Admitting ageing error when fitting growth curves: an example using the von Bertalanffy growth function with random effects

A way to explicitly incorporate ageing error into the estimation of von Bertalanffy growth function (VBGF) parameters using a random effects (RE) modeling framework is presented. This RE framework also accounts for the effects of selectivity on growth curve estimation by characterizing the distribution of true ages derived from multiple age reads using either an exponential or gamma distribution. Simulation testing across four life histories is used to compare the RE approach with standard nonlinear (SNL) approaches that use the primary, average, or median ages in growth estimation. Sensitivity tests compare the effects of assumed length and ageing error, selectivity, and recruitment variability on the estimation of growth curve parameters. Results support the use of the RE method using a gamma distribution over the SNL methods because RE method estimates of VBGF growth parameters were more precise across life histories and sensitivity trials. This general approach can be applied and expanded to other growth models. Applications demonstrate that the results from RE methods may differ in biologically important ways to those obtained from SNL approaches.