A Unified Approach to the Analysis of Fish Growth, Maturity, and Survivorship Data

This paper presents an approach to the analysis of growth, maturity, and survivorship data that unifies an extensive biometrics literature, particularly in fisheries and forestry. The model involves a probabilistic response y[Formula: see text] to a positive factor x[Formula: see text]. Because the relationship is asymptotic, the model can also be interpreted as a descriptor of biological growth, in which the asymptotic size is scaled to 1. The model generalizes earlier work by Gompertz, von Bertalanffy, Weibull, Richards, Chapman, and Schnute; it also extends the logit method introduced by Berkson. We identify reasonable curve families for the model, in which a transform parameter associated with x or y determines the curve shape, and we provide a complete analysis of curve types. We describe likelihood functions associated with two classes of data, typified by (1) size-at-maturity data and (2) time–mortality data. We illustrate the model's application to both data classes and show that it provides a useful extension to past methods of analysis.