Use of individual types of fishing effort in analyzing catch and effort data by use of a generalized linear model

Fishing effort is a function of many (continuous) variables which fishers can manipulate. However, when catch and fishing effort data are analysed using a generalized linear model, individual types of fishing effort usually enter as a composite quantity. But not all quantities can be combined into a composite quantity. Use of such data this way generally leads to a loss of information and incurs a model bias. In this paper, I analyse catch and effort data for the blue swimmer crab off South Australia by a direct use of individual types of fishing effort to extract a relative index of biomass, and use the concept of homogeneous functions to present some of the results. I also give formulae for choosing a combination of different types of fishing effort to effect a specified level of catch in both absolute and relative terms. Assuming that catch follows an independent gamma, normal, negative binomial, or Poisson distribution, fitting of a generalized linear model with a log-link function to the commercial catch and effort data suggests that: (1) the exploitable biomass remained relatively constant from 1 July 1983 to 30 June 1996; (2) the relative instantaneous rate of fishing mortality of a particular sex and age (if gear selectivity was constant over time) slightly increased over time; (3) a 1% increase in the number of days fished gave about 0.85% increase in catch whereas a 1% increase in the number of people on a boat led to only about a 0.45% increase in catch. This implies that use of a composite measure of fishing effort such as boat days and man days when analysing catch and effort data is inappropriate for this fishery. Although a generalized linear model may be a reasonable first-order approximation, catch and effort data are best interpreted through a process model.