Movement behaviour of fish, harvesting-induced habitat degradation and the optimal size of marine reserves
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Many models have assessed how marine reserves protect fish populations and—under certain conditions—simultaneously increase yield. Only recently have models considered the effects of fishing-induced habitat damage by assuming reduced population growth in fishing areas. Even though it is understood that fish movement patterns affect the functioning and design of marine reserves, fishing-induced changes in movement patterns, as a response to decreased habitat quality, have not been studied in this context. Our work explores how harvesting-induced movement behaviour of fish can affect optimal yield and size of a marine reserve. Our model is based on reaction-diffusion equations and recent advances in their application to strongly heterogeneous environments with sharp transitions in environmental conditions. We model movement behaviour in response to harvesting and habitat destruction via increased diffusion rates and increased preference for protected areas, and implement reduced reproduction as an effect of habitat degradation. We find an alternative mechanistic explanation for the empirical observation that high fish mobility may not decrease fish density inside a reserve. We also find that movement-behavioural responses of fish to harvesting can decrease the economic value of protected areas and increase their conservation value. For maximum sustainable yield, we find that a low harvesting rate and small protected area are optimal when fish show a strong preference for protected areas as a response to fishing efforts. On the other hand, a high harvesting rate and a large protected area are optimal if fish respond to harvesting by a strong increase in movement rates in fishing areas.
KeywordsFish movement behaviour Marine protected area Maximum sustainable yield Reaction-diffusion equation
YA and FL thank Michael Neubert for inspiring discussions. FL gratefully acknowledges funding by the Natural Sciences and Engineering Research Council of Canada through the Discovery Grants program (RGPIN-2016-04759) and a Discovery Accelerator Supplement (RGPAS-2016-492872). We also thank two reviewers for their valuable comments and suggestions.
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