Stabilizing selection,mutational bias,and the evolution of sex*

Stabilizing selection around a fixed phenotypic optimum is expected to disfavor sexual reproduction, since asexually reproducing organisms can maintain a higher fitness at equilibrium, while sex disrupts combinations of compensatory mutations. This conclusion rests on the assumption that mutational effects on phenotypic traits are unbiased, that is, mutation does not tend to push phenotypes in any particular direction. In this article, we consider a model of stabilizing selection acting on an arbitrary number of polygenic traits coded by bialellic loci, and show that mutational bias may greatly reduce the mean fitness of asexual populations compared with sexual ones in regimes where mutations have weak to moderate fitness effects. Indeed, mutation and drift tend to push the population mean phenotype away from the optimum, this effect being enhanced by the low effective population size of asexual populations. In a second part, we present results from individual‐based simulations showing that positive rates of sex are favored when mutational bias is present, while the population evolves toward complete asexuality in the absence of bias. We also present analytical (QLE) approximations for the selective forces acting on sex in terms of the effect of sex on the mean and variance in fitness among offspring.     

Interpretation of Data Obtained with Recombination-Defective Meiotic Mutants

Gene frequency distributions observed in large-scale surveys of species of Drosophila are shown to be incompatible with a genetic model involving neutral mutations and genetic drift alone. The data are, however, qualitatively similar to predictions based on an alternative model of natural selection for an optimal level of enzyme activity in addition to drift and mutation. The intensity of selection detected reduces the mean rate of gene substitution to less than one-quarter that expected on the neutral-allele hypothesis.     

Genetic Divergence under Uniform Selection. II. Different Responses to Selection for Knockdown Resistance to Ethanol among DROSOPHILA MELANOGASTER Populations and Their Replicate Lines

We have tested the hypothesis that genetic differences among conspecific populations may result in diverse responses to selection, using natural populations of Drosophila melanogaster. Selection for ethanol tolerance in a tube measuring knockdown resistance was imposed on five West Coast populations. In 24 generations the selected lines increased their mean knockdown times, on average, by a factor of 2.7. An initially weak latitudinal cline was steepened by selection. The two southernmost populations showed the same increases in the selected character, but differed consistently in their correlated responses in characters related to ethanol tolerance. This result indicates that the populations responded to selection by different genetic changes. Selection decreased female body weight and increased resistance to acetone, suggesting components of the response unrelated to ethanol metabolism. The Adhs allele was favored by selection in all populations at the onset, but increased in frequency only in the selected lines of the southernmost population. There was a correlation between latitude and Adh frequency changes, suggesting that fitnesses of the Adh alleles were dependent on the genetic background. Genetic background also had a large effect on the loss of fitness due to selection. Genetic drift between replicate lines caused more variation in selection response than initial genetic differences between populations. This result demonstrates the importance of genetic drift in divergence among natural populations undergoing uniform selection, since the effective population sizes approached those of small natural populations. Drift caused greater divergence between selected replicates than control replicates. Implications of this result for the genetic model of selection response are discussed.     

Selection maintains MHC diversity through a natural population bottleneck

A perceived consequence of a population bottleneck is the erosion of genetic diversity and concomitant reduction in individual fitness and evolutionary potential. Although reduced genetic variation associated with demographic perturbation has been amply demonstrated for neutral molecular markers, the effective management of genetic resources in natural populations is hindered by a lack of understanding of how adaptive genetic variation will respond to population fluctuations, given these are affected by selection as well as drift. Here, we demonstrate that selection counters drift to maintain polymorphism at a major histocompatibility complex (MHC) locus through a population bottleneck in an inbred island population of water voles. Before and after the bottleneck, MHC allele frequencies were close to balancing selection equilibrium but became skewed by drift when the population size was critically low. MHC heterozygosity generally conformed to Hardy-Weinberg expectations except in one generation during the population recovery where there was a significant excess of heterozygous genotypes, which simulations ascribed to strong differential MHC-dependent survival. Low allelic diversity and highly skewed frequency distributions at microsatellite loci indicated potent genetic drift due to a strong founder affect and/or previous population bottlenecks. This study is a real-time examination of the predictions of fundamental evolutionary theory in low genetic diversity situations. The findings highlight that conservation efforts to maintain the genetic health and evolutionary potential of natural populations should consider the genetic basis for fitness-related traits, and how such adaptive genetic diversity will vary in response to both the demographic fluctuations and the effects of selection.     

