Estimating prawn abundance and catchability from catch-effort data: comparison of fixed and random effects models using maximum likelihood and hierarchical Bayesian methods

Abstract

Abundance and catchability are crucial quantities in fisheries management, yet they are very difficult to estimate, particularly for short-lived invertebrates. Using two distinct approaches – a standard non-hierarchical model (NH) and a hierarchical Bayesian model (HB) – abundance and catchability coefficients from a fishery depletion process for banana prawns (Penaeus merguiensis) in northern Australia were estimated. Non-hierarchical models treated each stock and year separately and individually, whereas the hierarchical models assumed some form of common underlying population from which the parameters for the individual cases generated by the combination of stock and year were drawn. Two HBs were considered. In HB1 it was assumed that annual abundance and catchability parameters came from separate populations, or distributions, for each stock. In HB2 it was assumed that these stock region distributions were not separate, but had their parameters drawn from a common distribution. Thus in HB2 all stocks shared information at the regional level. The results for both NH and HB methods were similar in most cases, indicating a fair degree of stability irrespective of the particular form of model chosen. However, the NH method suffered because the data were analysed in generally small sections and in many cases these sections were too small to allow precise estimation of both parameters and confidence intervals. The deviations of point estimates between the HB1, HB2 and NH models were more marked in catchability coefficient estimates than in abundance estimates, and large relative deviations typically occurred in stock regions and years with low fishing efforts, low catch or poor depletion trends over time. We conclude that the combined analysis using HB was superior because it could handle limited data, yielded credible interval estimates for all parameters and was computationally more efficient.