Modeling growth of different developmental stages in bivalves

The 5 most common growth models (Gompertz, Special von Bertalanffy, Richards, Logistic and Generalized von Bertalanffy) were fitted to growth data comprising different developmental stages (i.e. free-swimming larvae, plantigrades, post-larvae and juveniles/adults) of the Caribbean pearl oyster Pinctada imbricata. As criteria for determining the most suitable model, the mean deviation of the data from the estimated growth curve (= mean square error, MSE), the deviation of the estimated asymptotic length of the observed maximum length obtained from a natural population, and the plot of the residuals against estimates were used. The Special von Bertalanffy and Richards models produce pure asymptotic curves and are therefore unable to simulate the exponential growth of the first 2 developmental stages (free-swimming larvae and plantigrades). Furthermore they tend to overestimate the asymptotic length. Gompertz, Logistic and the Generalized von Bertalanffy model, in contrast, produce sigmoid curves and thus are much more capable of modeling growth of the combined developmental stages, thereby, however, underestimating asymptotic length. Of all models, the Generalized von Bertalanffy model yields the best fit which is explained and discussed as a special mathematical property of its surface factor 'D'.