A general theory of fish stock assessment models

Fish stock assessment models are of four main types: simple production mode ls, models of Deriso type, depletion models, and age-dependent models. They were derived independently, except for models of Deriso type, which were d erived from an age-dependent model. For some fish stock assessments, practi tioners have to make tremendous efforts to identify the 'right' model. In t his 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 a re, under three or four assumptions, all deducible from an age-dependent mo del, and hence provide a general theory of fish stock assessment models and a basis for identifying models in studies of fish population dynamics. Als o, I derive seven new production models, each in a differential equation, a nd 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 equa tions) and give its analytical solution; and finally re-derive, in a more g eneral context, Deriso's system of difference equations and his delay diffe rence equation and give its analytical solution. (C) 2000 Elsevier Science B.V. All rights reserved.