THE INFLUENCE OF SELF-FERTILIZATION AND POPULATION DYNAMICS ON THE GENETIC STRUCTURE OF SUBDIVIDED POPULATIONS: A CASE STUDY USING MICROSATELLITE MARKERS IN THE FRESHWATER SNAIL BULINUS TRUNCATUS

The distribution of neutral genetic variability within and among sets of populations results from the combined actions of genetic drift, migration, extinction and recolonization processes, mutation, and the mating system. We here analyzed these factors in 38 populations of the hermaphroditic snail Bulinus truncatus. The sampling area covered a large part of the species range. The variability was analyzed using four polymorphic microsatellite loci. A very large number of alleles (up to 55) was found at the level of the whole study. Observed heterozygote deficiencies within populations are consistent with very high selfing rates, generally above 0.80, in all populations. These should depress the variability within populations, because of low effective size, genetic hitchhiking, and background selection, whatever the model of mutation assumed. However, that some populations exhibit much more variability than others suggests that historical demographic processes (e.g., population size variation, bottlenecks, or founding events) may play a significant role. A hierarchical analysis of the distribution of the variability across populations indicates a strong pattern of isolation by distance, whatever the geographical scale considered. Our analysis also illustrates how the mutation rate may affect population differentiation, as different mutation rates result in different levels of homoplasy at microsatellite loci. The effects of both genetic drift and gene flow vary with the temporal and spatial scales considered in B. truncatus populations.     

Mutant alleles of small effect are primarily responsible for the loss of fitness with slow inbreeding in Drosophila melanogaster.

Multilocus simulation is used to identify genetic models that can account for the observed rates of inbreeding and fitness decline in laboratory populations of Drosophila melanogaster. The experimental populations were maintained under crowded conditions for approximately 200 generations at a harmonic mean population size of Nh approximately 65-70. With a simulated population size of N = 50, and a mean selective disadvantage of homozygotes at individual loci approximately 1-2% or less, it is demonstrated that the mean effective population size over a 200-generation period may be considerably greater than N, with a ratio matching the experimental estimate of Ne/Nh approximately 1.4. The buildup of associative overdominance at electrophoretic marker loci is largely responsible for the stability of gene frequencies and the observed reduction in the rate of inbreeding, with apparent selection coefficients in favor of the heterozygote at neutral marker loci increasing rapidly over the first N generations of inbreeding to values approximately 5-10%. The observed decline in fitness under competitive conditions in populations of size approximately 50 in D. melanogaster therefore primarily results from mutant alleles with mean effects on fitness as homozygotes of sm < or = 0.02. Models with deleterious recessive mutants at the background loci require that the mean selection coefficient against heterozygotes is at most hsm approximately 0.002, with a minimum mutation rate for a single Drosophila autosome 100 cM in length estimated to be in the range 0.05-0.25, assuming an exponential distribution of s. A typical chromosome would be expected to carry at least 100-200 such mutant alleles contributing to the decline in competitive fitness with slow inbreeding.     

Temporal changes in allele frequencies in two reciprocally selected maize populations

The effects of breeding on allele frequency changes at 82 restriction fragment length polymorphism (RFLP) loci were examined in two maize (Zea mays L.) populations undergoing reciprocal recurrent selection, Iowa Stiff Stalk Synthetic and Iowa Corn Borer Synthetic #1. After 12 cycles of selection, approximately 30% of the alleles were extinct and 10% near fixation in each population. A test of selective neutrality identified several loci in each population whose allele frequency changes cannot be explained by genetic drift; interpopulation mean expected heterozygosity increased for that subset of 28 loci but not for the remaining 54 loci. Mean expected heterozygosity within the two subpopulations decreased 39%, while the between-population component of genetic variation increased from 0.5% to 33.4% of the total. Effective population size is a key parameter for discerning allele frequency changes due to genetic drift versus those resulting from selection and genetic hitchhiking. Empirical estimates of effective population size for each population were within the range predicted by the breeding method. Received: 10 June 1998 / Accepted: 29 April 1999     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

The exact values of the probability of fixation of underdominant chromosomal rearrangements.

