An Approach to Modeling Crustacean Egg-Bearing Fractions as a Function of Size and Season

We present an approach to the analysis of crustacean egg production ogives with emphasis on detecting seasonal trends. The relationship between the proportion of gravid females (by size) and season is a prerequisite to the estimation of egg production potentials of populations. The basic method consists of relating, for each sample, the proportion of berried females with their size through a three-parameter logistic function where the asymptote may be less than 1. We then provide guidance for detecting seasonal trends in the estimates of the parameters for the individual samples. This is accomplished by restricting the basic model such that some parameters are considered to be either fixed for all samples or as simple functions of time or environmental variables such as temperature. Parameter estimates are obtained via maximum likelihood methods, and comparisons between alternative models are presented graphically and using likelihood ratio tests. We illustrate the approach and its application with data for a tropical shrimp, Penaeus esculentus, from northern Australia.