An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters

A new method for estimating individual variability in the von Bertalanffy growth parameters of fish species is presented. The method uses a nonlinear random effects model, which explicitly assumes that an individual's growth parameters represent samples from a multivariate population of growth parameters characteristic of a species or population. The method was applied to backcalculated length-at-age data from the tropical emperor, Lethrinus mahsena. Individual growth parameter variability estimates were compared with those derived using the current "standard" method, which characterizes the joint distribution of growth parameter estimates obtained by independently fitting a growth curve to each individual data set. Estimates of mean von Bertalanffy growth parameters from the two methods were similar. However, estimated growth parameter variances were much higher using the standard method. Using the random effects model, the estimated correlation between population mean values of L-infinity and K was -0.52 or -0.42, depending on the marginal distribution assumed for K. The latter estimate had a 95% posterior credibility interval of -0.62 to -0.17. These represent the first reliable estimate of this correlation and confirm the view that these parameters are negatively correlated in fish populations; however, the absolute correlation value is somewhat lower than has been assumed.