Beeton, NJ and Hosack, GR and Wilkins, A and Forbes, LK and Ickowicz, A and Hayes, KR, Modelling competition between hybridising subspecies, Journal of Theoretical Biology, 486 Article 110072. ISSN 0022-5193 (2020) [Refereed Article]
Copyright 2019 Elsevier Ltd.
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.
|Item Type:||Refereed Article|
|Keywords:||dynamical systems analysis, Lotka-Volterra, climate change, invasive species, mate choice|
|Research Division:||Biological Sciences|
|Research Group:||Bioinformatics and computational biology|
|Research Field:||Bioinformatics and computational biology not elsewhere classified|
|Objective Division:||Expanding Knowledge|
|Objective Group:||Expanding knowledge|
|Objective Field:||Expanding knowledge in the mathematical sciences|
|UTAS Author:||Forbes, LK (Professor Larry Forbes)|
|Web of Science® Times Cited:||3|
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