Fitting a von Bertalanffy growth model to length-at-age data accounting for length-dependent fishing selectivity and length-stratified sub-sampling of length frequency samples

Response-biased sampling in the context of regression modelling occurs when sample units are selected with a probability that is a function of the response. In sampling to obtain fish to both age and measure for length there are two potential response-biased sampling processes when length is the response and age is the predictor variable. These sample processes are (i) the actual fishing process involving a particular gear, and (ii) the method of on-deck sub-sampling fish for ageing from the random length frequency sample. When the selectivity of the gear combined with availability of fish to be caught is length-dependent in (i) and when fixed sample sizes per length bin or class are employed in (ii) then both these sampling processes are response-biased. Response-biased sampling and its effect on parameter estimation has been studied for linear and generalized linear, and linear mixed models but since population-average length given age is assumed to follow the von Bertalanffy growth relationship this work extends previous work to general nonlinear models and combines two response-biased sampling processes. Maximum likelihood, naïve least squares, and inverse probability weighted least squares estimation are used to estimate the von Bertalanffy parameters for simulated and real data on the growth of the Patagonian toothfish (Dissostichus eleginoides) given a known selectivity function.