PREFERENTIAL MATING IN SYMMETRIC MULTILOCUS SYSTEMS: STABILITY CONDITIONS OF THE CENTRAL EQUILIBRIUM

ABSTRACT Several multilocus models that incorporate both preferential mating and viability selection are studied. Specifically, a class of symmetric heterozygosity models are considered that assign individuals to phenotypic classes according to which loci are in heterozygous state regardless of the actual allelic content. Otherwise, an arbitrary number of loci, number of alleles per locus, and arbitrary recombination scheme, viability parameters and preferential mating pattern based on phenotypes are allowed. The conditions for the stability of a central polymorphism are indicated and interpreted. The effects of viability and preference selection may be summarized in a single quantity for each phenotypic class, a generalized fitness. Preferential assortative mating alone can produce stability for a central polymorphism as in the case of viability selection when sexual attractiveness or general fitness increases with higher levels of heterozygosity. The situation is more complex with sexual selection.

NATURAL SELECTION OPPOSING ARTIFICIAL SELECTION: A TWO-LOCUS DETERMINISTIC SIMULATION

ABSTRACT A two-locus, two-allele metric trait was submitted to artificial truncation selection and to three types of opposing natural selection (two-locus extensions of directional selection, overdominance and underdominance) by numerical simulation in a large random-mating population. Limits to selection were generally reached by generation 100. Intermediate selection plateaus were found, with minor genes, for all three modes of opposing natural selection, but they were least frequent with underdominance. Multiple outcomes were common. In particular, fixation of the genotype favored by artificial selection was often associated with fixation of another genotype and/or with a central equilibrium; the end point actually reached depended on the genetic starting point of the simulation. In general, when the alleles favored by truncation selection were combined (positive linkage disequilibrium) in the base population, or when the trait was determined by major genes, artificial selection would prevail. Limitations inherent to this type of work are discussed, and possible avenues for further work on the antagonism between artificial and natural selection are proposed.

CENTRAL EQUILIBRIA IN MULTILOCUS SYSTEMS. I. GENERALIZED NONEPISTATIC SELECTION REGIMES

ABSTRACT The generalized nonepistatic selection regime encompasses combinations of multiplicative and neutral viability effects distributed across a set of loci. These subsume, in particular, mixtures of the classical modes of multiplicative and additive fitness evaluations for multilocus traits. Exact analytic conditions for existence and stability of a multilocus Hardy-Weinberg (H-W) polymorphic equilibrium cmfiguration are ascertained. It is established that the central H-W polymorphism is stable only if the component loci are "overdominant" and sufficient recombination is in force. The H-W central equilibrium is never stable for tight linkage whenever some multiplicative selection effects are contributed by at least two of the loci involved. In the case of additive selection expression and individual overdominant loci, the H-W polymorphism is stable independently of the level of recombination. In the context of "natural" recombination schemes, "more recombination" enhances the stability 3f the H-W polymorphic equilibrium.

Analysis of central equilibrium configurations for certain multi-locus systems in subdivided populations

SUMMARYThe multi-locus systems expressing non-epistatic and generalized symmetric selection lend themselves to the study of the stability of certain central polymorphic equilibria. These equilibria persist when any form of migration connects demes which share a common equilibrium. The analysis of the stability of the equilibrium in the global system is tractable, thus supplementing known protection results for two alleles at one locus with stability conditions on an internal equilibrium involving an arbitrary number of loci, each with an arbitrary number of alleles. Two of the principal findings are that stability of central Hardy–Weinberg type equilibria increase with ‘more’ migration and ‘more’ recombination. As a corollary, local stability in each deme implies stability in a system with migration superimposed; but instability in each deme when isolated does not imply instability when migration is superimposed.