Chaos from Linear Frequency-Dependent Selection
The American Naturalist 138 (1): 51-68. 1991.
The online version of this paper is still under construction. Some of the figures are low resolution. The equations are not finished being proof read.
The simplest diploid model of frequency-dependent selection can generate
periodic and chaotic trajectories for the allele frequency. The model
is of a randomly mating, infinite diploid population with non-overlapping
generations, segregating for two alleles under frequency-dependent viability
selection. The fitnesses of each of the three genotypes is a linear function
of the frequencies of the three genotypes. The region in the space of
the coefficients that yields cycles and chaos is explored analytically
and numerically. The model follows the period-doubling route to chaos
as seen with logistic growth models, but includes additional phenomena
such as the simultaneous stability of cycling and chaos. The general
condition for cycling or chaos is that the heterozygote deleteriously
effect all genotypes. The kinds of ecological interactions that could
give rise to these fitness regimes producing cycling and chaos include
cannibalism, predator attraction, habitat degradation, and disease transmission.
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