University Of Tasmania

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Modelling competition between hybridising subspecies

journal contribution
posted on 2023-05-21, 12:47 authored by Beeton, NJ, Hosack, GR, Wilkins, A, Lawrence ForbesLawrence Forbes, Ickowicz, A, Hayes, KR

The geographic niches of many species are dramatically changing as a result of environmental and anthropogenic impacts such as global climate change and the introduction of invasive species. In particular, genetically compatible subspecies that were once geographically separated are being reintroduced to one another. This is of concern for conservation, where rare or threatened subspecies could be bred out by hybridising with their more common relatives, and for commercial interests, where the stock or quality of desirable harvested species could be compromised. It is also relevant to disease ecology, where disease transmission is heterogeneous among subspecies and hybridisation may affect the rate and spatial spread of disease. We develop and investigate a mathematical model to combine competitive effects via the Lotka-Volterra model with hybridisation effects via mate choice. The species complex is structured into two classes: a subspecies of interest (named x), and other subspecies including any hybrids produced (named y). We show that in the absence of limit cycles the model has four possible equilibrium outcomes, representing every combination: total extinction, x-dominance (y extinct), y-dominance (x extinct), and at most a single coexistence equilibrium. We give conditions for which limit cycles cannot exist, then further show that the "total extinction" equilibrium is always unstable, that y-dominance is always stable, and that the other equilibria have stability depending on the model parameters. We demonstrate that both x-dominance and coexistence are achievable under a wide range of parameter values and initial conditions, which corresponds with empirical evidence of known competing-hybridising systems. We then briefly examine bifurcation behaviour. In particular, we note that a subcritical bifurcation is possible in which a "catastrophic" transition from x-dominance to y-dominance can occur, representing an invasion event. Finally, we briefly examine the common complication of time-varying carrying capacity, showing that such a case can make coexistence more likely. (C) 2019 Elsevier Ltd. All rights reserved.


Publication title

Journal of Theoretical Biology



Article number









School of Natural Sciences


Academic Press Ltd Elsevier Science Ltd

Place of publication

24-28 Oval Rd, London, England, Nw1 7Dx

Rights statement

Copyright 2019 Elsevier Ltd.

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences