Subtleties in, and practical problems with, the use of production models in fish stock assessment

Abstract

Simple and age-dependent production models are valuable tools for fish stock assessment. In this paper, I examine subtleties in, and practical problems with, the use of production models, infer about their consequences, and give their solutions. Specifically, I first demonstrate that production models conditional on catch (type I) can differ substantially in behaviour from those conditional on catch (type II) and on effort (type III). In so doing, I give analytical solutions to, and examine the behaviour of, the Schaefer production model conditional on catch (type I). I also develop, and briefly mention the differences in the behaviour of, a general age-dependent model and a general age-dependent production model, conditional both on catch and on effort. I then outline practical problems with the use of cpues and standardized cpues, and discuss subtleties in, and ways of, accounting for observation and process errors and specifying the initial age distribution of a fish population in age-dependent modelling. In particular, I provide a maximum entropy estimation of the initial age distribution of a fish population. I conclude with contrasting age-dependent production models with simple production models and with formulae for calculating the instantaneous fishing mortality in age-dependent production models.