Modeling time-varying growth using a generalized von Bertalanffy model with application to bloater (Coregonus hoyi) growth dynamics in Lake Michigan

摘要

A concurrent increase in lakewide abundance and decrease in size-at-age of bloater (Coregonus hoyi) in Lake Michigan have suggested density-dependent growth regulation. We investigated these temporal patterns by fitting a dynamic von Bertalanffy model and length-weight relationship with time-varying parameters to mean length- and weight-at-ages (ages 1-7) from annual surveys (1965-1999). We modeled yearling length, asymptotic size (L-infinity), and the parameters of a power relationship between mean weight and mean length (alpha and beta) as changing slowly over time using a random walk model. The Brody growth coefficient (k) was modeled as a linear function of L-infinity with year-specific random deviations. Our results support a positive relationship between L-infinity and k, indicating that under conditions supporting larger asymptotic lengths, individuals approach the asymptote more rapidly. We explored the relationship between year-specific growth parameters and indices of lakewide bloater abundance and found evidence of density-dependent growth. However, in the most recent years, L-infinity and yearling length have remained low in Lake Michigan despite low bloater abundances, suggesting the occurrence of a fundamental shift in the food web.