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Using reproductive values to define optimal harvesting for multisite density-dependent populations: example with a marine reserve
Brooks, E.N. (2002). Using reproductive values to define optimal harvesting for multisite density-dependent populations: example with a marine reserve. Can. J. Fish. Aquat. Sci. 59(5): 875-885
In: Canadian Journal of Fisheries and Aquatic Sciences = Journal canadien des sciences halieutiques et aquatiques. National Research Council Canada: Ottawa. ISSN 0706-652X, more
Peer reviewed article  

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Keywords
    Harvesting; Population density; Gadus morhua Linnaeus, 1758 [WoRMS]; Marine

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  • Brooks, E.N.

Abstract
    A new method for determining optimal harvest from age-structured populations with a density-dependent stock-recruit relationship is presented. The theoretical optimal harvest comes from removing the age-class with the smallest ratio of reproductive value to weight. The method is derived from considering the sensitivity of equilibrium egg production to harvest using results for density-dependent Leslie matrices. The method holds in both single- and multi-site contexts and is derived for both Ricker and Beverton-Rolt recruitment functions. I illustrate the method for a one-site model of Arcto-Norwegian cod (Gadus morhua) and obtain the same optimal strategy as previous methods, namely that age-class 6 should be harvested 45%. Including age-specific selectivities, the best constrained yields occur at a harvest rate of 11% on ages 5-12. This yield is 73% of the theoretical optimum. I considered the same model when a reserve is established and found that high transfer rates out of the reserve (where spawners attain a higher fecundity) produced greater yields that were 86% of the one-site (no reserve) yield. Also, if overfishing occurs at 1.5 and 2.0 times the optimal level in the one-site case, then most yields from the reserve model are greater than those from the one-site model.

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