A numerical analysis of the probability of fixation of a chromosomal mutation with partial sterility of the heterozygote in a single population is performed. Three different genetic models are considered: the first model entails constant selection against the heterozygote and is the model almost universally used in previous works; in the other two models selection against the heterozygote depends on its frequency. The exact values of the fixation probability are found by iterating transition matrices with genotype specification. Differences in results among models are small. The exact values found in the first model are compared to estimates obtained from approximations. Solutions based on diffusion models give good approximations when selection against the heterozygote is low, especially if the population is very small. For the higher values of the selection coefficient against the heterozygote, the estimates are rather imprecise, especially when the populations are not very small.     

Patterns of male sterility in a grasshopper hybrid zone imply accumulation of hybrid incompatibilities without selection

It is now widely accepted that post-zygotic reproductive isolation is the result of negative epistatic interactions between derived alleles fixed independently at different loci in diverging populations (the Dobzhansky-Muller model). What is less clear is the nature of the loci involved and whether the derived alleles increase in frequency through genetic drift, or as a result of natural or sexual selection. If incompatible alleles are fixed by selection, transient polymorphisms will be rare and clines for these alleles will be steep where divergent populations meet. If they evolve by drift, populations are expected to harbour substantial genetic variation in compatibility and alleles will introgress across hybrid zones once they recombine onto a genetic background with which they are compatible. Here we show that variation in male sterility in a naturally occurring Chorthippus parallelus grasshopper hybrid zone conforms to the neutral expectations. Asymmetrical clines for male sterility have long tails of introgression and populations distant from the zone centre show significant genetic variation for compatibility. Our data contrast with recent observations on 'speciation genes' that have diverged as a result of strong natural selection.     

The Island Model of Population Differentiation: A General Solution

The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.-A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.-The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to varphi, the coefficient of kinship, and the other, gamma, measures the rate of mutational divergence between the sub-populations.     

The genetics of adaptation: the roles of pleiotropy, stabilizing selection and drift in shaping the distribution of bidirectional fixed mutational effects

Pleiotropy allows for the deterministic fixation of bidirectional mutations: mutations with effects both in the direction of selection and opposite to selection for the same character. Mutations with deleterious effects on some characters can fix because of beneficial effects on other characters. This study analytically quantifies the expected frequency of mutations that fix with negative and positive effects on a character and the average size of a fixed effect on a character when a mutation pleiotropically affects from very few to many characters. The analysis allows for mutational distributions that vary in shape and provides a framework that would allow for varying the frequency at which mutations arise with deleterious and positive effects on characters. The results show that a large fraction of fixed mutations will have deleterious pleiotropic effects even when mutation affects as little as two characters and only directional selection is occurring, and, not surprisingly, as the degree of pleiotropy increases the frequency of fixed deleterious effects increases. As a point of comparison, we show how stabilizing selection and random genetic drift affect the bidirectional distribution of fixed mutational effects. The results are then applied to QTL studies that seek to find loci that contribute to phenotypic differences between populations or species. It is shown that QTL studies are biased against detecting chromosome regions that have deleterious pleiotropic effects on characters.     

Patterns of variation within and between Greek populations of Ceratitis capitata suggest extensive gene flow and latitudinal clines

Four natural Greek populations of Mediterranean fruit fly, Ceratitis capitata (Wiedemann), was studied for genetic variability at 25 enzyme loci. The comparison of polymorphism within and between populations shows two loci with high between-population heterozygosity (HT) and very high fixation index (F(ST)) values, suggesting the presence of balancing selection. The gradual decline of common allele frequency of the polymorphic loci tested indicated that latitudinal clines are present in Greece. Indirect estimates of gene flow based both on Wright's method (Nm*) and on the Slatkin's method (Nm*), which depends on the frequencies of rare alleles found in only one population, revealed a substantial amount of gene flow (Nm = 3.493 and Nm* = 3.197). These estimates of gene flow may well explain why the "introduced" Greek populations of C. capitata, in spite of their low genetic variability, display the same polymorphic loci. Gene flow in combination with natural selection and genetic drift may have played an important role to genetic differentiation in this species in Greece.     

