A General Fishery Model for a Size-Structured Fish Population

Abstract

This paper describes a fishery model based on size, rather than age, as the fundamental population variable. The model's key ingredient is a density function related to number of fish within any given size range. A key assumption is that selectivity in the fishery is determined by size, not age, and that fish can reach recruitment size at various ages. The theory easily yields moment equations comparable with those obtained recently by Fournier and Doonan; for example, the general moment equation here is derived in a four-line proof. The paper gives detailed recommendations for tailoring the new model to a specific fishery, where model complexity is determined by the available data. The new theory places earlier models of Deriso and Schnute in the context of generalized cohort analysis, where size-dependent mortality is allowed. In particular, the paper identifies a potential problem with these earlier models and proposes a solution. All results are interpreted biologically to provide both conceptual and analytical tools for stock assessment.