Abstract.
The nature of the association between two species may vary depending on population abundances, age or size of individuals, or environmental conditions. Interactions may switch between beneficial and detrimental depending on the net balance of costs and benefits involved for each species. We study the repercussion of the ecological setting on the outcomes of conditional or variable interactions by means of a model that incorporates density-dependent interaction coefficients; that is, interaction α-functions. These characterize the responsiveness and sensitivity of the association to changes in partner's abundance, and can take positive and negative values. Variable outcomes – and transitions between them – are categorized as homeo- or allo-environmental, that is, occurring under the same ecological setting, or not, respectively. Bifurcation analyses show that these dynamics are moulded by ecological factors that are: intrinsic to the nature of the association (concerning the sensitivity of the interaction), and extrinsic to the association itself (the quality of the environment referred to each species alone). The influence of these factors may be conflicting; consequently, the dynamics involve catastrophic events. In a facultative variable association, stable coexistence is expected when environmental conditions are adverse; otherwise, the exclusion of one species is the likely outcome. Remarkable situations as the switching of victim-exploiter roles illustrate the theoretical perspective.
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Received: 15 December 2001 / Revised version: 18 November 2002 / Published online: 28 February 2003
Key words or phrases: Variable population interactions – Conditional interactions – Costs and benefits – Density dependent interaction coefficient – Hysteresis – Symbiosis – Mutualism – Parasitism
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Hernandez, MJ., Barradas, I. Variation in the outcome of population interactions: bifurcations and catastrophes. J. Math. Biol. 46, 571–594 (2003). https://doi.org/10.1007/s00285-002-0192-4
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DOI: https://doi.org/10.1007/s00285-002-0192-4