GENETIC DIVERSITY AND POPULATION STRUCTURE IN CAMELLIA JAPONICA L. (THEACEAE)

Camellia japonica is a widespread and morphologically diverse tree native to parts of Japan and adjacent islands. Starch gel electrophoresis was used to score allelic variation at 20 loci in seeds collected from 60 populations distributed throughout the species range. In comparison with other plant species, the level of genetic diversity within C. japonica populations is very high: 66.2% of loci were polymorphic on average per population, with a mean number of 2.16 alleles per locus; the mean observed and panmictic heterozygosities were 0.230 and 0.265, respectively. Genotypic proportions at most loci in most populations fit Hardy-Weinberg expectations. However, small heterozygote deficiencies were commonly observed (mean population fixation index = 0.129). It is suggested that the most likely cause of the observed deficiencies is population subdivision into genetically divergent subpopulations. The overall level of population differentiation is greater than is typically observed in out-breeders: The mean genetic distance and identity (Nei's D and I) between pairs of populations were 0.073 and 0.930, respectively, and Wright's Fst was 0.144. Differences among populations appeared to be manifested as variation in gene frequencies at many loci rather than variation in allelic composition per se. However, the patterns of variation were not random. Reciprocal clinal variation of gene frequencies was observed for allele pairs at six loci. In addition, principal components analysis revealed that populations tended to genetically cluster into four regions representing the geographic areas Kyushu, Shikoku, western Honshu, and eastern Honshu. There was a significant relationship between genetic and geographic distance (r = 0.61; P < 0.01). Analysis of variance on allozyme frequencies showed that there was approximately four times as much differentiation among populations within regions, as among regions. It is likely that the observed patterns of population relationships result from the balance between genetic drift in small subpopulations and gene flow between them.     

Theoretical Modifications of Reciprocal Recurrent Selection

Reciprocal recurrent selection (RRS), which assumes overdominant loci to be important, alters two genetically different populations to improve their crossbred mean. Individual plants from two populations (A and B) are selfed and also crossed with plants from the reciprocal female tester population (B and A, respectively). Selection is based on the mean of crossbred families, and the selected individuals are randomly mated within A and B to form new populations.—We propose two alternatives to RRS. The first (RRS-I) uses, as the tester of population A, a population (LB) that is derived from population B by family selection for low yield. The second (RRS-II) is similar to RRS-I, but also uses, as the tester of B, a population (LA) that is derived from population A by family selection for low yield.—The expected crossbred means of RRS, RRS-I, and RRS-II were compared, assuming equal σP, at several cycles of selection for incomplete and complete dominance, and for several cases of overdominance (depending on the gene frequencies in A and B, and on the equilibrium gene frequency).—The choice of selection method depends on the importance of the effects of overdominant loci compared to loci exhibiting incomplete or complete dominance. If overdominance is unimportant, RRS-II is the best selection method, followed by RRS-I and RRS. If overdominance is important, both RRS and RRS-I are superior to RRS-II; RRS is preferred to RRS-I if the effects of overdominant loci are sufficiently important. If the genetic model is a mixture of levels of dominance at different loci, a combination of selection systems is suggested.     

MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS

Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that clonal lineages are unlikely to survive more than 10⁴ to 10⁵ generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept of the effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.     

The Maintenance of Genetic Variability in Two-Locus Models of Stabilizing Selection

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.     

Transposable elements, mutational correlations, and population divergence in Caenorhabditis elegans

Transposable element activity is thought to be responsible for a large portion of all mutations, but its influence on the evolution of populations has not been well studied. Using mutation accumulation experiments with the nematode Caenorhabditis elegans, we investigated the impact of transposable element activity on the production of mutational variances and covariances. The experiments involved the use of two mutator strains (RNAi-deficient mutants) that are characterized by high levels of germline transposition, as well as the Bristol N2 strain, which lacks germline transposition. We found that transposition led to an increase in mutational heritabilities, as well as to the intensification of correlation patterns observed in the absence of transposition. No mutational trade-offs were detected and mutations generally had a deleterious effect on components of fitness. We also tested whether the pattern of mutational covariation could be used to predict observed patterns of population divergence in this species. Using 15 natural populations, we found that population divergence of C. elegans in multivariate phenotypic space occurred in directions only partially concordant with mutation, and thus other evolutionary factors, such as natural selection and genetic drift, must be acting to produce divergence within this species. Our results suggest that mutations induced by mobile elements in C. elegans are similar to other spontaneous mutations with respect to their contribution to the microevolution of quantitative traits.     

Selection for mutational robustness in finite populations

We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation-selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate.