Patterns of change in the size spectra of numbers and diversity of the North Sea fish assemblage, as reflected in surveys and models

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1 ICES Journal of Marine Science, 53: Patterns of change in the size spectra of numbers and diversity of the North Sea fish assemblage, as reflected in surveys and models Jake Rice and Henrik Gislason Rice, J., and Gislason, H Patterns of change in the size spectra of numbers and diversity of the North Sea fish assemblage, as reflected in surveys and models. ICES Journal of Marine Science, 53: Trends were analysed over two decades in the size spectra of numbers and diversity of the North Sea fish assemblage. In trawl survey data, the abundance spectrum was smoothly linear each year. Both slopes and intercepts increased significantly over the period, reflecting the effects of fishing. The diversity size spectrum was curvilinear, with diversity increasing among smaller sizes and decreasing linearly over larger sizes. The slope of the linear component of the spectrum varied with a multi-year pattern, but without an overall trend. The much greater stability of the diversity spectrum compared with the abundance spectrum suggests that the fish community structure has remained fairly stable over the period, despite significant increases in harvesting on component populations. To explore the hypothesis that the regulation of the community structure arises from trophic interactions, the same community metrics were calculated from the output of a multi-species virtual population analysis of the major exploited fish predators and prey, parameterized with extensive catch data and feeding habits. Although many fewer species were included in the modelled assemblage than in the survey data, overall patterns were very similar. Annual abundance spectra were linear and slopes increased significantly and fairly smoothly over the 20 years, indicating significant effects of fishing on the size composition of the exploited fish assemblage. The annual diversity spectra were more dome-shaped than in the survey data. The shape showed no overall trend, but diversity of smaller size classes showed a different temporal pattern from the diversity of intermediate and large size classes. The patterns in modelled output are consistent with, but do not prove, the hypothesis that trophic interactions are an important factor in the fish community structure in the North Sea International Council for the Exploration of the Sea Key words: diversity, ecosystem effects of fishing, fish community structure, multi-species VPA, size spectra, trophic interactions. J. Rice: Department of Fisheries and Oceans, Pacific Biological Station, Nanaimo, BC, Canada V9R 5K6; H. Gislason: Danish Institute of Fisheries Research, Charlottenlund Castle, DK 2920 Charlottenlund, Denmark. Introduction Background Fish stock assessment tools often work retrospectively, reconstructing likely sizes and trajectories of individual stocks from time series of catch data and ancillary data (e.g. from surveys) if available. Related quantitative tools can project future stock sizes and trajectories, to explore possible future consequences of alternative management actions or environmental regimes (Ricker, 1975; Hilborn and Walters, 1994). Such projections require additional assumptions about, for example, the dependence of future recruitments on the sizes of the spawning stocks. Over the past decades there has been substantial interest in expanding the factors included in stock assessment and forecasting, to include, for example, predator prey interactions and effects of the physical environment on stock dynamics (e.g. Mercer, 1982; Rothschild, 1986; Daan and Sissenwine, 1991; Mann, 1993). This work is particularly advanced for stocks in the North Sea, where multi-species virtual population analysis (MSVPA) has become a routine component of assessment and management advice. MSVPA links the dominant predator fish stocks and the dominant prey fish stocks, estimating the age-specific rate of predation mortality each predator inflicts on each prey (Gislason and Helgason, 1985; Sparre, 1991). The expanded framework for assessment and advice is a step towards managing fisheries in the context of community level dynamics. In the North Sea (or any marine system), the community dynamics reflect the /96/ $18.00/ International Council for the Exploration of the Sea

