Frequency-Dependent Selection and the Maintenance of Genetic Variation: Exploring the Parameter Space of the Multiallelic Pairwise Interaction Model

Abstract

When individuals' fitnesses depend on the genetic composition of the population in which they are found, selection is then frequency dependent. Frequency-dependent selection (FDS) is often invoked as a heuristic explanation for the maintenance of large numbers of alleles at a locus. The pairwise interaction model is a general model of FDS via intraspecific competition at the genotypic level. Here we use a parameter-space approach to investigate the full potential for the maintenance of multiallelic equilibria under the pairwise interaction model. We find that FDS maintains full polymorphism more often than classic constant-selection models and produces more skewed equilibrium allele frequencies. Fitness sets with some degree of rare advantage maintained full polymorphism most often, but a wide variety of nonobvious fitness patterns were also found to have positive potential for polymorphism. An example is put forth suggesting possible explanations for multiallelic polymorphisms maintained despite positive FDS on individual alleles.

The Generation and Maintenance of Genetic Variation by Frequency-Dependent Selection: Constructing Polymorphisms Under the Pairwise Interaction Model

“…The region of parameter space that maintains polymorphism is minuscule for n . 4 (Trotter and Spencer 2007). In our constructed sets, the proportion that kept all alleles decreases approximately linearly with increasing n, a much less precipitous drop-off than that observed for random sets.…”

“…Potential for polymorphism: Historically (Lewontin et al 1978;Asmussen and Basnayake 1990;Star et al 2007;Trotter and Spencer 2007), the ''potential'' for polymorphism under any given model has been measured as the proportion of random initial allele frequencies and randomly generated fitness sets that maintain all alleles. In the context of the construction approach, then, one could measure a sort of potential as the proportion of runs that had the same numbers of final and equilibrium alleles.…”

“…Parameter-space approaches to modeling FDS (Asmussen and Basnayake 1990;Trotter and Spencer 2007) find that general FDS results in a greater potential for maintaining variation for any given number of alleles than the constant viability model. Nevertheless, the proportion of random sets that keep more than five alleles remains very low.…”

“…In this study, we continue our investigations of the potential for variation under FDS (see Trotter and Spencer 2007). We continue to use the PIM of FDS, this time incorporating a mutational process into the model.…”

“…In equilibrium-based models, FDS fitnesses tend to maintain more alleles than constant fitnesses (Trotter and Spencer 2007) but it is not at all clear that this increased potential for polymorphism under FDS extends to construction models. Does assuming PIM fitness, using a construction approach, lead to polymorphisms with more alleles than those produced using constant fitness?…”