. The low number of sets in each stratum and patchy distribution of fish contribute to the considerable impreci- sion associated with values of $. Estimates of Njt, obtained from sequential population analysis (SPA), are available for haddock age l and 2 f ~ r the periods 1970-1987 and 1970-1988, respectively (O'Boyle et all. 1989). Because the SPA was calibrated (sensu Rivard 1989) using survey estimates of the mean abundance s f haddock age 2-8, SPA estimates of abundance-at-age are not independent of the survey data. Estimates are unavailable for 1989- present owing to a systematic bias in the SPA methodology (Sinclair et al. H991), the source of which is currently unknown.

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1010 Can. J. Fish. Aquat. Sci. Vol. 52, 1995

Fig. 3. Definitions of density-dependent (BDHS) and density-independent (BHMS) habitat selection illustrating trends in distributional area, local abundance (nu,), and proportional abundance (nij)Njl) with increasing total abundance-at-age. The dotted and broken lines illustrate trends for optimal and marginal habitat, respectively.

The relationship between local density and total abundance has previously been expressed as a power function (Myers and Stokes 1989):

If the expansion or contraction of distributional area is density-dependent then there will be an negative or positive correlation, respectively, between bc and an index of local abundance (e.g., median local density).The parameters ad and b, are commonly estimated by log-transforming the data (Myers and Stokes 2989) which accounts for the hetero- scedasticity that is characteristic sf the relationship between JG, and N,,. This approach is problematic for juvenile haddock in NAFO Division 4X given the high frequency of zero values of observed for some strata (Table 1). Sec- ondly, the assumption that the coefficients estimated by log transforming data are equivalent to the coefficients for a power function is not always justified (Zar 1968). To address these concerns, an alternative modelling

approach was used. Generalized linear models (GLMs; McCullagh and Nelder 1991) allow a noncsnstant variance to be incorporated directly into the model. The Poisson distribution is often used when the dependent variable is count data. The model

DIHS

153 E[3,,1 = Pij, = exp(aij + b,N,,j,b can be fit using a Poisson error distribution. By definition, the variance scales positively with the mean for variables having a Poisson distribution such that:

[GI Var[Tij;l =

where +ij is a scale parameter representing extra-Poisson variation that results because organisms tend to show a patchy rather than a random distribution (PieHou 1977). Unlike log transformations of Eq. 4, Eq. 5 is defined for values of jut equal to zero for variables having a Poisson distribution.

Although Eq. 5 has a similar functional form to Eq. 4 (Fig. 4), there are several important differences. Given that Eq. 5 is inherently nonlinear it cannot be used to test for DIHS. It also differs from Eq. 4 in that )?,, equals exp(ai;) when Nj, equals zero. In theory, a nonzero value of the intercept is impossible. In practice, it results from extrapolating Eq. 5 beyond the range of the data for a stock that is not extinct. Consequently, exp(a,) should scale positively with median local density. If the distributional response of haddock to increasing abundance is consistent with DDHS then the values of bij estimated for Eq. 5 should also vary systematically among strata. For

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Table I. The frequency of nonzero values (% NZ), median, minimum, and maximum values of gij, for age 1 (1970-1987) and age 2 (1970-1988) haddock by stratum.

Age 1 Age 2

Stratum % NZ Median Min Max 96 NNZ Median Min Max

example, if increasing total abundance results in haddock expanding their distributional area into marginal habitat then bij would be expected to vary inversely with the median locd density. Alternatively, if increasing total abundance results in haddock contracting their distributional area into optimal habitat then 6, would be expected to be positively correlated with the median local density.

The parameters aU and bii were estimated for each stratum and age class using S-PLUS for Windows (Version 3.1). S-PLUS uses iteratively reweighted least squares algorithms to estimate parameters by the method of maximum likelihood (Chambers and Hastie 1992). Because the dependent variable was assumed to have a Poisson distributiy, a log link function was used. The scale parameter (+$ was estimated by dividing the residual deviance for the full model by the corresponding degrees of freedom. The difference between the residual deviance estimated for the full model (Eq. 5) and the residual deviance estimated for the reduced, or null, model:

was calculated. Thenfull model was accepted if this difference divided by +, was greater than the X2,,,,,,, value (a significance level of 0.07 was used because three strata had borderline probability values of 0.06 or 0.07; next lowest probability values were 0.19 for age I haddock and 0.37 for age 2 haddock). No tows were made in stratum 74 in 1984, therefore, estimates of 7 ,,,,,,,,, and y74,2,,984 are unavailable. Three observations @76,1,1985, )P70,2,B9799 and 7,,,,,,,,) were deleted from the analysis because they were more than three-fold higher than the next highest value of h, and were overly influential in model fitting.