2 Numbers and diversity of the North Sea fish assemblage 1215 combined effects of fishing mortality (F), predator prey interactions, and hydrographic influences on the constituent stocks. These factors interact. For example, as directed fishing selectively removes predators or prey, there are likely to be indirect responses within the food web. Although there is some basic theory developed for addressing these interactions among causes of community dynamics (e.g. May et al., 1979; Pimm and Hyman, 1987; Yodzis, 1994), the theory has not been tied analytically to fish stock assessment tools. Contrasting specific community metrics between MSVPA and research survey data may provide a means for investigating the relative contributions of fishing mortality and predator prey interactions to determining community dynamics. The survey data represent a consistent monitoring effort of both commercial and non-commercial species, over the past two decades. For many of the common fish predators and prey, MSVPA partitions the direct effects of fishing and predation mortality. The ICES Working Group on Ecosystem Effects of Fishing Activities has begun such investigations. Major results of the community analyses of North Sea survey data are reported elsewhere (ICES, 1992, 1994a; Greenstreet and Hall, in press). In this paper we build on those studies, and present the results of calculating the same community-level metrics for populations reconstructed with MSVPA. These analyses are important for two reasons: to investigate the hypothesis that marine community structure is due to trophic interactions, and as an indicator of our ability to forecast communitylevel effects of fishing. There are diverse theories regarding the causes of structure in aquatic communities (Steele, 1985; Kerfoot and Sih, 1987; Murdoch, 1994; but see Strong et al., 1984, for important cautions). However, all these theoretical frameworks would predict that much of the community structure present in the survey data is due to trophic interactions. Because MSVPA adds predator prey interactions to classic virtual population analysis (VPA) reconstructions of all major fish predator and prey stocks, community analyses of the MSVPA populations should reveal at least the major community-level patterns arising from trophic interactions. These analyses therefore investigate the core hypothesis that community structure, at least for larger marine taxa, is based on predator prey dynamics. We acknowledge that the analyses are not a perfect test of that hypothesis, because incorrect inferences in either direction are possible. Similar patterns could be present in both data sets for reasons other than trophic interactions, leading to a false positive inference. Terminal fishing mortalities in MSVPA are tuned to terminal Fs of single species VPAs, and the survey data are among the data sets used in tuning the single species VPAs (ICES, 1988). Therefore, population trajectories in MSVPA reconstructions and surveys are not wholly independent. However, the analytical relationship between MSVPA and survey numbers at age is very indirect for all but the oldest ages of the different species, so the potential for transferring pattern from surveys to MSVPA as artefacts should be low. Moreover, the community level patterns from analyses of survey data include many species not represented in MSVPA, so in the worst case the transfer of information is not just indirect but partial. None the less, neither data set is an unbiased, random sample of the full community. This might weaken the power of our analyses to find patterns at all. With analyses of low power, failure to find similar patterns might not justify rejection of the hypothesis that community structure is caused by trophic interactions. However, sampling methods (and therefore whatever bias is present) have been consistent over the survey period, and clear community patterns have been found in the survey data (ICES, 1992, 1994a). Even with the level of bias and comparatively high variance (Pennington, 1983; Smith and Gavaris, 1994) in these data, we can capture at least some community-level structure. The MSVPA analyses use the much more extensive catch data, and include all the major fish predators and many fish prey. Therefore, it is at least worth examining the possibility that similar community level patterns are present in the MSVPA reconstructions as well. It is possible that patterns found in survey data are due to the dynamics of various non-commercial species encountered in the surveys, but not present in MSVPA. If this line of argument is adopted, then analyses of MSVPA reconstructions would not be examining community patterns. However, one would also have to accept the corollary that commercial fisheries necessarily do not affect community structure of marine ecosystems. This position has interesting implications, although to this time it has had few proponents. The second reason why community analyses of MSVPA outputs are potentially important is that MSVPA can run in forecast mode, whereas surveys cannot. If similar community-level patterns are present in the survey data and the MSVPA output, then MSVPA can be used as an experimental tool. The community-level consequences of alternative management actions can be explored empirically in advance. Such information may be of value to resource managers and decision-makers, in addressing the biodiversity implications of alternative fishing options. We first describe the community-level metrics computed for the data sets. We then review the communitylevel patterns present in the survey data, while the bulk of the results address the patterns observed in the MSVPA output. The concluding portion contrasts the patterns present in the two analyses. The discussion evaluates the hypothesis of trophic causes of community

