Genetic Models of Frequency-Dependent Selection

Intraspecific competition is a phenomenon frequently described by ecologists. It has been invoked in the explanation of important evolutionary phenomena, such as for the maintenance of genetic variation or for the occurrence of disruptive selection with its possible consequences of ecological character displacement, reproductive isolation and, eventually, speciation. Recently, it was shown theoretically, though mainly by numerical simulation, that sympatric speciation can indeed be triggered by intraspecific competition. However, the generality and robustness of this finding with respect to a number of population genetic and ecological model assumptions is unknown and remains to be explored. Thefore, the main objective of this research project is the exploration of the consequences of various sets of assumptions regarding the genetic basis of the trait under frequency-dependent selection and the mating structure on the maintenance of genetic variation, the occurrence of disruptive selection, and the evolution of divergence within a population. Among the questions that shall be answered are the following. How strong must frequency dependence and assortative mating be such that a bimodal distribution of phenotypes is induced? How does this depend on the number and effects of the genes involved, and on the amount of recombination? Can assortative mating evolve by many small steps, i.e., by the accumulation of alleles at various loci that each increase the degree of assortment only slightly? This requires the formulation, extension, and analysis of mathematical models of the dynamics of the probability distribution of multilocus genotypes under recombination, frequency-dependent selection, and assortative mating. The methods include tools from the qualitative theory of dynamical systems as well as systematic numerical computations using a statistical approach for sampling a representative part of the parameter space.

In this project, the evolutionary consequences of frequency-dependent selection on the genetic structure of biological populations were investigated by using mathematical analysis and computer simulations of mathematical models. As is well known, biological evolution results from the interaction of natural selection with the hereditary mechanisms. Frequency-dependent selection means that the fitness of the various types of individuals depends on the frequency of the other types in the population. As an example, imagine birds that specialize on rare seeds that only they can crack because of their beak shape. They will have a selective advantage if the total amount of food available to the whole population is limited, but they are sufficiently rare to get enough food from their special resource. Frequency-dependent selection of this kind can induce disruptive selection, i.e., selection that favors extreme types. Many ecologists consider frequency-dependent selection as an important evolutionary force and invoke it for the explanation of several evolutionary phenomena, e.g., sympatric speciation. The consequences of frequency-dependent selection on the genetic structure of populations had been studied only under very simplifying ecological and, in particular, genetic assumptions. In this project, it could be shown in great generality that frequency-dependent selection which is strong enough to induce disruptive selection leads to high genetic diversity within a species. It could be demonstrated that the genes that have a large effect on the trait under selection will be polymorphic at an evolutionary equilibrium, in particular, there must be exactly two alleles present in high frequency at such loci. What is completely new and important in this context is that these statements could be mathematically quantified in several respects, so that predictions become feasible. As a consequence, also long- term evolution of the underlying genetic architecture could be studied. For assortatively mating populations, in which individuals choose their mating partners based on common phenotypic similarities, the conditions were explored under which an evolutionary splitting of the species in two can occur. Thus, new insights into the theory of (sympatric) speciation could be gained.