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25-MultiSpecies - MULTISPECIES MODELS All of the models...

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Spawners Recruits S eq MULTISPECIES MODELS All of the models that we have examined so far have been based on the notion that we have a fishery harvesting from a single stock of fish. This is a gross oversimplification of the real situation in most fisheries. Most types of fishing gear catch a variety of fish species and most fishing vessels operate in a variety of fisheries, with the consequence that few fisheries can fairly be classified as being exclusively single species. Furthermore, there are likely to be ecological linkages between the various species harvested, either because the organisms feed on each other or because they share a common food source. As you might imagine, the models for multispecies fisheries can be very complicated. We will examine a few examples of simple multispecies models to illustrate the general principles involved in analyzing a multispecies fishery. Technical Interactions in Multispecies Fisheries Technical interactions between fish stocks occur when several stocks share the same geographic region and are caught together by the fishing gear, but the stocks do not exert any strong biological or ecological influence over each other. That is, the biological interactions among the stocks are sufficiently small that they can be ignored. In salmon fisheries this is often described as the problem of a mixed stock fishery. To illustrate the problem consider the following hypothetical example, from Ricker (1958), on the Supplemental Reading list. We have three salmon stocks having different spawner-recruit relationships, but all with the same unexploited equilibrium stock size. R=S A B C To proceed further we must express the equilibrium catch as a function of the exploitation rate. For a Ricker SR model the equilibrium stock size S eq is related to the exploitation rate μ according to the following S eq ln a 1 μ - ( 29 b = FW431/531 Copyright 2008 by David B. Sampson Multispecies - Page 160
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Exploitation Rate Equilibrium Catch μ MSY and the equilibrium catch C eq is related to μ according to C eq R S eq ( 29 S eq - = a ln a 1 μ - ( 29 b exp b - ln a 1 μ - ( 29 b ln a 1 μ - ( 29 b - = C eq ln a 1 μ - ( 29 b 1 μ - ( 29 ln a 1 μ - ( 29 b - = ln a 1 μ - ( 29 b μ 1 μ - = For our three salmon stocks we get the following picture of equilibrium catch versus exploitation rate. Notice that the stocks have different maximum equilibrium catches (MSY) and that they occur at different exploitation rates. If we set our exploitation rate so as to maximize the combined catches, we would end up eliminating the least productive stock. To guard against this problem many of our salmon stocks are managed to protect the weakest stock.
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