3 1216 J. Rice and H. Gislason structure, reviews the possible effects of sampling bias on our findings, and considers the usefulness of MSVPA as a tool for investigating community dynamics. Methods Community metrics A large number of community metrics have been proposed, and several major reviews have not identified any clear best metric (Gauch, 1982; Jongman et al., 1987; James and McCulloch, 1990). We use two metrics considered to be particularly informative by ICES (1994a). Both are based on size spectra, i.e. the variation in a community property across the size range of fish in the community. One metric is the traditional biomass size spectrum, proposed by Sheldon et al. (1972), and explored for fish assemblages in Murawski and Idoine (1992), Pope et al. (1987), and Pope and Knights (1982). The underlying hypothesis, based on trophodynamic transfer efficiencies, is that although the richness and relative abundances of species in a series of samples is highly variable, the biomass and numbers of individuals (pooled across all species) decreases log-linearly with size. Details of the theory remain controversial, and many variants of community size spectra have been proposed (log numbers, log biomass, length classes, weight intervals, continua, categories). However, the conceptual basis of size-dependent community properties is accepted widely (e.g. Peters, 1983; Platt 1985) and has been linked to traditional fisheries contexts (Beyer, 1989; Murawski and Idoine, 1992). Theorists propose that the slope and intercept of size spectra are properties which can be contrasted across different communities, or within a single community over time. From theory, differences in productivity should appear as differences in intercepts, whereas differences in transfer efficiencies and mortality rates should appear as differences in slopes (Borgmann, 1987; Boudreau and Dickie, 1992; Boudreau et al., 1991; Thiebaux and Dickie, 1992, 1993; Sprules and Goyke, 1994). In reality, for data with reasonable levels of sampling error, slopes and intercepts usually become correlated, so the patterns in slopes and intercepts cannot be interpreted independently. Our models fit ln numbers within a size interval to ln size interval for estimating the slopes and intercepts in the results section. The second metric is the diversity size spectrum. Although numerous diversity indices have been developed and applied (Peet, 1974; Pielou, 1984; Magurran, 1988), few have examined the shape of the spectrum as a function of size. The theoretical foundation is developed elsewhere (Gislason and Rice, 1996), but the conceptual foundation is straightforward. For a typical community, fewer organisms are present in larger size classes. This necessarily reduces the difference in abundance between the rarest and commonest species, and increases the probability that a species will have zero abundance in larger size classes. Both factors should cause diversity to decrease across size classes. Departures from linearity could reflect a variety of additional processes affecting the distribution of organisms among species. For most data sets, a dome is expected because sampling artefacts cause the diversity of the smallest size classes to be underestimated. In the survey data, the smaller size categories of some species are not fully vulnerable to the survey gear, so the catches are made up disproportionately of more vulnerable species. In MSVPA, partial recruitment of younger ages of an included species is not an issue. However, many uncommon small species are not included in MSVPA, so the true diversity of the smallest size groups is still underestimated. For our analyses we used the Shannon Wiener index, because this metric is more sensitive to the relative abundances of species than to the richness of species (Magurran, 1988). This property was desirable, because for analyses of the MSVPA output richness is fixed by the model. For both metrics, the important consideration was not the slope or intercept of a spectrum for a particular year, but how the spectrum changed over a 15-year period. These dynamics over time, in the face of intense fishing pressure, should give insight into the ability of processes that structure communities to either compensate for, or be disrupted by, human interference. We explored these trends by regressing the annual estimates of slopes and intercepts of the spectra on year. The probability levels associated with these regressions may be biased, because although the annual surveys are independent, the populations being sampled (or reconstructed by MSVPA) have age and size structure that is autocorrelated. Therefore we present residual plots as well as plots of trends, and focus our discussion on patterns rather than probabilities. Survey data The North Sea survey data were from the English Groundfish Trawl Survey, which has been conducted consistently since Sampling is independent across years, with a common sampling design, so trends in samples reflect trends in populations. Years were available for analyses, but the data from 1992 and 1993 might not be comparable with data from earlier years because the fishing gear was changed from a Granton trawl to a GOV ( Grande Ouverture Verticale ) in The gears may have different capture efficiencies for at least some sizes of some species. Sampling procedures and data-processing steps

