Additivity properties in metapopulation models: implications for the assessment of marine reserves

Marine reserves increase both aggregate (system-wide) catches and population levels when the dispersal benefits from the reserve are greater than the opportunity cost of closing the area to fishing. Although the general nature of this condition is clear, how the underlying bioeconomic drivers interact to determine the outcome is not. In this paper, we develop a class of spatially explicit models that enable us to explore how different assumptions regarding connectivity and dispersal can lead to different assessments of marine reserves. The analysis also illustrates how the incorporation of space into models of resource exploitation raises fundamental questions about the relationship of aggregate biological production to the production levels in each patch. We show that models with the supraadditivity property-system-wide production is greater than the sum of patch production with no dispersal-are more likely to predict that the benefits of marine reserves outweigh the costs.