Summary: 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 \(R_0=R_0(u)\) are functions of \(u\). For a general matrix model, we show that \(r\) and \(R_0\) share critical values and extrema at values \(u=u^*\) for which \(r(u^*)=R_0(u^*)=1\). This allows us to re-interpret, in terms of the more analytically tractable quantity \(R_0\), a fundamental bifurcation theorem for nonlinear 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.