Genetic variability maintained by mutation and overdominant selection in finite populations

Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (ν) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.     

Genetic variability of body weight in two goose strains under long-term selection

Body weight is one of the most important traits in any genetic improvement program in geese for at least 2 reasons. First, measurements of the trait are very easy. Second, body weight is correlated with a number of other meat performance traits. However, the genetic background of body weight shows considerable complexity. Three genetic models (with direct, maternal genetic and permanent maternal environmental effects) were employed in this study. Records of 3076 individuals of maternal strain W11 and 2656 individuals of paternal strain W33 over 6 consecutive generations, kept in the pedigree farm of Ko?uda Wielka, were analysed. Body weight (in kilograms) was measured in weeks 8 (BW8) and 11 (BW11). The inbreeding levels in both populations were relatively low (0.14% and 0.02% for W11 and W33, respectively), therefore these effects were not included in the linear models to estimate genetic parameters. Three fixed effects (hatch period, sex and year) were included in each linear model. Two criteria (AIC, BIC) were used to check the goodness of fit of the models. The computations were performed by WOMBAT software. In general, the genetic parameter estimates varied across the traits, models and strains studied. Direct additive heritability estimates ranged from 0.0001 (for BW11 of W33) to 0.55 (for BW11 of W33). Maternal and total heritabilities were also variable. Estimates of ratios of direct-maternal effect covariance in phenotypic variance were both positive and negative, but they were negligible, whereas ratios of the permanent environmental maternal variance to phenotypic variance were close to zero. Both of the applied criteria of model adequacy indicate that the model with maternal genetic and environmental effects should be considered as optimal. Genetic trends were close to zero. It seems that they were influenced by long-term selection. Similar tendencies have been observed for phenotypic trends, as well.     

Genetic variability and advance under four selection procedures in wheat pedigree breeding programme

Summary Four methods of generation advance (SPS, SSD, BP and MMS) were compared in F₃ and F₄ generations. In the F₃ generation, the SPS and SSD methods of generation advance proved superior to the BP and MMS methods for grain yield per plant and for at least one of the yield component traits. The F₃ SSD population did not differ significantly from the F₃ SPS for any of the traits. However, the F₃ SSD population retained more range and cv for different traits than with other methods of generation advance. F₄ progenies derived from F₃ SSD population were significantly superior for grain yield than lines derived from the other three F₃ populations. The MMS method of generation advance proved useful for increasing the 1,000-grain weight for which initial selection was made.Part of Ph.D. Thesis submitted by senior author to Haryana Agricultural University, Hisar     

Beneficial mutation selection balance and the effect of linkage on positive selection

When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this article, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.     

Genetic variability following selection of Haemonchus contortus with anthelmintics

Genetic diversity in nematodes leads to variation in response to anthelmintics. Haemonchus contortus shows enormous genetic diversity, allowing anthelmintic resistance alleles to be rapidly selected. Anthelmintic resistance is now a widespread problem, especially in H. contortus. Here, I compare the genes involved in anthelmintic resistance in H. contortus with those that confer susceptibility or resistance on the free living nematode Caenorhabditis elegans. I also discuss the latest knowledge of genes associated with resistance to benzimidazoles, levamisole and the macrocyclic lactones and the need for DNA markers for anthelmintic resistance.     

Genetic variability at neutral markers,quantitative trait land trait in a subdivided population under selection

Genetic variability in a subdivided population under stabilizing and diversifying selection was investigated at three levels: neutral markers, QTL coding for a trait, and the trait itself. A quantitative model with additive effects was used to link genotypes to phenotypes. No physical linkage was introduced. Using an analytical approach, we compared the diversity within deme (H(S)) and the differentiation (F(ST)) at the QTL with the genetic variance within deme (V(W)) and the differentiation (Q(ST)) for the trait. The difference between F(ST) and Q(ST) was shown to depend on the relative amounts of covariance between QTL within and between demes. Simulations were used to study the effect of selection intensity, variance of optima among demes, and migration rate for an allogamous and predominantly selfing species. Contrasting dynamics of the genetic variability at markers, QTL, and trait were observed as a function of the level of gene flow and diversifying selection. The highest discrepancy among the three levels occurred under highly diversifying selection and high gene flow. Furthermore, diversifying selection might cause substantial heterogeneity among QTL, only a few of them showing allelic differentiation, while the others behave as neutral markers.     

Maintenance of multilocus variability under strong stabilizing selection

We present exact conditions for stability of monomorphic equilibria in a general multilocus multiallele system and of specific polymorphic equilibria in general one- and two-locus multiallele systems. We show how these exact results on one- and two-locus systems can be used in approximate analysis of polymorphic equilibria in multilocus systems under selection strong relative to recombination. We determine conditions for existence and stability of polymorphic equilibria in specific models of quadratic stabilizing selection on additive polygenic traits.     

Quantitative variability and multilocus polymorphism under epistatic selection

We study multilocus polymorphism under selection, using a class of fitness functions that account for additive, dominant, and pairwise additive-by-additive epistatic interactions. The dynamic equations are derived in terms of allele frequencies and disequilibria, using the notions of marginal systems and marginal fitnesses, without any approximations. Stationary values of allele frequencies and pairwise disequilibria under weak selection are calculated by regular perturbation techniques. We derive conditions for existence and stability of the multilocus polymorphic states. Using these results, we then analyze a number of models describing stabilizing selection on additive characters, with some other factors, and determine the conditions under which genetic quantitative variability is maintained.     

Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.     

Relative roles of mutation and selection in the maintenance of genetic variability

The extent and pattern of protein and DNA polymorphisms are discussed with emphasis on the mechanism of maintenance of the polymorphisms. Statistical studies suggest that a large proportion of genetic variability at the molecular level is maintained by a mutation-drift balance. At some loci, such as those for histocompatibility in mammals, however, a form of overdominant selection seems to be involved. In the presence of overdominant selection, polymorphic alleles may be maintained for tens of millions of years, so that the number of nucleotide differences between alleles is often very large, as in the case of self-incompatibility alleles in plants. There are also an increasing number of examples in which an adaptive change of a morphological or physiological character is caused by a single nucleotide substitution. Nevertheless, these mutations seem to be a small proportion of the total nucleotide changes that contribute to genetic variability and evolution. Although there are many examples of frequency-dependent selection, this form of selection is apparently unimportant for the maintenance of genetic variability except in some special cases. Observations on the evolutionary change of DNA suggest that the driving force of evolution is mutation rather than selection.     

The balance between pleiotropic mutation and selection,when alleles have discrete effects

The theory of pleiotropic mutation and selection is investigated and developed for a large population of asexual organisms. Members of the population are subject to stabilising selection on Omega phenotypic characters, which each independently affect fitness. Pleiotropy is incorporated into the model by allowing each mutation to simultaneously affect all characters. To expose differences with continuous-allele models, the characters are taken to originate from discrete-effect alleles and thus have discrete genotypic effects. Each character can take the values nxDelta where n=0,+/-1,+/-2, em leader, and the splitting in character effects, Delta, is a parameter of the model. When the distribution of mutant effects is normally distributed around the parental value, and Delta is large, a "stepwise" model of mutation arises, where only adjacent trait effects are accessible from a single mutation. The present work is primarily concerned with the opposite limit, where Delta is small and many different trait effects are accessible from a single mutation.In contrast to what has been established for continuous-effect models, discrete-effect models do not yield a singular equilibrium distribution of genotypic effects for any value of Omega. Instead, for different values of Omega, the equilibrium frequencies of trait values have very different dependencies on Delta. For Omega=1 and 2, decreasing Delta broadens the width of the frequency distribution and hence increases the equilibrium level of polymorphism. For all sufficiently large values of Omega, however, decreasing Delta decreases the width of the frequency distribution and the equilibrium level of polymorphism. The connection with continuous trait models follows when the limit Delta-->0 is considered, and a singular probability density of trait values is obtained for all sufficiently large Omega.     

The G matrix under fluctuating correlational mutation and selection

Theoretical quantitative genetics provides a framework for reconstructing past selection and predicting future patterns of phenotypic differentiation. However, the usefulness of the equations of quantitative genetics for evolutionary inference relies on the evolutionary stability of the additive genetic variance-covariance matrix (G matrix). A fruitful new approach for exploring the evolutionary dynamics of G involves the use of individual-based computer simulations. Previous studies have focused on the evolution of the eigenstructure of G. An alternative approach employed in this paper uses the multivariate response-to-selection equation to evaluate the stability of G. In this approach, I measure similarity by the correlation between response-to-selection vectors due to random selection gradients. I analyze the dynamics of G under several conditions of correlational mutation and selection. As found in a previous study, the eigenstructure of G is stabilized by correlational mutation and selection. However, over broad conditions, instability of G did not result in a decreased consistency of the response to selection. I also analyze the stability of G when the correlation coefficients of correlational mutation and selection and the effective population size change through time. To my knowledge, no prior study has used computer simulations to investigate the stability of G when correlational mutation and selection fluctuate. Under these conditions, the eigenstructure of G is unstable under some simulation conditions. Different results are obtained if G matrix stability is assessed by eigenanalysis or by the response to random selection gradients. In this case, the response to selection is most consistent when certain aspects of the eigenstructure of G are least stable and vice versa.     

The distribution of allelic effects under mutation and selection

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.     

Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.