EVOLUTION OF SIMPLE POPULATION-DYNAMICS

We investigated the evolution of demographic parameters determining th e dynamics of a mathematical model for populations with discrete gener ations. In particular, we considered whether the dynamic behaviour wil l evolve to stability or chaos. Without constraints on the three param eters - equilibrium density, growth rate and dynamic complexity - simp le dynamics rapidly evolved. First, selection on the complexity parame ter moved the system to the edge of stability, then the complexity par ameter evolved into the region associated with stable equilibria by ra ndom drift. Most constraints on the parameters changed these conclusio ns only qualitatively. For example, if the equilibrium density was bou nded, drift was slower, and the system spent more time at the edge of stability and did not move as far into the region of stability. If the equilibrium density was positively correlated with the complexity, th e opposing selection pressures for increased equilibrium density and f or reduced complexity made the edge of stability evolutionarily stable : drift into the stable region was prevented. If, in addition, the gro wth rate was bounded, complex dynamics could evolve. Nevertheless, thi s was the only scenario where chaos was a possible evolutionary outcom e, and there was a clear overall tendency for the populations to evolv e simple dynamics.