4 Numbers and diversity of the North Sea fish assemblage 1217 Table 1. Statistics of fit of linear models to annual number spectra from survey data. For statistics of model fit, df=1,7 for all regressions. Model fits, plus parameter estimates, standard errors, and t value for Ho that parameter=0 are based on same number of observations (8 size-classes). Model fit Slope Intercept Year F p r 2 Est. s.e. t Est s.e. t *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***p< are described in ICES (1992). The 50 most common species, representing more than 99% of all fish taken in the surveys (and all species included in MSVPA) were included in analyses. Rarer species were sampled poorly, and therefore excluded. This introduced a small bias but increased precision of the diversity estimates. Records were binned set-by-set into 10 cm size classes. Data were pooled across the entire North Sea, to match the spatial scale of MSVPA. Details of intermediate data-processing steps are presented in ICES (1994a). MSVPA data The MSVPA output analysed here was derived from the keyrun produced at the 1993 meeting of the ICES Multispecies Assessment Working Group (ICES, 1994b). The run was based on catch-at-age for 11 commercially exploited North Sea species from , stomach content data for cod, haddock, saithe, whiting, and mackerel from 1981, and 1991, biomass of other food assumed constant, and terminal fishing mortalities selected in accordance with the values used by single-species working groups (consult ICES (1988, 1994b) for details). MSVPA produces reconstructions of numbers-at-age. Where the oldest age was a plus group, this group was dropped because it was not possible to assign a plus group to length classes. The numbers-at-age matrices were multiplied by annual age length keys based on surveys (augmented with commercial sampling for a few species), to produce the numbers-at-length by species and year. These values were also binned in 10 cm intervals, and analysed using the same programmes as used with the survey data. VPA reconstructions show intrinsic autocorrelation over time. This will be important for model fitting, as estimates of slopes, intercepts, and patterns of residuals cannot be considered completely independent over years. Results Survey data A linear model with ln size-class as the only term fit the ln number and diversity spectra well for all years (Tables 1 and 2). All intercepts and all slopes were significantly different from 0, with all slopes negative. For later years the numbers in size-classes above 60 cm were so small that a floor effect was present (Fig. 1). This effect meant it would be increasingly difficult to detect a continued change in slope for either spectrum, but the linear model continued to fit the data well in later years. In all years the diversity spectra were noticeably non-linear (Fig. 2), so linear models fit the number spectra better than the diversity spectra in 15 out of 17 years. The diversity of the cm size-class was consistently lower than the diversity in the cm (and in 2 years, the cm) size-class. As explained in the methods, some curvilinearity may be an artefact of either differential catchability of various species below 20 cm or of excluding very rare species (of which a

5 1218 J. Rice and H. Gislason Table 2. Statistics of fit of linear models to annual diversity spectra from survey data. See Table 1 for details. Model fit Slope Intercept Year F p r 2 Est. s.e. t Est. s.e. t *** *** *** *** *** *** *** Figure 1. Ln numbers per ln 10 cm size-class vs ln size-class for surveys in 1977, 1982, 1988, and Line is linear model fit to number size spectrum. Figure 2. Diversity per 10 cm size vs size-class for surveys in 1977, 1982, 1988, and Line is linear model fit to diversity size spectrum.

6 Numbers and diversity of the North Sea fish assemblage 1219 Figure 3. Regression of slopes of annual number spectra from surveys in years, (a) Trend line and estimates of annual slopes. (b) Time series of residuals from regression. disproportionate number were small). However, some of the curvilinearity may be a biological property of the community. This issue is being explored through analyses of other survey data where the sampling artefacts should show up in different size groups, but results are not yet available. These departures from non-linearity prompted the fitting of a truncated normal model to the data. In every case the fits improved somewhat, but for most years the improvement in fit was not large enough to justify estimation of the additional parameters, according to Akaiki s Information Criterion (Statistical Sciences Inc., 1993). Rather than use poorly determined parameter estimates for non-linear models, we focus on the portion of the diversity spectrum which was linear, and where sampling efficiency