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.     

Recurrent inversion polymorphisms in humans associate with genetic instability and genomic disorders

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Polymorphism maintenance in populations with mixed random mating and apomixis subjected to stabilizing and cyclical selection

We analysed a diploid population model with a mixed breeding system that includes panmixia and apomixis. Each individual produces a part (ss) of its progeny by random mating, the remainder (1-ss) being a result of precise copying (vegetative reproduction or apomixis) of the parental genotype. Both constant and periodically varying selection regimes were considered. In the main model, the selected trait was controlled by two diallelic additive or semidominant loci, A/a and B/b, whereas the parameter of breeding system (ss) was genotype-independent. A numerical iteration of the evolutionary equations were used to evaluate the proportion (V) of population trajectories converging to internal (polymorphic) fixed points. The results were the following. (a) A complex pattern of dependence of polymorphism stability on interaction among the breeding system, recombination rate, and the genetic architecture of the selected trait emerged. (b) The recombination provided some advantage to sex at intermediate period lengths and strong-to-moderate selection intensities. (c) The complex limiting behavior (CLB) was quite compatible with sexual reproduction, at least within the framework of pure genetic (not including variations in population density) models of multilocus varying selection.     

The mating system and genetic significance of polycarpy in the neem tree (Azadirachta indica)

The objectives of this study were to estimate the outcrossing rate and to explain genetic consequences of the development of seed in the endocarp in a natural population of neem in Bangladesh. Cotyledons of germinated open-pollinated seeds of individual trees were analyzed by starch-gel electrophoresis to examine allozymes. Three loci with clear Mendelian segregation were used to estimate outcrossing rate. A multilocus mixed mating model was used to evaluate the mating system. The population exhibited high outcrossing rates both for multilocus (t_m=0.90±0.024) and mean single-locus (t_s=0.92±0.020) estimates. The difference between these two parameters (t_m–t_s=0±SE 0.038) was insignificant, indicating that there was no ’biparental inbreeding’ in the population. The degree of variance of the estimates of multilocus outcrossing rates decreased when two or more loci were included. In order to elucidate the significance of polycarpy a total of 471 seeds were counted out of 440 endocarps. This mechanism appears to be a possible way of avoiding inbreeding. The results indicated that the studied neem population was predominantly allogamous. Received: 10 January 1999 / Accepted: 10 April 1999     

Preliminary genetic study inCandida utilis: II. Conditions controlling mating and sporulation

Hybrid formation inCandida utilis was studied by assaying for the formation of prototrophs after mixing different auxotrophic strains. Various physiological conditions were considered following a mathematical experimental design. Parental cells grown in minimal medium up to stationary phase and mated for 16 hours gave the highest yield of prototrophs. The sporulation capacity of hybrid cells was tested under different conditions and was significantly stimulated by acetate. The presence of ascus-like structures in different media, the detection of recombinants among the progeny, and analyses of DNA content in different strains suggest thatC. utilis is a homothallic organism and the hybrids are true diploid cells.     

The covariance of relatives derived from a random mating population.

Attention is drawn to errors common in the derivation of forms for the genotypic covariance of noninbred relatives from a Hardy-Weinberg population of diploids. A synthesis of Fisher's least-squares method of partitioning the genotypic variance and Malécot's probability method of expressing kinship, yields a general form. For one locus, the form is $\text{(P}{}_{\mathrm{ss}}\text{+ P}{}_{\mathrm{sd}}\text{+ P}{}_{\mathrm{ds}}\text{+ P}{}_{\mathrm{dd}}\text{)}\text{1}\text{2}\text{σ}{}_{\mathrm{a}}{}^2\text{+ (P}{}_{\mathrm{ss}}\text{P}{}_{\mathrm{dd}}\text{+ P}{}_{\mathrm{sd}}\text{P}{}_{\mathrm{ds}}\text{) σa}{}_{\mathrm{d}}{}^2$, where σ_a² is the additive genetic variance, α_d² is the variance of dominance deviations, p_ij is the probability that parental gamete i is identical by descent to parental gamete j, i = s, d indexes the parents of one relative, and j = s, d indexes those of the other. The form provides a framework for obtaining the covariance of relatives from an equilibrium population with linkage.     

On the increase of chromosome mutations under random mating.

After a short introduction on karyotypes and chromosome mutations, we review the ways by which a chromosome mutation can increase in a random mating population, despite the mutation's deleterious effect on the fertility of heterozygotes. Random drift, segregation distortion, viability advantage, and recombination modification are the mechanisms considered. When possible, the models are illustrated with examples of chromosome mutations involving autosomes in mammals, but the arguments apply, of course, to any genetic factor in any outbreeding species that causes a fertility decrease in heterozygotes.     

