Biomedical subjects
Publications and source records attributed to S Lessard.
We correct an equation characterizing the additive allelic effects on fitness determined at many loci without the assumption of random mating given in Ewens (1989, 1992) and we show that the additive genetic variance in fitness divided by the mean fitness is equal to a partial change in the mean fitness from one generation to the next as stated in Ewens (1989).
We show that the Fundamental Theorem of Natural Selection in Ewens' sense is valid in the case of fertility selection: the additive genetic variance in fertility divided by the mean fertility is exactly equal to the partial change in the mean fertility from the current generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from on generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from one generation to the next but keeping unchanged the additive values. The only hypothesis on mating is that it does not affect the allelic frequencies in the sense that these are the same before and after mating in the parental generation, which occurs for a wide range of mating patterns going from random mating to several regular systems of inbreeding and cases of assortative mating. The fertility of couples is determined by the genes at an arbitrary number of loci, and the additive (average) allelic allelic effects are defined by a linear system of equations, which is used to extend Ewens' optimality principle to the case of fertility selection.
Relatedness arising in kin selection theory is measured by a variable taking as values two pedigree indices in populations with inbreeding when selection is weak. This variable reduces to a single pedigree index when inbreeding is caused by partial selfing or partial sib-mating. General inclusive fitness formulations of kin selection models based on such a variable of relatedness are proposed.
The equilibrium configurations for a two-locus multialle model of sex-linked meiotic drive are studied with regard to the recombination fraction:limit cycles can occur in the case of small recombination while stable equilibrium points associated with linkage equilibrium can exist for an intermediate range of recombination values depending on the equilibrium sex ratio, linkage disequilibrium at nearby equilibrium points taking turn with loser linkage. The evolutionary dynamics in two-locus sex-ratio distortion systems is enlightened: while equilibria with a sex ratio closer to 1/2 are more likely to be stable with respect to perturbations on the frequencies of sex-ratio distorters that are represented at equilibrium, such equilibria are also more vulnerable to the invasion of mutant distorters when there is some degree of linkage with the sex-determining locus. For X-linked multimodifier systems of sex-ratio distortion, differential fertilities and viabilities are incorporated and a maximum principle is suggested.
The evolutionary dynamics in general two-sex two-phenotype frequency-dependent selection models are studied with respect to underlying multi-allele one-locus genetic systems. Two classes of equilibria come into play: genotypic equilibria, with equilibrium allelic frequencies independent of the phenotype, and phenotypic equilibria, which are characterized by equal mean phenotypic fitnesses. The exact conditions for genotypic equilibria to exist and be stable and for phenotypic equilibria to exist and be evolutionarily attractive are examined. Using adequate definitions of mean fitnesses in general contexts of frequency-dependent selection in dioecious populations, we show that two phenotypes, when they can coexist in the population, tend to balance their fitnesses as far as is allowed by the genetic system as more alleles responsible for phenotype determination are introduced into the population.
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Theoretical one-locus multiallele sex-determination models are found to admit even sex ratio equilibrium surfaces besides the equilibria for corresponding one-locus multiallele viability models. Both types of equilibria can be defined in terms of a single spectral radius function, the former corresponding to level surfaces and the latter to critical points. The stable equilibria in the corresponding viability models are associated with the local maxima, and the equilibrium structures for the sex-determination models can be fully described. Several optimality properties of the even-sex-ratio equilibrium surfaces can be deduced.
General frequency-dependent selection models based on two phenotypic classes are analyzed with underlying one-locus multiallele phenotypic determination systems in diploid populations. It is proved that the mean phenotypic fitnesses tend to equality over discrete generations and genetic mutations if a phenotypic polymorphism is to be maintained. The exact conditions are examined. The present results are valid for a wide class of models whenever random groupings or assortative patterns based on phenotype and affecting fitness, linearly or not, are independent of sex, mating preferences, or kinship. They can also be applied to two-sex haploid models.
The equilibrium structures for various multiallele sex-determining genetic models of panmictic populations with sex expression depending on the genotypes of either the zygote or a parent are described. Even-sex-ratio equilibrium surfaces can exist apart from equilibrium points having coincident male and female allelic frequency sets. The latter (symmetric) equilibrium states entail biased sex ratios. A stable symmetric equilibrium and an even-sex-ratio equilibrium segregating the same alleles cannot coexist. The tendency to evolve toward an even-sex ratio is embodied by the following optimality property: starting from an equilibrium having a biased sex ratio, mutant sex-determining alleles can accumulate only in the case in which in the augmented system all attainable equilibrium states have a sex ratio closer to one to one.
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