is likely to be comparable among the species, and contrast the diversity in the smallest size groups separately. The slopes of the number spectra become more negative over the years. A regression of annual slope on year was highly significant (r 2 =0.77, F (1,15) =22.2, p<0.0003). Residuals showed a distinct pattern that was consistently negative for the earlier and later years, and positive in the mid-1980s (Fig. 3). The intercepts of the number spectra increase marginally over period (r 2 =0.56, F (1,15) =7.1, p=0.02; Fig. 4), although this might be simply because of a significant correlation (r 2 =0.81, p<0.001) between slopes and intercepts (see discussion in Draper and Smith (1981)) rather than because of an increase in productivity of the fish community. The slope of the diversity spectra did not change over the period. A regression of annual slope on year was not significant (r 2 =0.46, F (1,15) =4.1, p=0.07), nor was the regression of intercepts (r 2 =0.11, F (1,15) =0.19, p=0.67). However, there were sequences of negative and positive residuals for both slopes and intercepts over years, Figure 4. Regression of intercepts of annual number of spectra from surveys in years, (a) Trend line and estimates of annual intercepts. (b) Time series of residuals from regression. Figure 5. Regression of slopes of annual diversity spectra from surveys in years, (a) Trend line and estimates of annual slopes. (b) Time series of residuals from regression. suggesting some multi-year pattern to the variation in the diversity spectra, despite the absence of an overall trend (Fig. 5). MSVPA data A linear model with size-class as the only term also fits the number spectra of the MSVPA estimates well for all years (all R 2 >0.89, all p values <0.0001). All intercepts and slopes were significantly different from 0 (Table 3). There was little indication of a floor effect at large size-classes (Fig. 6). The dome-shaped pattern of the diversity spectra was much more marked than in the survey data. Diversity metrics peaked in the cm size-class from

7 1220 J. Rice and H. Gislason Table 3. Statistics of fit of linear models to annual number of spectra from MSVPA data. For statistics of model fit, df=1,8 for all regressions (9 size-classes). See Table 1 for details. Model fit Slope Intercept Year F p r 2 Est. s.e. t Est. s.e. t *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Figure 6. Ln numbers per ln 10 cm size-class vs size-class for MSVPA output in 1974, 1980, 1986, and Line is linear model fit to number size spectrum. Figure 7. Diversity per 10 cm size vs size-class for MSVPA output in 1974, 1980, 1986, and Line is linear model fit to diversity size spectrum.

8 Numbers and diversity of the North Sea fish assemblage 1221 Table 4. Statistics of fit of linear models to annual diversity spectra from MSVPA data. See also Tables 1 and 3. Model fit Slope Intercept Year F p r 2 Est. s.e. t Est. s.e. t , and in the cm size-class from 1977 onward (Fig. 7). To allow comparisons between the MSVPA and survey data sets, the cm size-class was not included in regressions. Despite the marked dome in the annual spectra, the linear regressions were significant for most years (Table 4). The only poor fits (r 2 <0.40, p>0.10) were in the periods and 1988, due to the large difference in diversity in the size-classes just below and above <30 cm. The decline in diversity as length increased beyond 30 cm was similar between years (Fig. 7). Further exploration of fitting parabolic models to the diversity spectra is warranted. To address the objectives of this paper, we examine the patterns of variation over years in the three components of the spectra, rather than the overall linear slope of the spectrum. These components are the minimum diversity in the size-classes below 30 cm and above 70 cm and the maximum diversity in the intermediate size-classes. Together these three components determine the curvilinearity of the full spectrum, and the slope of the linear decline over larger sizes. Also, they are interpretable within a trophodynamic context. As in the surveys, the slopes of the number of spectra become more negative over years (regression on year; r 2 =0.58, F (1,17) =23.8, p<0.0001), and the pattern of decline was not smoothly linear (Fig. 8). From intervention analysis, the change in slopes was not significant from 1972 to 1978 (F (1,4) =3.1, p=0.16), and highly significant thereafter (r 2 =0.74, F (1,11) =32.0, p<0.0002, slope= ). The intercepts of the number spectra do not change significantly over the 19 years (r 2 =0.16, Figure 8. Regression of slopes of annual number of spectra from MSVPA in years, (a) Trend line and estimates of annual slopes. (b) Time series of residuals from regression. F (1,17) =3.3, p=0.09), and are not correlated with the annual slopes (r 2 = 0.21, p=0.38). The autocorrelation in MSVPA estimates does cause time trends in the residuals of the regression of intercepts on years (Fig. 9). The linear component of the diversity spectra becomes less negative over time (regression on year; r 2 =0.63, F (1,17) =29.4, p<0.0001, slope= diversity units per year). There were also noteworthy patterns in the annual residuals (Fig. 10). Intervention analysis indicates that there was no trend in the slopes from 1972 to 1980 (F (1,7) =0.63, p=0.45), and from 1981 to

