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

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Abstract
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 (0 .ltoreq. y .ltoreq. 1) to a positive factor .times. (0 .ltoreq. .times. .infin.). 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 .times. 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.

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