Models of frequency-dependent selection with mutation from parental alleles

Polymorphism and the Red Queen: the selective maintenance of allelic variation in a deteriorating environment

Although allelic variation is ubiquitous in natural populations, our theoretical models are poor at predicting the existence and properties of these observed polymorphisms. In this study, inspired by Van Valen's Red Queen hypothesis, we modeled the effect of viability selection in a deteriorating environment on the properties of allelic variation in populations subject to recurrent mutation. In Monte Carlo simulations, we found that levels of polymorphism consistently built up over time. We censused the simulated populations after 10,000 generations of mutation and selection, revealing that, compared with models assuming a constant environment, the mean number of alleles was greater, as was the range of allele numbers. These results were qualitatively robust to the addition of genetic drift and to the relaxation of the assumption that the viabilities of phenogenotypes containing a new mutation are independent of each other (i.e. incorporating a model of generalized dominance). The broad range of allele numbers realized in the simulated populations-from monomorphisms to highly polymorphic populations-more closely corresponds to the observed range from numerous surveys of natural populations than previously found in theoretical studies. This match suggests that, contrary to the views of some writers, selection may actively maintain genetic variation in natural populations, particularly if the selective environment is gradually becoming harsher. Our simulations also generated many populations with heterozygote advantage, a mismatch with real data that implies that this selective property must arise extremely rarely in natural populations.

The Selective Maintenance of Allelic Variation Under Generalized Dominance

Simple models of viability selection acting on variation at a single diploid locus only maintain multiple alleles for very restricted sets of fitnesses. Most of these models assume that fitnesses are independent, even if the genotypes share alleles. Here, we extend this result to a model with generalized dominance interactions, in which fitnesses are strongly affected by what we call the “primary effects” of the genotype’s component alleles, so that genotypes with shared alleles have correlated fitnesses. Nevertheless, in keeping with previously reported results, we also show that such fitness sets are easily constructed over time if recurrent mutation is occurring simultaneously. We find that such models maintain less variation over time than do (previous) models with independently sampled fitnesses, especially when the effects of genetic drift are taken into account. We also show that there is a weak tendency for greater weighting of primary effects to evolve over time.

The maintenance of single-locus polymorphism by maternal selection

Population geneticists have long been interested in the ability of natural selection to maintain the levels of standing variation observed in natural populations. Here, we study the polymorphism-maintaining properties of maternal selection, in which the fitness of an individual is a function of its own and its mother’s genotype. Using a model proposed by Gavrilets, we first estimate the proportion of parameter/state space that preserves allelic variation, before investigating the construction of polymorphism over time through the joint action of mutation and selection. These two methods, the “parameter-space” and “constructionist” approaches, respectively, enable us to draw some general conclusions. We argue that, even though the proportion of parameter-state space allowing multiallele polymorphism is greater under maternal selection than under the standard model of constant viability selection, the former is, in fact, less likely to maintain large numbers of alleles. Nevertheless, variation that is balanced by maternal selection is likely to show elements of heterozygous advantage and be resistant to depletion by genetic drift. We observe that the population mean fitness frequently decreases after the successful invasion of a new mutation, but such declines are usually temporary.