Freddy Bugge Christiansen

ON CONDITIONS FOR EVOLUTIONARY STABILITY FOR A CONTINUOUSLY VARYING CHARACTER

The two conditions for stability of an evolutionary equilibrium, the m-stability and the δ-stability conditions, are discussed. The m-stability condition is a condition for the convergence of the population toward the equilibrium, and the δ-stability condition coresponds to a local version of the classic evolutionarily stable strategy (ESS) condition. Together the two conditions provide the condition for a continuous stable strategy. The convergence stability condition corresponds to the requirement for convergence due to initial increase of rare alleles in a monomorphic population, and the local ESS stability condition corresponds to the stability of a monomorphic population at the evolutionary equilibrium against the increase of rare alleles. In this way, an evolutionary equilibrium that is convergence stable, but not local ESS stable, will tend to become polymorphic. The local ESS stability condition therefore contributes more to a description of the dynamics of variation at an evolutionary equilibrium than to the description of the stability of the evolutionary equilibrium. However, the characterization of a polymorphic evolutionary equilibrium cannot be reached by studying the initial increase of rare variant alleles, just as this method cannot describe all aspects of the convergence stability either. Combining these analyses provides a powerful tool in the initial exploration of evolutionary equilibriums of complicated systems, and convergence stable and local ESS unstable equilibriums point toward very interesting polymorphic evolutionary stable states. The analysis is illustrated on a model for intraspecific exploitative competition that may show monomorphic and polymorphic evolutionarily stable equilibriums.

Evolution of marine invertebrate reproductive patterns

Abstract A simple model of the evolution of reproductive patterns in marine benthic invertebrates is presented. The aim is to discuss the dichotomous distribution of forms into those which produce a large number of small eggs with planktotrophic development, and those which produce a small number of large eggs with direct or lecithotrophic development. The fecundity of adult individuals is assumed to be inversely proportional to egg size, and the mortality of planktonic larvae is assumed to be density independent and size dependent. The growth of planktonic larvae is assumed to be sigmoid with metamorphosis occurring at a given size. The model concludes that there are at most two evolutionarily stable egg sizes. Depending on larval growth rate and death rate, the metamorphosis size, a smaller egg size, or both may be evolutionarily stable. The predictions of the model are compared to patterns observed in nature. Illustrative data are supplied mainly from prosobranch molluscs.

Hard and Soft Selection in a Subdivided Population

Hard and soft selection are compared in a population subdivided into random mating subpopulations. The possibility for protected polymorphism is greater with soft than with hard selection. Protected polymorphism is more readily achieved with increasing isolation, an effect that is more pronounced with hard selection. The results are discussed in relation to selection components.

MATE AVAILABILITY AND FECUNDITY SELECTION IN MULTI-ALLELIC SELF-INCOMPATIBILITY SYSTEMS IN PLANTS

We investigate mate availability in different models of multiallelic self‐incompatibility systems in mutation‐selection‐drift balance in finite populations. Substantial differences among self‐incompatibility systems occur in average mate availability, and in variances of mate availability among individual plants. These differences are most pronounced in small populations in which low mate availability may reduce seed set in some types of sporophytic self‐incompatibility. In cases where the pollination system causes a restriction in the number of pollen genotypes available to an individual plant, the fecundity of that plant depends on the availability of compatible pollen, which is determined by its genotype at the incompatibility locus. This leads to an additional component of selection acting on self‐incompatibility systems, which we term “fecundity selection.” Fecundity selection increases the number of alleles maintained in finite populations and increases mate availability in small populations. The strength of fecundity selection is dependent on the type of self‐incompatibility. In some cases, fecundity selection markedly alters the equilibrium dynamics of self‐incompatibility alleles. We discuss the population genetic consequences of mate availability and fecundity selection in the contexts of conservation management of self‐incompatible plant species and experimental investigations on self‐incompatibility in natural populations.

