Calculation of population-level fishing mortality for single- versus multi-area models: application to models with spatial structure

Abstract

Spatial considerations in stock assessment models can be used to account for differences in fish population dynamics and fleet distributions, which, if otherwise unaccounted for, could result in model misspecification leading to bias in model results. Calculating an overall fishing mortality rate (F) across spatial components is not straightforward but is often required for harvest management. We examined effects of spatial assumptions on model results under different approaches for calculating F. We show that (i) F can differ by as much as 50% depending on the spatial structure of the model; (ii) for multi-area models, F changes with size of area for all but one approach; and (iii) results are sensitive to model assumptions about catchability between areas and the spatial distribution of effort and abundance. Findings suggest caution be taken when interpreting results between models with different spatial structures. When comparing single- with multi-area models, we recommend adding F across areas when catchability is the same between areas and either effort or abundance is proportional to area. Otherwise no single approach can be expected to be superior in all cases. We suggest simulation be used to evaluate the best approach to meet particular management objectives.