Published on Thu Sep 16 2021

Weak selection and the separation of eco-evo time scales using perturbation analysis

Gerlee, P.

Under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The error between the composite solution, which describes the dynamics for all times, and the solution to the full model scales linearly with the strength of selection.

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Abstract

We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation. We apply this method to a model of public goods dynamics and show that the error between the composite solution, which describes the dynamics for all times, and the solution to the full model scales linearly with the strength of selection.