Dorn: Environmental covariates of Merlucaus productus growth 



267 



Age, yrs 



Figure 4 



Growth-increment regression curves with different initial growth-increment 

 coefficients (gf,) for male and female Pacific whiting Merluccius productus. 

 The distribution of actual growth increments for the years 1978-89 illustrates 

 the saddle-shaped variability of length-at-age statistics based on fishery sam- 

 pling (W 211). Points represent observed annual growth increments per age- 

 group per year. 



Table 5 



Analysis of variance of annual length increments using the nonlinear regres- 

 sion model. The coefficient g„ is an intercept term: exp(g„) estimates the 

 growth increment from age 1 to age 2. The coefficient g, determines the 

 slope of the exponential decline of the annual growth increment with age 

 under average environmental conditions. Terms relating to covariates are 

 identified as either intercept terms (gj) or as slope terms (g,). 



Source 



df 



SS 



Mean square F -value P>F 



go (sex) 

 go (temp.) 

 gj (biomass) 

 gi (temp.) 

 Error 



204 



4067.8 

 12.6 

 93.5 

 36.3 

 17.4 

 711.4 



4067.8 

 12.6 

 93.5 

 36.3 

 17.4 

 3.5 



1166.5 



3.6 



26.8 



10.4 



5.0 



Parameter 



Estimate 



SE of estimate 



go 



gi 



go (sex) 



go (temp.) 



gi (biomass) 



gi (temp.) 



1.995 

 -0.383 



0.058 

 -0.544 

 -0.086 



0.099 



0.038 

 0.015 

 0.029 

 0.098 

 0.027 

 0.043 



growth increments from 1983. The parameter esti- 

 mates followed the same trend as the results in Table 

 5, with increases in sea-surface temperature associated 

 with large reductions in growth of younger fish, and 

 a decreasing percent reduction with age. 

 For population biomass, an increase of 200,000t 



(~10% of the mean population biomass) 

 would cause a 5% reduction in annual 

 growth at age 4, and the percent reduction 

 would increase with age, reaching a 10% 

 reduction at age 7. Because the intercept 

 term for biomass was not significant, 

 growth of the age-1 fish would not be af- 

 fected by changes in population biomass. 

 During the 10 years studied, range in adult 

 biomass was from 26% above to 22% below 

 the mean of 1.771 million t (1978-87). This 

 lack of contrast in adult biomass makes 

 any interpretation very tentative, but the 

 results do suggest that the effect of pop- 

 ulation density on growth is relatively 

 small in comparison with the effect of 

 temperature. 



None of the other environmental covari- 

 ates or measures of population density 

 tested in the model were significant. The 

 coefficient for upwelling was highly signifi- 

 cant in a model without temperature, but 

 when temperature was included in the re- 

 gression, upwelling was no longer signifi- 

 cant. Because water temperature and the 

 upwelling index are statistically correlated 

 off the coast of Oregon (Kruse and Huyer 

 1983), the parallel effects of temperature 

 and upwelling index are not unexpected. 

 The same parallel effect was found be- 

 tween year-class abundance and adult 

 biomass. However, adult biomass ac- 

 counted for more of the variability in 

 annual growth than did year-class abun- 

 dance. This suggests that the crowding 

 that occurs when a strong year-class 

 recruits to the population is experienced 

 by all the adults, and not just the individ- 

 uals which make up the strong year-class. 

 Figure 5 shows the standardized resid- 

 uals from the final model, plotted against 

 age and year. No trends are evident with 

 respect to age. This plot also shows that 

 the use of the estimation variances as 

 weighting terms in the least-squares fit 

 was successful in stabilizing the error vari- 

 ance with respect to age. However, there 

 still is a noticeable trend in the standard- 

 ized residuals by year, with positive resid- 

 uals associated with the earlier years in the time-series 

 (1979 and 1980), and negative residuals with the later 

 years (1985 and 1987). This indicates that the environ- 

 mental covariates examined thus far are not completely 

 successful in accounting for the decline in mean length- 

 at-age over the past decade. 



< 0.001 

 0.059 



<0.001 

 0.002 

 0.026 



