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Fishery Bulletin 100(3) 



Generalized additive models (GAM, Hastie and Tibshi- 

 rani, 1990) and linear models were used to relate univari- 

 ate and multivariate indices, individual species CPUEs, 

 and presence-absence data to the independent variables. 

 Additive models were used to allow for nonlinear relation- 

 ships between the dependent and independent variables. 

 A GAM is a nonparametric regression that uses smooth 

 functions of the independent variables in place of linear 

 functions and allows different probability distributions for 

 the data. We initially assumed that species richness fol- 

 lowed a Poisson distribution (counts), that the Shannon- 

 Wiener index, log-transformed CPUEs, and all indices of 

 species composition followed a normal distribution, and 

 that presence-absence data followed a binomial distribu- 

 tion. The dependent variables were then modeled as the 

 sum of nonparametric functions ( smoothing splines ) of the 

 hypothesized independent variables. If no evidence of non- 

 linearity was found, linear terms were substituted for the 

 smoothing splines. Residuals from each regression model 

 were examined for violations of the underlying assump- 

 tions (error distribution and homogeneity of variance) and 

 for outliers. Specifically, we examined residuals graphi- 

 cally by means of histograms, quantile-quantile plots, and 

 plots of residuals against time and against other covari- 

 ates. We further conducted formal tests of goodness-of-fit 

 of the residuals against the assumed error distributions 

 after each model fit. Model fits were generally deemed ad- 

 equate, unless noted otherwise in the results. 



To identify and evaluate the significance of relationships 

 between species composition and explanatory variables 

 we first chose the most appropriate regression model, then 

 quantified the contribution of each explanatory variable 

 to the model fit. A stepwise procedure based on the Akaike 

 information criterion (Hastie and Tibshirani, 1990) was 

 used to select a subset of significant variables. As a mea- 

 sure of model fit we computed a pseudo-coefficient of deter- 

 mination (pseudo-r^), or the fraction of the total deviance 

 explained by the model, as a surrogate for the familiar r~ 

 (Swartzman et al., 1992). The importance of individual 

 variables in the model fits was evaluated similarly by us- 

 ing a pseudo-coefficient of partial determination based on 

 reduced models that exclude the variable of interest (= 1 - 

 deviance of best model/deviance of reduced model). 



Trends in the abundance of those species that were 

 strongly associated with the time index were examined 

 in greater detail by haul. For this analysis we treated 

 zero and nonzero catches separately to test for 1 ) changes 

 in the catch rate of a species over time based on positive 

 catches only (CPUE-where-present) and 2) changes in the 

 frequency of occurrence of a species over time (by estimat- 

 ing the probability of a nonzero haul). To test for changes 

 in the CPUE-where-present of these species, we used an 

 analysis of covariance model of the following form: 



\og(CPUE-where-present) = area + depth stratum + 

 gear + {area x depth stratum ) + px year 



Errors were assumed to be normally distributed, thus 

 CPUE-where-present was assumed to follow a lognormal 



distribution. A separate linear time trend was estimated 

 and evaluated for significance within each depth stratum 

 in each area (/3 parameters). The interaction term (area 

 X depth stratum) was omitted if it was not significant at 

 the 5% level. Strata within the same statistical area and 

 depth stratum were pooled, unless fitting separate regres- 

 sion lines to each of the 48 strata improved the overall fit 

 significantly. If the slope of the regression did not differ 

 among areas or depth strata at the 5% level, data were 

 further pooled across areas or depth strata (or both) to 

 obtain the most parsimonious model. 



The probability of nonzero hauls was estimated simi- 

 larly using a logistic regression model (McCullagh and 

 Nelder, 1989): 



logl 



Pr(CPf7£;>0) 



: area + depth stratum + 



l-Pr(CPUE>0), 

 gear + (area x depth stratum ) + fix year. 



where the number of positive catches (CPUE>0) was 

 assumed to follow a binomial distribution. The most par- 

 simonious models for each species were used to test the 

 null hypothesis that there was no significant (linear) trend 

 in the catch rate (CPUE-where-present) or frequency of 

 occurrence (Pr{CPUE>0|) over time. The null hypothesis 

 was rejected if the slope P was significantly different from 

 zero at the 5% level. 



Results 



Arrowtooth flounder had the highest average CPUE 

 (kg/km^) and the highest frequency of occurrence during 

 all surveys (Table 2). Walleye pollock was second in 

 most years, followed by Pacific cod and Pacific halibut. 

 However, in 1996, the estimated CPUE of Pacific Ocean 

 perch exceeded that of pollock, cod, and halibut. Sablefish, 

 five other flatfish species, two Sebastes species, and Atka 

 mackerel (Pleurogrammus monopteiygius) were other 

 important species by CPUE (> 200 kg/km'-, Table 2). The 

 most abundant species, including gadids and most of the 

 flatfishes, were generally also the most widespread spe- 

 cies in the survey (>50'7f frequency of occurrence). In spite 

 of relatively high CPUEs, rockfishes, Atka mackerel, and 

 yellowfin sole (Limanda aspera) had low frequencies of 

 occurrence (4-40%), indicating high local abundances and 

 a more restricted spatial distribution. 



Independent variables used in the analysis of species 

 richness, diversity, CPUE, and species composition were 

 moderately correlated (Table 3). The largest correlations 

 were between area swept and year (-0.452), due to a 

 reduction in haul duration after 1987, between depth 

 and temperature (-0.407), and between Julian day and 

 alongshore distance (-0.383). Depth and bottom tempera- 

 ture on the shelf and slope are invariably confounded and 

 their effects may generally be difficult to separate. The 

 confounding between Julian day and AD was extreme in 

 some years (e.g. r=-0.79 in 1993) because sampling vessels 

 traveled from west to east during most surveys. However 



