Abstract
In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brown, G. and J. Roughgarden (1997). A metapopulation model with private property and a common pool. Ecol. Econ. 22, 65–71.
Brown, L. D. and N. D. Murray (1992). Population genetics, gene flow, and stock structure in Haliotis rubra and Haliotis laevigata. In Abalone of the World: Biology, Fisheries and Culture, S. A. Shepherd et al. (Eds), pp. 24–33, Oxford: Fishing News Books.
Clark, C. W. (1976). Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 1st edn, New York: Wiley.
Clark, C. W. (1984). Strategies for multispecies management: objectives and constrains, in Exploitation of Marine Communities, R. M. May (Ed.), pp. 303–312, Berlin: Springer.
Frank, K. T. (1992). Demographic consequences of age-specific dispersal in marine fish populations. Can. J. Fish. Aquat. Sci. 49, 2222–2231.
Frank, K. T. and W. C. Leggett (1994). Fisheries ecology in the context of ecological and evolutionary theory. Annu. Rev. Ecol. Syst. 25, 401–422.
Gordon, H. S. (1954). The economic theory of a common-property resource: the fishery. J. Polit. Econ. 62, 124–142.
Hilborn, R. and C. J. Walters (1987). A general model for simulation of stock and fleet dynamics in spatially heterogeneous fisheries. Can. J. Fish. Aquat. Sci. 44, 1366–1369.
Horwood, J. W. (1990). Near-optimal rewards from multiple species harvested by several fishing fleets. IMA J. Math. Appl. Med. Biol. 7, 55–68.
Leung, A. W. (1995). Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka system. App. Math. Optim. 31, 219–241.
Munro, G. R. (1992). Mathematical bioeconomics and the evolution of modern fisheries economics. Bull. Math. Biol. 54, 163–184.
Murphy, E. J. (1995). Spatial structure of the Southern Ocean ecosystem: predator-prey linkages in Southern Ocean food webs. J. Anim. Ecol. 64, 333–347.
Prince, J. D. (1992). Using a spatial model to explore the dynamics of an exploited stock of the abalone Haliotis rubra. In Abalone of the World: Biology, Fisheries and Culture, S. A. Shepherd et al. (Eds), pp. 305–317. Oxford: Fishing News Books.
Prince, J. D, T. L. Sellers, W. B. Ford and S. R. Talbot (1987). Experimental evidence for limited dispersal of haliotid larvae (genus Haliotis; Mollusca: Gastropoda). J. Exp. Mar. Biol. Ecol. 106, 243–264.
Pulliam, H. R. (1988). Source, sink, and population regulation. Am. Nat. 132, 652–661.
Shepherd, S. A. and L. N. Brown (1993). What is abalone? Implications for role of refugia in conservation. Can. J. Fish. Aquat. Sci. 50, 20001–20009.
Sinclair, M. (1988). Marine populations: An Essay on Population Regulation and Speciation. Seattle: Univ. Wash. Press.
Tuck, G. N. and H. P. Possingham (1994). Optimal harvesting strategies for a metapopulation. Bull. Math. Biol. 56, 107–127.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Supriatna, A.K., Possingham, H.P. Optimal harvesting for a predator-prey metapopulation. Bull. Math. Biol. 60, 49–65 (1998). https://doi.org/10.1006/bulm.1997.0005
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1006/bulm.1997.0005