Abstract
The concept of density-dependent population growth is fundamental to our understanding of how populations persist. While it is generally agreed that negative density dependence must occur at high densities, the direction of density dependence may be negative (pure negative density dependence) or positive (demographic Allee effect) at low densities. In this article, we present a technique to link the direction of density dependence to generic ecological factors. This technique involves exploiting the presence of a particular bifurcation, known as a saddle-node-transcritical interaction. We first provide a method to detect this bifurcation in a given model and then demonstrate its ecological relevance using several existing mechanistic models. With a mathematical framework in place, we are able to identify scenarios in which neither a weak Allee effect nor pure negative density dependence are possible. More generally, we find conditions on parameter values that are necessary for transitions between pure negative density dependence and demographic Allee effects to occur.
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This publication has emanated from research conducted with the financial support of Science Foundation Ireland under the grant number SFI/13/IA/1923.
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The following supplementary material is available for this article:
Section S1 Study of the normal form of the saddle-node-transcritical interaction
Section S1.1 Bifurcation structure when c > 0
Section S2 Discrete-time example
Section S3 Centre-manifold projection for emergent Allee effect model
Section S4 Evaluation of cubic terms at codimension-2 point
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Donohue, J.G., Piiroinen, P.T. A technique for analysis of density dependence in population models. Theor Ecol 11, 465–477 (2018). https://doi.org/10.1007/s12080-018-0380-5
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DOI: https://doi.org/10.1007/s12080-018-0380-5