Biomedical subjects

Kristan A Schneider

Publications and source records attributed to Kristan A Schneider.

3 recordsLinked to original sources

PubMed2006

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition.

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.

Alleles↗

PubMed2006

Intraspecific competitive divergence and convergence under assortative mating.

Ecologically driven sympatric speciation has received much attention recently. We investigate a multilocus model of a quantitative trait that is under frequency-dependent selection caused by intraspecific competition and acts as mating character for assortment. We identify the conditions that lead to the establishment of reproductively isolated clusters. This may be interpreted as evolutionary splitting or sympatric speciation. In our model, there are parameters that independently determine the strength of assortment, the costs for being choosy, and the strength of frequency-dependent natural selection. Sufficiently strong frequency dependence leads to disruptive selection on the phenotypes. The population consists of (sexual) haploid individuals. If frequency dependence is strong enough to induce disruptive selection and costs are absent or low, the result of evolution depends in a distinctive nonlinear way on the strength of assortment: under moderately strong assortment, less genetic variation is maintained than under weak or strong assortment, and sometimes there is none at all. Evolutionary splitting occurs only if frequency dependence and assortment are both strong enough and costs are low. Even then, the evolutionary outcome depends on the genetics and the initial conditions. The roles of the number of loci, of linkage, and of asymmetric selection are also explored.

Animals↗

PubMed2005

Competitive divergence in non-random mating populations.

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.

Animals↗