Bias in common catch-curve methods applied to age frequency data from fish surveys

Abstract

Catch curve analysis is often used in data-limited fisheries stock assessments to estimate total instantaneous mortality (Z). There are now six catch-curve methods available in the literature: the Chapman-Robson, linear regression, weighted linear regression, Heincke, generalized Poisson linear, and random-intercept Poisson linear mixed model. An assumption shared among the underyling probability models of these estimators is that fish collected for ageing are sampled from the population by simple random sampling. This type of sampling is nearly impossible in fisheries research because populations are sampled in surveys that use gears that capture individuals in clusters and often fish for ageing are selected from multi-stage sampling. In this study, I explored the effects of multi-stage cluster sampling on the bias of the estimates of Z and their associated standard errors. I found that the generalized Poisson linear model and the Chapman-Robson estimators were the least biased, whereas the random-intercept Poisson linear mixed model was the most biased under a wide range of simulation scenarios that included different levels of recruitment variation, intra-cluster correlation, sample sizes, and methods used to generate age frequencies. Standard errors of all estimators were under-estimated in almost all cases and should not be used in statistical comparisons.