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Spontaneous Patchiness in a Host-Parasitoid Integrodifference Model

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Abstract

Observations of a host-parasitoid interaction in which victims are significantly less motile than their exploiters suggest the possibility of stable spatial pattern in a fairly homogeneous environment. Findings of pattern formation in continuous-time models are not fully able to account for this behavior. Those findings often rely on questionable biological conditions, and more fundamentally, the continuous nature of time in such models does not reflect the reality of the observed interaction. In this paper, we introduce a discrete-time spatial model of the interaction. The final state of our model is often a striking spatial pattern, similar to those observed. We analyze the model, describe its transient behavior, and find the conditions under which these spatial patterns occur, as well as an estimate of maximum possible patch size under those conditions. We also discuss the existence of such conditions in the natural system.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Davis, CA, 95616, USA

    R. W. Wright

  2. Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA

    Alan Hastings

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  1. R. W. Wright
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  2. Alan Hastings
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Correspondence to R. W. Wright.

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Wright, R.W., Hastings, A. Spontaneous Patchiness in a Host-Parasitoid Integrodifference Model. Bull. Math. Biol. 69, 2693–2709 (2007). https://doi.org/10.1007/s11538-007-9236-7

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  • DOI: https://doi.org/10.1007/s11538-007-9236-7

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