Inbreeding depression due to overdominance in partially self-fertilizing plant populations.

The effect of the rate of partial self-fertilization and viability selection on the magnitude of inbreeding depression was investigated for the overdominance genetic model. The influence of these factors was determined for populations with equilibrium genotypic frequencies. Inbreeding depression was measured as the normalized disadvantage in mean viability of selfed progeny as compared to outcrossed progeny. When caused by symmetric homozygous disadvantage at a single locus it is shown always to be less than one-third. Moreover, for fixed rates of self-fertilization, its maximum value is found at intermediate levels of homozygous disadvantage. As the rate of self-fertilization increases, inbreeding depression increases and the homozygote viability that results in maximum depression tends toward one-half the heterozygote viability. Symmetric selection against homozygotes at multiple loci can lead to substantially higher values than selection at a single-locus. As the number of independent loci involved increases, inbreeding depression can reach high levels even though the selfing rate is low. Viability distributions for progenies produced from both random mating and self-fertilization were derived for the case of symmetric selection at independently assorting multiple loci. Distributions of viabilities in progenies resulting from mixtures of selfing and outcrossing were shown to be bimodal when inbreeding depression is high.

Convergence to equilibrium in a genetic model with differential viability between the sexes.

A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.

The significance of over- and underdominance for the maintenance of genetic polymorphisms. II. Overdominance and instability with random mating.

Part I of the present series demonstrates that globally stable polymorphic equilibria may show underdominance in Darwinian fitness. Hence, overdominance in fitness can no longer be conceived of as a necessary condition for the stability of a polymorphism. In the present paper, the question is posed as to whether overdominance is at least sufficient for this stability. A population of randomly mating individuals is considered, where selection operates uniquely through differential fecundities of particular mating types and may generate either a heterozygote excess or deficit relative to Hardy-Weinberg proportions. It turns out that both unstable central overdominance and stable central underdominance are possible and that their occurrence is strongly related to an excess or a deficiency of heterozygotes in the vicinity of the regions of instability or stability. As one consequence, the above suggested sufficiency of heterozygote superiority is not valid, even in random mating populations. Based on the results of both papers of this series, which demonstrate the inadequacy of over- and underdominance as indicators of stability or instability, a modified overdominance principle is discussed. This principle states that a biallelic polymorphism is maintained if the heterozygote is superior in its degree of "heterogamous self-replication" to the degrees of "autogamous self-replication" of the corresponding homozygotes. It is derived with the help of fractional fitnesses, and it is pointed out that certain ratios of these may be more useful for finding evolutionary constants which govern the maintenance of genetic polymorphisms than are ratios of total fitnesses.

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability.

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.

Reproductive systems in conifer seed orchards : 3. Female and male fitnesses of individual clones realized in seeds of Pinus sylvestris L.

In order to quantify female and male fitness values of clones in a Pinus sylvestris L. seed orchard, multilocus-genotypes of parental clones were compared with those of open pollinated seeds in the bulked orchard crop. Female and male contributions to individual seeds were distinguished by observing enzyme gene loci active in both endosperm and embryo tissue. Seed probes from two successive flowering periods were surveyed. The female and male fitnesses of five parental clones measured relative to the population mean were derived. The contributions of four clones were found to be sexually asymmetric. One clone, for instance, made exclusively female contributions in one flowering period. Variations existed in fitness values between clones. Deviations in sex specificity occurred between flowering periods: one clone contributed asymmetrically in both periods, but in sexually reversed proportions. A method to comprehensively quantify and illustrate the observed phenomena is proposed.

Reproductive systems in conifer seed orchards : 2. Reproductive selection monitored at an LAP gene locus in Pinus sylvestris L.

In a Scots pine seed orchard the genetic structures at an enzyme gene locus active in pine seeds were compared among the parental clones and the allorchard seeds produced over a period of three years. The genotypes of the seeds were identified as ordered pairs consisting of the female and male contribution. The sexual reproductive function monitored at the studied locus differed significantly between the two sexes. This fact proves the necessity of taking sexual asymmetry into account in studies of reproductive selection. This is done by comparing the observed genotypic structures among the offspring with the corresponding multiplicative structure expected under random gametic fusion. Additionally, accounting for partial self-fertilization increased the conformity between the observed and the hypothesized model structures. The differences in female and male gametic contributions to the offspring were used to estimate female and male relative fitness components. Significant deviations between the allelic and/or genotypic structures of orchard clones and their seed, and between seed lots collected in different years, may reduce the efficiency of realizing breeding gains in seed orchards.

Deviations of Genotypic Structures from Hardy-Weinberg Proportions under Random Mating and Differential Selection between the Sexes.

Population genetic models, such as differential viability selection between the sexes and differential multiplicative fecundity contributions of the sexes, are considered for a single multiallelic locus. These selection models usually produce deviations of the zygotic genotype frequencies from Hardy-Weinberg proportions. The deviations are investigated (with special emphasis put on equilibrium states) to quantify the effect of selective asymmetry in the two sexes. For many selection regimes, the present results demonstrate a strong affinity of zygotic genotype frequencies for Hardy-Weinberg proportions after two generations, at the latest. It is shown that the deviations of genotypic equilibria from the corresponding Hardy-Weinberg proportions can be expressed and estimated by means of selection components of only that sex with the lower selection intensity. This corresponds to the well-known fact that viability selection acting in only one sex yields Hardy-Weinberg equilibria.