Evolution of simple population dynamics

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Abstract
We investigated the evolution of demographic parameters determining the dynamics of a mathematical model for populations with discrete generations. In particular, we considered whether the dynamic behaviour will evolve to stability or chaos. Without constraints on the three parameters-equilibrium density, growth rate and dynamic complexity-simple dynamics rapidly evolved. First, selection on the complexity parameter moved the system to the edge of stability, then the complexity parameter evolved into the region associated with stable equilibria by random drift. Most constraints on the parameters changed these conclusions only qualitatively. For example, if the equilibrium density was bounded, 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, the opposing selection pressures for increased equilibrium density and for reduced complexity made the edge of stability evolutionarily stable: drift into the stable region was prevented. If, in addition, the growth rate was bounded, complex dynamics could evolve. Nevertheless, this was the only scenario where chaos was a possible evolutionary outcome, and there was a clear overall tendency for the populations to evolve simple dynamics.