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Coexistence of two types on a single resource in discrete time

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Abstract

Armstrong and McGehee (1980) have shown that two species modeled in continuous time can coexist on a single resource provided that one species oscillates autonomously. This paper demonstrates the parallel result in discrete time. I consider a deterministic model of two asexual types in a single patch competing for a single resource, and show that such systems generically produce oscillatory coexistence or bistability if one of the types displays periodic or chaotic behavior in isolation. The conditions for coexistence or bistability are derived in terms of the convexity of the functions describing fitness as a function of resource availability. I also analyze whether or not a stable type, a type with a stable equilibrium population size when considered in isolation, can invade a periodic orbit of an unstable type, and show that the same convexity condition distinguishes these two cases. The widely considered exponential or Ricker model for population dynamics lies on the boundary between the two cases and is highly degenerate in this context.

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  1. Center for Applied Mathematics, Cornell University, 14853, Ithaca, NY, USA

    F. R. Adler

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  1. F. R. Adler
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Adler, F.R. Coexistence of two types on a single resource in discrete time. J. Math. Biol. 28, 695–713 (1990). https://doi.org/10.1007/BF00160232

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  • DOI: https://doi.org/10.1007/BF00160232

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