322 



Fishery Bulletin 9 1(2). 1993 



the null hypothesis. However, all 16 correlations were 

 negative for the Pacific sardine (Table 61. 



Regression coefficients were significant in models of 

 Pacific sardine and chub mackerel. The model of north- 

 ern anchovy spawning success fit relatively poorly 

 (Table 5), and although the overall model was statisti- 

 cally significant, the individual regression coefficients 

 were not. 



According to the Schwarz criterion S, the models 

 using combined data were marginally preferable to the 

 models using climate data for chub mackerel and north- 

 ern anchovy (S increased in the third significant figure). 

 For sardine, the combined model was strongly prefer- 

 able (S in ratio 2:1). Even allowing that the chub mack- 

 erel and northern anchovy models passed this test, 

 the only stock to pass all three tests for suspicion of 

 contaminant effects was the Pacific sardine. 



Discussion 



A somewhat similar biostatistical study was conducted 

 by Martin Marietta Environmental Systems to exam- 

 ine possible effects of contaminants on fishes in five 

 estuaries of the U.S. Atlantic coast, with emphasis on 

 the Hudson-Raritan basin (Summers et al. 1985, 1987). 

 The study used a categorical regression model of his- 

 torical landings (Rose et al. 1986); the autoregressive 

 model did not attempt biological or demographic real- 

 ism. After accounting for the effects of hydrographic 

 conditions and previous stock sizes, Summers et al. 

 (1987) detected correlations related to contaminant 

 variables including dissolved oxygen, dredging, and bio- 

 chemical oxygen demand. The study concluded that 

 there were consistent patterns of anthropogenic influ- 



Table 6 



Statistical criteria used to screen models of spawning success of three coastal pelagic fish 

 stocks off southern California. As predictors, models used parent stock-size and principal 

 components derived from measures of climate and of contaminant loadings. Models were 

 required to meet all three criteria in this table before being considered suggestive of 

 contaminant influences on spawning success. 



Statistical 

 criterion 



Northern 

 anchovy 



Number of significant negative correlations with 

 contaminants thought to be deleterious 1 12 required!. 



Significance of coefficients in model that included 

 contaminants. 



Improved fit of model including contaminants, compared 

 with model including only climate. (Improvement judged 

 by Schwarz criterion. I 



11 



ences among similar stocks across different estuaries. 

 In a second categorical regression study, Summers et 

 al. (1990), while expressing some reservations about 

 ultimate causes, concluded that sewage loadings have 

 had a negative effect on white bass Morone americana 

 production in the Choptank River, Maryland. 



The present study was not undertaken with the ex- 

 pectation of finding clear evidence that contaminants 

 affected fish stocks, nor clear evidence to the contrary. 

 We knew of many reasons that contaminant effects 

 might be difficult to detect, including major theoreti- 

 cal and practical difficulties in the data, shortcomings 

 in biological knowledge, and the limitations of avail- 

 able statistical methodology (for details, see Appen- 

 dix). As expected, we failed to detect contaminant ef- 

 fects on anchovy or chub mackerel, although we are 

 unable to state whether this reflects a lack of such 

 effects or merely low statistical power. In contrast, the 

 results for Pacific sardine suggest that contaminant 

 stress, at a time of severe overfishing, contributed to 

 the decline and collapse of this stock. Partly because 

 we searched for the best among many possible models, 

 we cannot attach any level of statistical certainty to 

 this suggestion. Our search selected a model of high 

 explanatory power (R 2 =83%) in which contaminants 

 were strongly represented, and that, we believe, makes 

 a strong case for further research into the question. 

 Important areas of research would include investigat- 

 ing how such a model of historical events, not formu- 

 lated a priori, can be statistically validated (or invali- 

 dated); which individual contaminants may have 

 contributed to the stock collapse; and by what mecha- 

 nisms contaminants may have played a role in the 

 decline of Pacific sardine. 



An alternative hypothesis 

 about Pacific sardine is that the 

 true spawning-success relation- 

 ship is depensatory rather than 

 linear, and thus depensation, 

 rather than exogenous influ- 

 ences, mediated the decline of 

 the stock. Consistent with this 

 hypothesis, the stock-size com- 

 ponent of our model (Fig. 7a) 

 fits the observed spawning-suc- 

 cess data quite well until the 

 mid-1950s (years of very low 

 population size) when the 

 stock-size component predicts 

 higher spawning success than 

 was observed. To examine this 

 alternative hypothesis in more 

 detail, we fit spawning-success 

 models using the following 

 variant of the gamma function: 



Fish stock 



Pacific 

 sardine 



Chub 

 mackerel 



16 



yes 



yes 



yes 



yes 



