Two fish species competition model with nonlinear interactions and equilibrium catches
Tóm tắt
Two species competition model is built up by assuming the hypothetical second order interactions in order to consider effects of exploitation on two competing fish species with non-linear interactions. Most important characteristic of this model, compared withLotka-Volterra type linear competition model, is that this model can possess multiple stable equilibrium points. Therefore there is a possibility that two species keeping the equilibrium state at one stable equilibrium point will be attracted to the other stable equilibrium point after a heavy perturbation. In this model reversible change of the fishing pressure does not always results in that of the equilibrium catch. In this sence MSY concept for single species can not be extended to this model. If there are multiple stable equilibrium points, the change of the dominant fish species, catastrophic and irreversible change of each equilibrium catch may be observed when the perturbation by the exploitation is added. This phenomenon immediately reminds us of the change of the dominant fish species between Japanese common mackerel and Pacific saury in the northwest Pacific Ocean. In case of the management of two competing fish species with nonlinear interactions, the consideration on the balance between the fishing pressure for each species may be as important as the decision on the catch limit for each species. MSY level for each species based on the single-species theory could be quite erroneous.
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Tài liệu tham khảo
Allee, W. C. (1951)Cooperation among animals with human implications. Schuman, New York (Revised Edition ofSocial Life of Animals, Norton, New York, (1938) 233 pp.
Beverton, R. J. H. andS. J. Holt (1957) On the dynamics of exploited fish population,Fish. Invest., Lond., Ser. 2,19: 533 pp.
Larkin, P. A. (1963) Interspecific competition and exploitation.J. Fish. Res. Bd. Can. 20: 647–678.
Lewontin, R. C. (1969) The meaning of stability.Brookhaven Symp. Biol. 22: 13–24.
Lotka, A. J. (1925)Elements of physical biology. Williams and Willkins, Baltimore, Md., reprinted 1956, Dover, New. York.
May, R. M. (1973)Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton. 265 pp.
Mitani, F. (1970) On the long-term fluctuation of the pelagic fish resorurces.Bull. Jap. Soc. Fish. Oceanogr. 16: 187–191.
Neave, F. (1953) Principles affecting the size of pink and chum salmon population in British Columbia.J. Fish. Res. Bd. Canada. 9: 450–491.
Rosenzweig, M. L. andR. H. MacArthur (1963) Graphical representation and stability conditions of predator-prey interactions.Amer. Natural. 97: 209–223.
Schaefer, M. B. (1957) Some considerations of population dynamics and economics in relation to the management of the commercial marine fisheries.J. Fish. Res. Bd. Canada. 14: 669–681.
Sutherrland, J. P. (1974) Multiple stable points in natural communities.Amer. Natural. 108: 859–873.
Vandermeer, J. H. (1973) Generalized models of two species interactions: A graphical analysis.Ecology 54: 809–818.
Volterra, V., (1928) Variations and fluctuations of the number of individuals in animal species living together.J. Cons. perm. Int. Explor. Mer 3: 3–51.