Baba et al.: An environmentally based growth model for |uvenile Corbicu/a /aponica 



19 



Model selection and application 



Model 4 was the best in terms of AIC among four base 

 models (Table 1, models 1-4); ages were categorized in 

 relation to winter; and the relationship between dRIRL 

 and dRIRS was expressed by Equation 8. 



Four models were made by removing each independent 

 variable from model 4 (Table 1, models 4.1 to 4.4). The effect 

 of one age categorization — segregation of ages between the 

 first and second winters — was insignificant on the model, 

 because the model was significantly improved by its re- 

 moval in terms of AIC. The effects of the other independent 

 variables were significant on the model, because the model 

 was significantly worse by their removal in terms of AIC. 

 The effects of salinity and turbidity were insignificant on 

 the model, because adding each variable made the model 

 significantly worse in terms of AIC (Table 1, models 4.5 and 

 4.6). Consequently, model 4. 1 was the best model to describe 

 the relationships among environmental factors, ages, and 

 growth of C. japonica juveniles spawned in 1997. 



The coefficient value for age categorization of before the 

 second winter (-18.3) is much smaller than that of after the 

 second winter (-10.0) (Table 1). This difference suggests 

 that the growth response of C. japonica juveniles is much 

 less susceptible to environmental factors before the second 

 winter than after. 



Peaks of the dRIRL corresponded with peaks of water 

 fluorescence, when the water temperature was warmer 

 than about 10°C, especially before the second winter (Fig. 3, 



B and C). Therefore, food supply is the most influential fac- 

 tor when the water temperature is above about 10°C. The 

 slow growth or no growth during winter is due to the low 

 water temperatures. The dRIRL reached a plateau after 30 

 May 1999. This was due to two factors: water fluorescence 

 was relatively intense after 30 May 1999 (Fig. 3B); and the 

 growth response of C. japonica to the environmental factors 

 was more susceptible after the second winter than before. 



The confidence limits of all the coefficients seem to be 

 reasonably estimated by the profile likelihood method 

 (Table 2). These results also guarantee the convergence of 

 the model because the model was frequently optimized to 

 seek each confidence limit with different starting values. 

 We repeated the optimization at least 20 times to seek each 

 confidence limit. On other models, we also confirmed the 

 convergences as well. 



The largest extreme value distributions estimated by 

 model 4.1 fitted the shell lengths of C. japonica juveniles 

 very well (Fig. 4). 



Discussion 



Model formulation and application 



Largest extreme value distribution is apparently better 

 than normal distribution to describe the single cohort of 

 C. japonica that spawned in 1997. This distribution has a 

 mode and a longer tail toward the larger side. If the shell 