Implications for interannual variation in size-at-age Density-dependent habitat selection implies that the proportional abundance of haddock in each stratum (n..JN,,) varies systematically with increasing total abun&nce (Fig. 3). Interannual variation in the proportional abundance of haddock in each stratum could potentially generate correlations between mean size-at-age and total abundance-at-age given the east-west gradient in body size of juvenile haddock (Fig. 2). For example, an inverse correlation could result if the proportion of haddock occupying strata to the east of Browns Bank increases with increasing total abundance-at-age while the proportion on Browns Bank and in the Bay of Fundy decreases. A positive correlation would result from a disproportionately large expansion into the Bay of Fundy.

To assess the potential for density-dependent habitat selection generating correlations between mean size-at- age and total abundance-at-age the total abundance of age j haddock in each stratum (6,) was estimated as

where p0 is the predicted local density of age j haddock in stratum i for a given value of total abundance-at-age (the subscript t was dropped to distinguish the predicted local density from the observed local density) and Ai is the total area sf stratum i (see Table 2 in Marshall and Frank (1994) for values of A,). Estimates of 9ij were obtained from Eq. 5 for strata having statistically significant values of bU. Otherwise, Eq. 7 was used to estimate $u. To examine trends in the relative distribution among different subareas sf the stock range, strata groupings were

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Fig. 4. Two models used to describe the relationship between total abundance (lVjt) and local density ( Ti i t ) . ( A ) y,, = a i ,N ,~~; (B) y,, = exp(a,, + bipjtj,). The shaded area represents the range of N,, for which values s f yij, are unknown for stocks that are not extinct.

0

abundance

compared rather than individual strata. Therefore, the cumulative abundance of age y' haddock was calculated for three groupings of strata as

where the subscripts SS, BB, and BF denote the Scotian Shelf east s f Browns Bank, Browns Bank, and Bay of Fundy, respectively. Strata 82-84 were not included in any of the groupings because the low proportion of nonzero values of jut associated with these deep strata (Table 1 ) suggests that they are outside of the range occupied by juvenile haddock. The proportional abundance of age j haddock in each of the strata groupings was estimated as the

abundance in that grouping (Assj or tBBj or hBFj) divided by the total for the strata groupings (nsSj + fiBBJ + A,,,).

For age 1 haddock, only 5 of 16 (3 1%) strata had statistically significant values of b,, whereas, 82 of 17 (7 1%) strata had significant vdues of 6, for age 2 haddock (Table 2). For age 2 haddock nonsignificant values of h, were usually associated with strata having very low values of I,, (e.g., strata 70, 82, 83, and 84). Strata having nonsignificant values of b, for age 1 haddock included strata where haddock were abundant (e.g., stratum 81) as well as strata where haddock were scarce (e.g., strata 78, 82, 84, 91, and 95). A lack of correlation between local density and total abundance for all or a majority of strata would be expected if the centre sf distribution was shifting over time. However, the distribution of age 1 haddock is consistently centered on and around Browns Bank (stratum 80). The low number sf strata showing a response to increasing total abundance could reflect the relatively restricted spatial distribution of age 1 haddock, which are smaller and therefore less mobile than age 2 haddock. Three of the five strata showing positive correlations between lscal density and total abundance were offshore banks (strata 73, 75, and 80). Spawning adults occur on these banks (Waiwood and Buzeta 1989) and they are also sites of high concentrations of haddock eggs and larvae (Hurley and Campana 1989). Therefore, the three offshore banks represent a retention area for haddock during their first year.

As expected, values of a , scaled positively with the median lscal density for both age 1 (Fig. 5A) and age 2 (Fig. 6A) haddock, indicating that the intercept was higher in strata where haddock are comgmtively abundant. Despite relatively few observations, values of b, were inversely correlated with median local density for age I haddock (Fig. 5B) . An inverse correlation between b, and median local density was also observed for age 2 haddock (Fig. 6B). Because values of b, reflect the degree of curvature in the relationship between 9,, and N,,, curvature was greatest in strata where juvenile haddock were relatively scarce, i.e., the median local density was low. This result is consistent with the definition of DDHS given in Fig. 3 whereby haddock respond to increased total abundance by expanding their distribution into habitat where they are compar- atively scarce when abundance is low. This result also agrees with the positive correlation observed between an indirect estimate of distributional area (mean distance from the centre of distribution) and total abundance for age 2 haddock observed by Marshall and Frank (1994).

