A general theory of fish stock assessment models

Fish stock assessment models are of four main types: simple production models, models of Deriso type, depletion models, and age-dependent models. They were derived independently, except for models of Deriso type, which were derived from an age-dependent model. For some fish stock assessments, practitioners have to make tremendous efforts to identify the ‘right’ model. In this paper, I develop a general age-dependent model, a general age-dependent production model and a general age-dependent depletion model, demonstrate that simple production models, models of Deriso type and depletion models are, under three or four assumptions, all deducible from an age-dependent model, and hence provide a general theory of fish stock assessment models and a basis for identifying models in studies of fish population dynamics. Also, I derive seven new production models, each in a differential equation, and where possible, give their analytical solutions; derive a new production model in a system of two differential equations (which, if conditioning on fishing effort and discretized, becomes Deriso’s system of difference equations) and give its analytical solution; and finally re-derive, in a more general context, Deriso’s system of difference equations and his delay difference equation and give its analytical solution.