9 1222 J. Rice and H. Gislason Figure 9. Regression of intercepts of annual diversity spectra from MSVPA in years, Trend line (not significant) and estimates of annual intercepts. Figure 10. Regression of slopes of annual diversity spectra from MSVPA in years, (a) Trend line and estimates of annual slopes. (b) Time series of residuals from regression (F (1,8) =0.49, p=0.50). The interval 1980 to 1984, however, encompasses a significant change in the slopes (r 2 =0.94, F (1,3) =47.2, p=0.006, slope= diversity units per year; Fig. 10). For perspective, this rate of change is less than 1% of the maximum diversity attained by the intermediate size-classes, and about 2.5% of the diversity displayed in the largest size-classes. The period of rapid change in slope also includes the period when the annual linear models fit most poorly. The overall weak trend in the slopes of the diversity spectra disguises stronger trends in the three components of the dome. There was no trend over years in the minimum diversity in the size groups <30 cm (F (1,17) =0.79, p=0.39; Fig. 11). However, the diversity displayed by the largest size groups >70 cm showed an increasing trend (r 2 =0.33, F (1,17) =8.5, p=0.0095). The increase occurred from 1972 to 1980 (r 2 =0.78, F (1,7) =25.5, p=0.0015, slope=0.022 diversity units per year), and was stable thereafter (F (1,9) =3.1, p=0.11). The maximum diversity attained by the intermediate size groups showed two separate trends. It increased Figure 11. Regression on year of MSVPA estimates, , of (a) Annual minimum diversity in cm size-classes; (b) annual minimum diversity in cm size-classes; (c) annual maximum diversity in cm size-classes. significantly over the early years ( ; r 2 =0.77, F (1,10) =29.4, p=0.0004; slope=0.018 diversity units per year), but then decreased for the remainder of the period ( ; r 2 =0.94, F (1,7) =117.4, p<0.0001; slope= diversity units per year). In summary, the diversity of both intermediate and large sizes increased throughout the 1970s, whereas the diversity of the smaller sizes remained unchanged. Therefore, the trend in the slopes from was small, and the models fit progressively worse. From 1982 onward the diversity of the small and large size groups did not change, whereas the maximum diversity attained by the intermediate size groups decreased systematically. This improved the fits of the overall models (Table 4), while leaving the overall slope fairly constant. It is only in the brief period between 1980 and 1983 that individual trends in diversity of the small, intermediate, and large size groups fail to combine in a way which left the slope of the diversity spectrum constant overall.

10 Numbers and diversity of the North Sea fish assemblage 1223 Synthesis Number spectra The survey and the MSVPA series both show a change in the distribution of numbers across size groups, with larger size groups containing progressively less of the fish biota over time. This effect is attributed to increasing exploitation rates on North Sea stocks. Although the slopes cannot be compared directly, the floor effect is more prominent in the survey data than in the MSVPA estimates. This is expected, because the surveys see a higher proportion of smaller fish than MSVPA, but proportions of the larger are more comparable. The goodness-of-fit and the similarities in pattern between the two number spectra suggest that MSVPA may be a useful tool for forecasting. Impacts of various management and environmental interventions on the MSVPA number spectra could be estimated and extrapolated to possible impacts on the larger assemblage of fish. Such extrapolations should be done with great caution until we understand more of how number spectra reflect assemblage dynamics, and establish the degree of independence of the MSVPA and survey data. However, this is the first empirical forecasting tool that can be used in such applications. Diversity spectra The diversity size spectra appear more curvilinear than the number size spectra, particular for the MSVPA species. Some portion of the apparently lower diversities in the smaller size groups is an artefact because very rare species were deleted from the survey data. MSVPA exaggerates this effect, because a much higher proportion of small species than large species is not included in the model. The fewer species in the smaller size groups correspondingly lower the diversity in these groups and worsen the performance of linear models. Partial catchability of small-sized fish would also lower diversity and contribute to a dome-shaped size spectrum. However, the number size spectrum is linear for size groups >10 cm, suggesting the surveys and MSVPA are not missing large numbers of smaller fish. They just have lower diversity in the smaller sizes. Further model fitting and analyses of data sets from other types of sampling are required to remove the artefacts and clarify