With the exception of stratum 90, strata in the Bay of Fundy (strata 85, 91, and 95) were characterized by low values of a, and high values of b , relative to strata lying to the east sf Browns Bank. According to the definition of DDHS given in Fig. 3, these strata represent marginal habitat. This conclusion is consistent with the observation that, as total abundance-at-age increased, the frequency of occurence of age 2 haddock (i.e., percent nonzero observations of y,,) increases more rapidly in areas lying to the east of Browns Bank relative to the Bay of Fundy (Marshall and Frank 1994). Increased catch rates of juvenile

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Table 2. Estimates of a,i and &, and standard errors, degrees of freedom, estimates of the scale parameter $,, and the probability (a) that the difference in residual deviances for the reduced and full model divided by $,i is greater than X2a,,, , by stratum for age 1 and 2 haddock.

b, SE(bij1 Stratum Age a,, SE(a,) (X 10-l) (X lw5) df $, a

Note: No nonzero values of were observed for age 1 haddock in stratum 71 and the iteratively rewelghted least squares algorithm used to estimate the parameters failed to converge for age 1 haddock in stratum 83 and age 2 in stratum 71.

haddock in strata $5, 91, and 95 would only be expected for exceptionally strong year classes of haddock.

Differences in the proportional abundance of age 1 haddock among subareas of the stock range indicate that the majority of age 1 haddock are found on Browns Bank or in strata lying to the east of Browns Bank (Fig. 7A). A very small proporti~n (910%) of age H haddock are found in the Bay of Fundy. There was little change in the progor- tional abundance of age 1 haddock as total abundance-at- age increased for all three subareas of the stock range. The proportional abundance of age 2 haddock was apprsx- irnately equal (-33%) for the three subareas (Fig. 7B). Although there was a slight decrease in the proportional

abundance of age 2 haddock in strata east of Browns Bank with increasing abundance, variation observed with increasing abundance-at-age was negligible relative to differences between the two age classes. Two mechanisms could potentially explain the increased abundance of age 2 haddock in the Bay of Fundy: (i) directed migration of juveniles from Browns Bank to the Bay of Fundy during their sec- ond year; and (ii) enhanced survival of juveniles in the Bay of Fundy. Published analyses of the available tagging data (McCracken 1956; HaIliday and McCracken 1970) have not examined the former mechanism explicitly. If survival is positively correlated with growth rates then the latter mechanism is possible.

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Fig. 5. (A) The relationship between the median value ~f Fig. 6. (A) The relationship between the median value of yii, and aii for age 1 haddock. (B) The relationship yo, and a. f ~ r age 2 haddock. (B) The relationship between the median value of yij, and bG f ~ r age 1 between the median value of ye, and bii for age 2 haddock. The corresponding strata number is indicated. haddock. The corresponding strata number is indicated.

Median vijt Discussion

MacCall (31990) observed that "once a unit stock has been defined, geography is often ignored" by fisheries scien- tists. This viewpoint is changing as the number of studies that model the distributional response to variation in total abundance increases. The quantitative approaches that have been used to describe these responses fall into three gen- eral categories: ( k ) estimation of indices that are assumed to be proportional to distributional area (e.g., Murawski and Finn 1988; Creccs md Overholtz 1999); (e'i) modelling the relationship between local density and total abundance (e.g., Myers and Stokes 8989); and (iid) examining how the the proportion of the stock occupying different subareas of the stock range changes with total abundance (e.g., the distributional index proposed by Swain and Sinclair (11994) estimates the area containing 95% of the age class). Figure 3 provides the conceptual basis for linking these three approaches. Obtaining consistent results using a combination of approaches reduces the likelihood that results are biased by relying on distributional indices that scale positively with total abundance (Marshall and Frank 1994; Swain and SincZair 1994).

Median yijt

Density-dependent habitat selection by groundfish, man- ifested as either an expansion or contraction of distributional area with increasing total abundance, appears to be common place in marine groundfish (Myers and Stokes 1989; Swain and Wade 1993; this study). Recent analyses of long-term variation in size-at-age suggests that spatial gradients in growth rates within the unit stock are also common (Brodey 1989; Toressn 1990; Rijnsdoqs and van Leeuwen 1 992; Sgrgensen 1992). DDHS, in co~~junctissna with spatial gradients in growth rates, represents one possible mechanism for generating density-dependent growth. Toreson (1990) concluded that density-dependent growth of Norwegian spring-spawned herring (CBupeu har~ngus ) was the result of increased dispersion of juvenile herring belong- ing to strong year-classes to areas with lower tempera- tures. However, DDHS is not likely to generate significant correlations between mean size-at-age and total abundance-at-age for juvenile haddock in the southwestern Scotian Shelf because the proportional abundance s f juveniles remains approximately constant for three subareas of differing growth rates. Mean length-at-age, estimated for the entire stock as well as for each of the three

