Adaptive Dynamics Based on Ecological Stability
what kind of mutant cannot invade the resident population,
and what kind of mutant can invade the resident population?
what kind of mutant is able to substitute the resident clone,
and when does a stable coexistence arise?
We assume that the system of mutants and residents can be modelled by a Lotka-Volterra system.We will suppose that the phenotype space is a subset of Rn and the interaction function describing the dependence of the parameters of the Lotka-Volterra dynamics on the phenotypes of the interacting individuals is smooth and mutation is small. We shall answer the preceding questions in terms of possible mutation directions in the phenotype space, based on the analysis of ecological stability. Our approach establishes a connection between adaptive dynamics and dynamical evolutionary stability.
KeywordsResident Population Interaction Function Interior Equilibrium Adaptive Dynamic Volterra Model
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