If the demographic parameters in a matrix model for the dynamics of a structured population are dependent on a parameter u, then the population growth rate r = r(u) and the net reproductive number R0 = R0(u) are functions of u. For a general matrix model, we showthat r and R0 share critical values and extrema at values u = u* for which r(u*) = R0(u*) = 1. This allows us to re-interpret, in terms of the more analytically tractable quantity R0, a fundamental bifurcation theorem for non-linear Darwinian matrix models from the evolutionary game theory that concerns the destabilization of the extinction equilibrium and creation of positive equilibria. Two illustrations are given: a theoretical study of trade-offs between fertility and survivorship in the evolution of an evolutionarily stable strategies and an application to an experimental study of the evolution to a genetic polymorphism.
- Darwinian matrix models
- Net reproductive number
- The evolutionary game theory
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics