Extending the von Bertalanffy growth model using explanatory variables

von Bertalanffy parameters are usually estimated for a species, perhaps by sex, in some well-defined geographical area. An alternative way to estimate von Bertalanffy parameters is to model them in a general fixed-effects nonlinear model. For this model, the length of the ith individual is modeled as y(i) = f(phi, t(i), x(i)) + epsilon(i), where y(i) is the length and t(i) is the age of the ith specimen at the time of sampling, phi are the unknown parameters required to model von Bertalanffy growth, and x(i) are covariates associated with the ith specimen that minimally contain sex information (x(i)), but may also contain additional covariates. Standard nonlinear least squares and associated likelihood methods can be used to estimate parameters for this model. For Pacific ocean perch (Sebastes alutus), we model the effect that depth of collection has on estimated von Bertalanffy growth parameters: for sablefish (Anoplopoma fimbria), we model the effects due to latitude of collection: and for walleye pollock (Theragra chalcogramma) in the eastern Bering Sea, we model the effects due to variations in year classes. Results illustrate how modeling von Bertalanffy growth parameters directly using explanatory variables can be used to describe how growth relates to geographic, environmental, or biological factors.