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Fig. 7. Variation in the proportional abundance sf haddock with total abundance-at-age for three strata groupings. Strata groupings correspond to Browns Bank (BB; dotted line), Scotian Shelf east of Browns Bank (SS; broken line) and the Bay of Fundy (BF; solid line). (A) Age 1 haddock. (B) Age 2 haddock.

abundance

subareas, was not correlated with total abundance-at-age for both age 1 and 2 haddock (Table 3).

Modelling the relationship between local density and total abundance has other applications. The statistical model described by Eq. 5 could easily be expanded to include the effects of density-independent variables (e.g., temger- ature and salinity) that are known to influence the catch rates of groundfish (Murawski and Finn 1988; Polacheck and Vglstad 1993; Perry and Smith 1994; Smith et al. 1994). Models describing the relationship between local density and total abundance could also be used to assess whether the management unit adequately resolves stock dynamics. Under the assumption that immigration and emigration are negligible, local density must increase for some, if not all, strata as total abundance increases. A high pra- portion of nonsignificant or negative correlations could be indicative of a stock complex. For example, Myers and Stokes (1989) observed that positive correlations between local density and SPA estimates of abundance-at-age were observed for whiting (Merlangius rnerlangus) in the western half of the North Sea, whereas negative correlations

Table 3. Number of observations (n), correlation coefficient (r), and significance ( p ) for correlations between mean size-at- age and total abundance-at-age.

Age Area n r

1 Stock SS BB BF

2 Stock SS BB BF pp -- - - - -

Note: Estimates of mean size-at-age for the entire stock are from Table 14 of Hurley et al. (1992). Estimates of mean size-at-age for strata east of Browns Bank (SS), Browns Bank (BB), and the Bay of Fundy (BF) were calculated as the arithmetic average of all observations for which both age and length were known.

were observed in the eastern half sf the North Sea. They concluded that there were two separate stocks of whiting and that the abundance of the two stocks did not covary through time.

Modelling the distributional response of marine fish stocks can also be used to test ecological theory at the population level. For example, optimal foraging theory predicts that mirnds distribute themselves such that foraging efficiency (i.e., the per capita rate of resource utilization) is maximized (Stephens and Krebs 1986). This strategy results in the ideal free distribution (ED; Fretwell 1972). The HFD assumes that foragers have perfect knowledge of resource availability, and foragers are free to move among habitats (i.e., have equal competitive abilities). A recent review of empirical studies that test for the IFD found systematic deviations such that animals were consistently more abundant in resource-poor habitat than was predicted by theory (Kennedy and Gray 1993). Observations for marine fish stocks illustrate limitations of the IFD at the population level. The gradient in habitat suitability, as defined by the distributional response of juvenile haddock to increasing abundance, did not correspond to the spatial gradient in growth rates. For example, a large portion of the Bay of Fundy (strata 85, 91, and 95) was classified as marginal habitat in a distributional sense despite the rapid growth mtes observed in these strata (Fig. 2). Thus, resource utilization does not appear to be maximized in juvenile haddock. Given that haddock maintain this spatial gradient in size-at-age throughout their life, the assumption that they are free to move among habitats according to resource availability is probably invalid.

Investigations into density-dependent growth in haddock and other species sf marine groundfish have a long history of inconsistent results (see Daan et al. 1990 and Ross and Nelson 1992 for reviews). The lack s f consensus may result from the failure to test for specific mechanisms that could generate variation in growth rates. Several issues

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Can. J. Fish. Aquat. Sci. Vo1. 52, 1995

are critical: (i) how and why do growth rates vary within cohorts (spatial scales of variation); (ki) at what stage do differences among cohorts become significant (temporal scales of variation); and (iii) what factors, density dependent or density independent, contribute to intercohort variation in growth rates. For stocks that exhibit distinct spatial gradients in growth rates, modelling the distributional response to interannual variation in abundance is critical to devel- oping and testing hypotheses about factors regulating growth in marine fish populations.

We gratefully acknowledge the technical assistance s f J.E. Simon and thank B . M . Gillis , S.J. Smith, and D.P. Swain for reviewing the manuscript. This study was supported by a Natural Sciences and Engineering Research Council (NSERC) postgraduate scholarship and a Killam Memorial postgraduate scholarship to C.'F.M. and a NSEWC research grant to K.T.E

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