Dynamics of transitions between population interactions: a nonlinear interaction alpha-function defined

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Abstract
In nature, two populations may interact in different ways during their lifetime, and even undergo transitions from one type of interaction to another. A model for the dynamics of these transitions has been developed in this study. The interaction coefficients αiin the Lotka–Volterra equations are re-interpreted as nonlinear functions of population densities Ni, Nj, modulated by environmental parameters, which offers the possibility of a change in sign. Transitions can take place owing to variations in population density (endogenous effect), or in the environmental parameters (exogenous effect). Models for both facultative and obligate associations are examined. Graphical stability analyses show that multiple density equilibria are possible, accounting for the occurrence of the transitions.