Evolution and intraspecific exploitative competition I. One-locus theory for small additive gene effects

Using the model of exploitative competition of R. H. MacArthur and R. Levins (1967, Amer. Natur. 101, 377–385), evolution at a gene locus which influences the niche position is considered. The locus has multiple alleles, and the contributions of the alleles to the genotypic value are additive. The resource spectrum and the utilization functions of the genotypes are assumed to be Gaussian. Evolution will make the mode of the niche converge to the resource optimum, as long as the allele contributions are small compared to the distance between the mode of the niche and the resource optimum. When this distance is of the same order of magnitude as the allele contributions, then the globally stable equilibrium will maintain at most two alleles in the population, unless the allele contributions are large. Classical overdominance is not needed to maintain polymorphism. This result predicts high linkage disequilibrium in similar multilocus models. It is concluded that intraspecific competition can be a powerful force in maintaining two-allele polymorphisms, and that it can maintain high linkage disequilibrium among closely linked loci.

Sufficient Conditions for Protected Polymorphism in a Subdivided Population

Sufficient conditions for protected polymorphism at an autosomal locus are developed for a diploid dioecious population subdivided into randomly mating subpopulations. Conditions are formulated in principle as simple algebraic relations between selection and migration under the restriction that migration is independent of the genotype in the considered locus and that selection does not influence the relative size of the subpopulations. Migration models with random outbreeding and homing are analyzed in detail. Homing toward the neighborhood of the birthplace enhances the possibility for polymorphism.

Fusion of two divergent fungal individuals led to the recent emergence of a unique widespread pathogen species.

In a genome alignment of five individuals of the ascomycete fungus Zymoseptoria pseudotritici, a close relative of the wheat pathogen Z. tritici (synonym Mycosphaerella graminicola), we observed peculiar diversity patterns. Long regions up to 100 kb without variation alternate with similarly long regions of high variability. The variable segments in the genome alignment are organized into two main haplotype groups that have diverged ∼3% from each other. The genome patterns in Z. pseudotritici are consistent with a hybrid speciation event resulting from a cross between two divergent haploid individuals. The resulting hybrids formed the new species without backcrossing to the parents. We observe no variation in 54% of the genome in the five individuals and estimate a complete loss of variation for at least 30% of the genome in the entire species. A strong population bottleneck following the hybridization event caused this loss of variation. Variable segments in the Z. pseudotritici genome exhibit the two haplotypes contributed by the parental individuals. From our previously estimated recombination map of Z. tritici and the size distribution of variable chromosome blocks untouched by recombination we estimate that the hybridization occurred ∼380 sexual generations ago. We show that the amount of lost variation is explained by genetic drift during the bottleneck and by natural selection, as evidenced by the correlation of presence/absence of variation with gene density and recombination rate. The successful spread of this unique reproductively isolated pathogen highlights the strong potential of hybridization in the emergence of pathogen species with sexual reproduction.

Inbreeding depression and outbreeding depression in plants

The genetic mechanism underlying an ‘Optimal outcrossing distance’ in plants (sensu Price and Waser) is discussed. Monte Carlo simulations of a population subdivided as a one-dimensional stepping-stone are used to evaluate possible genetic mechanisms. A simple genetic model with two types of unlinked loci, underdominant and partially dominant, with multiplicative effects on fitness, is found to create an ‘Optimal outcrossing distance’ under a wide range of parameter values. The results are compared to, and discussed in relation to a two-locus epistatic model, previously investigated by Campbell and Waser, and found to give very similar results.

Environment-sensitive Epigenetics and the Heritability of Complex Diseases

Genome-wide association studies have thus far failed to explain the observed heritability of complex human diseases. This is referred to as the “missing heritability” problem. However, these analyses have usually neglected to consider a role for epigenetic variation, which has been associated with many human diseases. We extend models of epigenetic inheritance to investigate whether environment-sensitive epigenetic modifications of DNA might explain observed patterns of familial aggregation. We find that variation in epigenetic state and environmental state can result in highly heritable phenotypes through a combination of epigenetic and environmental inheritance. These two inheritance processes together can produce familial covariances significantly higher than those predicted by models of purely epigenetic inheritance and similar to those expected from genetic effects. The results suggest that epigenetic variation, inherited both directly and through shared environmental effects, may make a key contribution to the missing heritability.

Population Genetic Theory of the Cost of Inbreeding

Single gene models for the evolution of rates of selfing and sib mating in the presence of an inbreeding depression of fitness are treated. In models in which the genetic constitution of the male gamete pool available for random mating is not affected by prior inbreeding, an allele which increases the rate of inbreeding will succeed, provided the inbreeding depression is not too large. The opposite result holds when the proportion of male genotypes available for random mating are reduced according to their rate of prior inbreeding.