Selectivity's distortion of the production function and its influence on management advice from surplus production models

• Selectivity curve and the measure of abundance have substantial impacts on the shape of the production function and the management-related quantities.
• Parameters of the production function are influenced by biological processes.
• Time-varied production parameters did not improve the fit of production model to the data.
• Caution is advised when applying surplus production models to populations fished by gears with substantially different selectivity patterns.

Surplus production models (e.g. the Schaefer, Fox, and Pella–Tomlinson models) aggregate the dynamics of a fish population into a simple function of abundance and do not explicitly represent biological and fishing processes. It has been shown that the shape of the production function depends on biological parameters such as natural mortality, growth, and the stock–recruitment relationship. It also depends on the age-specific selectivity of the fishery. We evaluate the influence of the selectivity curve on the shape and productivity rate parameters of the production function and compare it with the influence of biological processes. We then compare results of a stock assessment based on bigeye tuna (Thunnus obesus) in the eastern Pacific Ocean when the production function is assumed to be known. The results illustrate that the selectivity curve and the measure of abundance used (e.g. spawning biomass or vulnerable biomass) have a substantial impact on the shape of the production function and, consequently, management advice. However, the fits of the model to the relative index of abundance are not significantly improved when the known time-varied productivity rate and shape parameters are incorporated. This provides additional evidence that surplus production models should not be used for routine stock assessments, particularly outside the realm of full management strategy evaluation.