Equilibrium reference point calculations for the next generation of spatial assessments

Fish populations with spatial structure inherently violate the assumption of a single well-mixed stock, necessitating the use of spatially-structured population dynamics models. Accounting for spatial structure accurately and easily is a major goal for the next generation of stock assessment software development. Reference points (e.g., limit or target harvest rates and their associated biomass) are inherent to stock assessments and are often calculated under equilibrium conditions. However, the calculation process can be challenging for spatially-structured population dynamics models. We outline how to calculate equilibrium quantities within spatially-structured models where density-dependence in recruitment is local. We compare those values to equivalent situations when density-dependence in recruitment is global, thereby extending the set of population dynamics models on which spatially-structured stock assessments could be based. Results suggest that our method for calculating reference points under the assumption of local density-dependence can be performed using a straightforward optimization routine, and provide clearer understanding of the effects of fishing on a spatially-structured population. Finally, we address areas of research and development needed to integrate spatially-structured population dynamics models within existing management systems.