EVOLUTION OF STABILITY PARAMETERS IN SINGLE-SPECIES POPULATION-MODELS - STABILITY OR CHAOS

Several difference equations commonly used to model density-dependent population growth of a single population in a constant environment show a period doubling bifurcation scenario from stability to chaos as one or more parameters are varied. Models of evolutionary change in such parameters are studied analytically. Whether the population will evolve towards stability or towards chaos is model-dependent. This is caused by model-dependent differences in the coupling of stability evolution to selection for increased carrying capacity, and differences in whether the parameters act predominantly at high or at low densities. Generally, stability is favored by selection at high densities while unstability is favored at low densities. As the former selection pressure tends to be stronger, it is likely that a deterministically fluctuating population with constant carrying capacity will evolve towards Stability. © 1992.