Summary: 1
CHAOS FROM LINEAR FREQUENCY­DEPENDENT SELECTION
LEE ALTENBERG
Department of Zoology, Duke University, Durham, NC 27706
Submitted February 13, 1989; Revised March 9, 1990; Accepted May 20, 1990 1
Abstract.---The simplest diploid model of frequency­dependent selection can gen­
erate periodic and chaotic trajectories for the allele frequency. The model is of
a randomly mating, infinite diploid population with non­overlapping generations,
segregating for two alleles under frequency­dependent 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 cy­
cles and chaos is explored analytically and numerically. The model follows the
period­doubling 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 fit­
ness regimes producing cycling and chaos include cannibalism, predator attraction,
habitat degradation, and disease transmission.
The possibilities for complex dynamical behavior from even the simplest models
of population growth regulation (May, 1974, 1976) have led to the examination of

Source: Altenberg, Lee - Department of Information and Computer Science, University of Hawai'i at Manoa

Collections: Computer Technologies and Information Sciences