Fishing yield, curvature and spatial behavior: Implications for modeling marine reserves

Abstract

Given a paucity of empirical data, policymakers are forced to rely on modeling to assess potential impacts of creating marine reserves to manage fisheries. Many modeling studies of reserves conclude that fishing yield will increase (or decrease only modestly) after creating a reserve in a heavily exploited fishery. However, much of the marine reserves modeling ignores the spatial heterogeneity of fishing behavior. Contrary to empirical findings in fisheries science and economics, most models assume explicitly or implicitly that fishing effort is distributed uniformly over space. This paper demonstrates that by ignoring this heterogeneity, yield-per-recruit models systematically overstate the yield gains (or understate the losses) from creating a reserve in a heavily exploited fishery. Conversely, at very low levels of exploitation, models that ignore heterogeneous fishing effort overstate the fishing yield losses from creating a reserve. Starting with a standard yield-per-recruit model, the paper derives a yield surface that maps spatially differentiated fishing effort into total long-run fishing yield. It is the curvature of this surface that accounts for why the spatial distribution of fishing effort so greatly affects predicted changes from forming a reserve. The results apply generally to any model in which the long-run fishing yield has similar curvature to a two-patch Beverton-Holt model. A simulation of marine reserve formation in the California red sea urchin fishery with Beverton-Holt recruitment, eleven patches, and common larval pool dispersal dynamics reinforces these results. © 2004 Rocky Mountain Mathematics Consortium.