The generation and maintenance of genetic variation by frequency-dependent selection: constructing polymorphisms under the pairwise interaction model

Frequency-dependent selection remains the most commonly invoked heuristic explanation for the maintenance of genetic variation. For polymorphism to exist, new alleles must be both generated and maintained in the population. Here we use a construction approach to model frequency-dependent selection with mutation under the pairwise interaction model. The pairwise interaction model is a general model of frequency-dependent selection at the genotypic level. We find that frequency-dependent selection is able to generate a large number of alleles at a single locus. The construction process generates multiallelic polymorphisms with a wide range of allele-frequency distributions and genotypic fitness relationships. Levels of polymorphism and mean fitness are uncoupled, so constructed polymorphisms remain permanently invasible to new mutants; thus the model never settles down to an equilibrium state. Analysis of constructed fitness sets reveals signatures of heterozygote advantage and positive frequency dependence.     

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.     

The genetic mating structure of subdivided populations I. Open-mating model

The genetic mating structure of a subdivided population can describe how parental genotypes gave rise to zygotes. When parents of the same genotype are considered together as one class (“open-mating”), three independent parameters of inbreeding and mating structure are needed to describe this structure at a diallelic locus. One is Wright's fixation index F. The other two are mating structure parameters, derived herein and termed the “effective selfing” rate E and the “inbreeding assortative selfing” rate D. E is the genetically equivalent proportion of self-fertilization at a single locus, and is given by standardized second and third central moments of gene frequencies of mates. E is a summary measure of inbreeding that includes effects due to self-fertilization and mating to relatives, as well as correlations between mates induced by Wahlund effects and/or selective diversification among neighborhoods. The second parameter D measures the tendency of inbred or more homozygous individuals to effectively self more (or less) than outbred or more heterozygous individuals. D is related to the maintenance of variation of inbreeding among individuals and/or to the prevalence of spatial variation of selection. D is independent of E, but together with E controls the generational change of inbreeding, ΔF. Extensions of the model to unequal allele frequencies in male vs female mates, and to multi-allelic loci, are also examined.     

The association of three indicators of developmental instability with mating success in humans

Developmental instability (DI) has been proposed to relate negatively to aspects of evolutionary fitness, like mating success. One suggested indicator is fluctuating asymmetry (FA), random deviations from perfect symmetry in bilateral bodily traits. A meta-analytically robust negative association between FA and number of lifetime sexual partners has been previously shown in men and women. We examined the relationship between bodily FA across twelve traits and indicators of quantitative mating success in 284 individuals (141 males, age 19–30 years). Two further indicators of DI, minor physical anomalies (MPAs) and asymmetry in palmar atd angles, were also assessed. For men, no significant associations were detected, whereas for women, unexpected positive relationships of FA with the number of lifetime sexual partners and one-night stands emerged. Thus, in a large sample and using a more highly aggregated FA index, our study fails to replicate previous findings, though equivalence testing also did not support deviation from previous meta-analytic estimates, especially for men. No associations were found for MPAs and FA in atd angles in either sex.     

Characteristics of myotonic dystrophy in Istria: molecular genetic approach. Part II: Analysis of genetic polymorphisms

One of the world highest prevalence estimates of myotonic dystrophy (DM) has been reported in the Croatian region Istria. To analyse the population genetic characteristics of DM locus in Istria, two intragenic and three extragenic polymorphic markers were tested. The Southern blot technique was used for D19S63 locus analysis, whereas PCR analysis was performed for CKMM, Alu polymorphism, DMPK (G/T) intron 9/HinfI polymorphism, and D19S207 genetic markers. The compound haplotypes segregating with DM were established. A complete association between the DM mutation and D19S63, D19S207, intron 9/HinfI polymorphism and Alu polymorphism markers were found. In all DM chromosomes: D19S63 and Alu markers had the allele 1 in common; D19S207 had the allele 3 in common, DMPK (G/T) intron 9/HinfI marker had the allele 2 in common. The analysis of CKMM polymorphism revealed genotype heterogeneity; in DM chromosomes either allele 2 or allele 4 were found. The haplotype analysis in the population of Croatian Istria supports the linkage disequilibrium between the DM mutation and Alu polymorphism, intron 9/HinfI polymorphism, D19S63 and D19S207 markers as reported worldwide. The results of the haplotype analysis suggest a common origin of the mutation in Istrian population.