Abstract
A Coupled Map Lattice (CML) model, for host-parasitoid Nicholson–Bailey interactions, with an explicit spatial distribution of partial refuge areas, is presented by considering the parasitoid attack rate as a patch dependent parameter. The effect of habitat heterogeneity on the dynamics of both populations, that is, on their spatial distribution and temporal behavior is analyzed. Our results show that depending on many features such as position, size, and fragmentation of a refuge, as well as the dispersal parameters of hosts and parasitoids, together with the parasitoid attack rate, the inclusion of refuges may as well stabilize as destabilize the host-parasitoid dynamics. The results are analyzed for the local and the global scales. Spatial patterns resulting from such heterogeneous patchy environments are also obtained.
Similar content being viewed by others
References
Briggs, C.J., Hoopes, M.F., 2004. Stabilizing effects in spatial parasitoid-host and predator-prey models: a review. Theor. Popul. Biol. 65, 299–315.
Cobbold, C.A., Lewis, M.A., Lutscher, F., Roland, J., 2005. How parasitism affects critical patch-size in a host-parasitoid model: application to the forest tent caterpillar. Theor. Popul. Biol. 67, 109–125.
Comins, H.N., Hassell, M.P., May, R.M., 1992. The spatial dynamics of host-parasitoid systems. J. Anim. Ecol. 61, 735–748.
Edelstein-Keshet, L., 1988. Mathematical Models in Biology. Random House, New York.
Hassell, M.P., 2000. The Spatial and Temporal Dynamics of Host-Parasitoid Interactions. Oxford University Press, New York.
Hassell, M.P., Comins, H.N., May, R.M., 1991. Spatial structure and chaos in insect population dynamics. Nature 353, 255–258.
Holt, R.D., Hassell, M.P., 1993. Environmental heterogeneity and the stability of host-parasitoid interactions. J. Anim. Ecol. 62, 89–100.
Kot, M., 2001. Elements of Mathematical Ecology. Cambridge University Press, Cambridge.
Křivan, V., 1998. Effects of optimal antipredator behavior of prey on predator-prey dynamics: The role of refuges. Theor. Popul. Biol. 53, 131–142.
Lynch, L.D., Bowers, R.G., Begon, M., Thompson, D.J., 1998. A dynamic refuge model and population regulation by insect parasitoids. J. Anim. Ecol. 67, 270–279.
McNair, J.N., 1986. The effects of refuges on predator-prey interactions: a reconsideration. Theor. Popul. Biol. 29, 38–63.
Murdoch, W.W., Luck, R.F., Swarbrick, S.L., Walde, S.J., Reeve, J.D., Yu, D.S., 1989. A refuge for red scale under control by Aphytis: structural aspects. Ecology 70(6), 1707–1714.
Murdoch, W.W., Luck, R.F., Swarbrick, S.L., Walde, S., Yu, D.S., Reeve, J.D., 1995. Regulation of an insect population under biological control. Ecology 76(1), 206–217.
Murdoch, W.W., Swarbrick, S.L., Luck, R.F., Walde, S., Yu, D.S., 1996. Refuge dynamics and metapopulation dynamics: an experimental test. Am. Nat. 147(3), 424–444.
Murdoch, W.W., Briggs, C.J., Swarbrick, S., 2005. Host suppression and stability in a parasitoid-host system: experimental demonstration. Science 309, 610–613.
Murray, J.D., 1989. Mathematical Biology. Springer, Berlin.
Nicholson, A., Bailey, V.A., 1935. The balance of animal populations. Part 1. Proc. Zool. Soc. Lond. 3, 551–598.
Singh, B.K., Subba Rao, J., Ramaswamy, R., Sinha, S., 2004. The role of heterogeneity on the spatiotemporal dynamics of host-parasitoid metapopulation. Ecol. Model. 180, 435–443.
Wright, R.W., Hastings, A., 2007. Spontaneous patchiness in a host-parasitoid integrodifference model. Bull. Math. Biol. 69, 2693–2709.
Zhou, S.R., Wang, G., 2006. One large, several medium, or many small? Ecol. Model. 191, 513–520.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mistro, D.C., Rodrigues, L.A.D. & Varriale, M.C. The Role of Spatial Refuges in Coupled Map Lattice Model for Host-Parasitoid Systems. Bull. Math. Biol. 71, 1934–1953 (2009). https://doi.org/10.1007/s11538-009-9432-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-009-9432-8