the degree to which diversity size spectra are truly dome-shaped. There is a need for a theoretical exploration of this problem as well. Recent theory has suggested number-size spectra are parabolic within trophic levels (Thiebaux and Dickie, 1992, 1993; Sprules and Goyke, 1994), but there has been no treatment of the problem for diversity spectra across trophic levels. The development of a solid theoretical foundation for the shape of the diversity size spectra might provide another means for linking the dynamics of highly variable recruitment of smaller fish to the relatively more stable populations of their predators. One major thrust in these analyses was to explore the role of trophodynamics in maintaining the observed stability in the survey diversity spectra. The results here are ambivalent. In an absolute sense, there were statistically significant changes in the linear component of the diversity spectra from MSVPA populations, so the patterns in MSVPA and the survey data differed. However, over the 1970s, diversity increased at the same rate in the size groups well represented in MSVPA. Between 1972 and 1982 the average annual changes in diversities of intermediate and large size groups was (SE=0.0038) and (SE=0.0044), respectively. This produced a widening gap between the diversity of the smallest size groups (which was not changing) and the increasing diversity of the larger size groups. Then, over just 2 years in the early 1980s the gap was narrowed again, as the maximum diversity declined back towards earlier values. This restabilized the overall linear component of the diversity size spectrum. From these patterns, it is possible that the distribution of diversity among size groups, like the distribution of numbers and biomass, is being regulated. Trophodynamic causes of the regulation could account for two of the patterns present in these analyses. In each case the analyses suggest a testable hypothesis for future investigation. One pattern is the parallel changes in diversity across all size groups of major fish predators. If predator diversity is being regulated, either the diversity of the largest size groups should be decreasing in the 1990s to correspond to the observed decline in diversity in the intermediate size groups, or the diversity of intermediate size groups should have stabilized. The other pattern is that the major shifts in diversity in the fish predator size groups occurred when the difference between the diversities of predators and prey size groups became anomalously large. That response, once begun, occurred swiftly. This property predicts the circumstances which should cause changes in trends in diversity of predator size groups. Perturbing the diversity of the prey sizeclasses (reflecting, perhaps, recruitment failure or booms) would be informative here. However, the lack of trend in diversity of the prey size-classes may suggest such perturbations are unrealistic, even though pulses and failures of recruitment of individual species do occur. Conclusions (1) The number size spectra were similar between surveys and MSVPA data. Both data sources were consistent with current theory on biomass and number size spectra. Both showed marked community-level effects of fishing over the 1970s and 1980s.

11 1224 J. Rice and H. Gislason (2) The diversity size spectra were much more curvilinear in the MSVPA than in the survey data. MSVPA was designed to include a higher proportion of the large piscivorous species than of the smaller species they prey on. This property appears as relatively lower diversity in the smallest two size-classes. (3) The diversity spectra changed over time, but had no overall trend. Moreover, most of the change occurred over a brief period, with periods of stability before and after the period of change. This suggests that the early 1980s was an important period for the North Sea fish community, and warrants detailed study. (4) The changes in the diversity spectra reflect different trends in the smaller and the intermediate sizeclasses. The intermediate and larger size-classes show parallel trends. (5) The changes in diversity spectra are more prominent in the MSVPA analyses. The patterns are consistent with the hypothesis (but do not prove) that trophodynamic processes regulate community level properties. (6) More modelling of the shape of the diversity size spectra is needed, as is a firmer theoretical basis for the models. (7) Although firm conclusions must await further analyses, MSVPA may be a useful tool for exploring community level consequences of fisheries and environmental perturbations, at least for the larger fish in the community. Acknowledgements We thank all those involved collecting and maintaining the English Groundfish Survey data, particularly Brian Rackham and John Pope for making the data available to us for this work. We also thank Colin Wallace and Rob Kronlund for assistance with programming and analysis. The editors of these proceedings and two reviewers provided many suggestions which improved both content and clarity. 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