Variation in the outcome of population interactions: bifurcations and catastrophes

Journal of Mathematical Biology
Maria-Josefina Hernandez, Ignacio Barradas

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 alpha-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 facu...Continue Reading

Citations

Apr 20, 2011·Journal of Theoretical Biology·Yuanshi Wang, Donald L DeAngelis
Jul 11, 2009·Journal of Theoretical Biology·Maria-Josefina Hernandez
May 13, 2014·Bulletin of Mathematical Biology·Yuanshi Wang, Hong Wu
Oct 13, 2006·The Journal of Animal Ecology·Andrew R ThompsonRussell J Schmitt
Oct 8, 2009·Ecology Letters·J Nathaniel Holland, Donald L DeAngelis
Jun 13, 2015·Royal Society Open Science·Faustino Sánchez-GarduñoTatiana T Marquez-Lago
Nov 23, 2017·Mathematical Biosciences and Engineering : MBE·Yuanshi Wang, Hong Wu
May 9, 2018·Mathematical Biosciences·Marisabel Rodriguez MessanYun Kang

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