Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

Note on the computation of critical effective population sizes.

This work extends the work of Whitlock in examining the critical effective population sizes from the fixation of both deleterious and beneficial mutations under drift and selection to prevent mutation breakdown of the population. The validity of approximations for the probability of fixation depends on the nature of the assumed distribution for the fitness effect of both types of mutations. Using no approximation for the probability of fixation and assuming a heavy tailed fitness effect distribution, the current model indicates that the coefficients of variation for the fitness effect distributions of both types of mutations and the fitness effect distribution mean for the beneficial mutations are important predictors of the critical effective population size. The current model further predicts that very small populations can be sustained if the fitness effect variances for both types of mutations and the mean for beneficial mutations are large.     

The joint effects of background selection and genetic recombination on local gene genealogies

Background selection, the effects of the continual removal of deleterious mutations by natural selection on variability at linked sites, is potentially a major determinant of DNA sequence variability. However, the joint effects of background selection and genetic recombination on the shape of the neutral gene genealogy have proved hard to study analytically. The only existing formula concerns the mean coalescent time for a pair of alleles, making it difficult to assess the importance of background selection from genome-wide data on sequence polymorphism. Here we develop a structured coalescent model of background selection with recombination and implement it in a computer program that efficiently generates neutral gene genealogies for an arbitrary sample size. We check the validity of the structured coalescent model against forward-in-time simulations and show that it accurately captures the effects of background selection. The model produces more accurate predictions of the mean coalescent time than the existing formula and supports the conclusion that the effect of background selection is greater in the interior of a deleterious region than at its boundaries. The level of linkage disequilibrium between sites is elevated by background selection, to an extent that is well summarized by a change in effective population size. The structured coalescent model is readily extendable to more realistic situations and should prove useful for analyzing genome-wide polymorphism data.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Dynamic sampling bias and overdispersion induced by skewed offspring distributions

Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions. The resulting allele-frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the forward-in-time dynamics, especially with selection. Here, we employ an asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele-frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law.     

Using coalescent simulations to test the impact of quaternary climate cycles on divergence in an alpine plant-insect association

The Quaternary climate cycles forced species to repeatedly migrate across a continually changing landscape. How these shifts in distribution impacted the evolution of unrelated but ecologically associated taxa has remained elusive due to the stochastic nature of the evolutionary process and variation in species-specific biological characteristics and environmental constraints. To account for the uncertainty in genealogical estimates, we adopted a coalescent approach for testing hypotheses of population divergence in coevolving taxa. We compared genealogies of a specialized herbivorous insect, Parnassius smintheus (Papilionidae), and its host plant, Sedum lanceolatum (Crassulaceae), from the alpine tundra of the Rocky Mountains to null distributions from coalescent simulations to test whether tightly associated taxa shared a common response to the paleoclimatic cycles. Explicit phylogeographic models were generated from geologic and biogeographic data and evaluated over a wide range of divergence times given calibrated mutation rates for both species. Our analyses suggest that the insect and its host plant responded similarly but independently to the climate cycles. By promoting habitat expansion and mixing among alpine populations, glacial periods repeatedly reset the distributions of genetic variation in each species and inhibited continual codivergence among pairs of interacting species.     

GroEL and the maintenance of bacterial endosymbiosis

Many eukaryotic organisms have symbiotic associations with obligate intracellular bacteria. The clonal transmission of endosymbionts between host generations should lead to the irreversible fixation of slightly deleterious mutations in their non-recombinant genome by genetic drift. However, the stability of endosymbiosis indicates that some mechanism is involved in the amelioration of the effects of these mutations. We propose that the chaperone GroEL was involved in the acquisition of an endosymbiotic lifestyle not only by means of its over-production, as proposed by Moran, but also by its adaptive evolution mediated by positive selection to improve the interaction with the unstable endosymbiont proteome.     

Natural selection at linked sites in humans

Theoretical and empirical work indicates that patterns of neutral polymorphism can be affected by linked, selected mutations. Under background selection, deleterious mutations removed from a population by purifying selection cause a reduction in linked neutral diversity. Under genetic hitchhiking, the rise in frequency and fixation of beneficial mutations also reduces the level of linked neutral polymorphism. Here we review the evidence that levels of neutral polymorphism in humans are affected by selection at linked sites. We then discuss four approaches for distinguishing between background selection and genetic hitchhiking based on (i) the relationship between polymorphism level and recombination rate for neutral loci with high mutation rates, (ii) relative levels of variation on the X chromosome and the autosomes, (iii) the frequency distribution of neutral polymorphisms, and (iv) population-specific patterns of genetic variation. Although the evidence for selection at linked sites in humans is clear, current methods and data do not allow us to clearly assess the relative importance of background selection and genetic hitchhiking in humans. These results contrast with those obtained for Drosophila, where the signals of positive selection are stronger.     

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.     

The effect of selection on genealogies

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.     

Selective Strolls: Fixation and Extinction in Diploids Are Slower for Weakly Selected Mutations Than for Neutral Ones

In finite populations, an allele disappears or reaches fixation due to two main forces, selection and drift. Selection is generally thought to accelerate the process: a selected mutation will reach fixation faster than a neutral one, and a disadvantageous one will quickly disappear from the population. We show that even in simple diploid populations, this is often not true. Dominance and recessivity unexpectedly slow down the evolutionary process for weakly selected alleles. In particular, slightly advantageous dominant and mildly deleterious recessive mutations reach fixation slightly more slowly than neutral ones (at most 5%). This phenomenon determines genetic signatures opposite to those expected under strong selection, such as increased instead of decreased genetic diversity around the selected site. Furthermore, we characterize a new phenomenon: mildly deleterious recessive alleles, thought to represent a wide fraction of newly arising mutations, on average survive in a population slightly longer than neutral ones, before getting lost. Consequently, these mutations are on average slightly older than neutral ones, in contrast with previous expectations. Furthermore, they slightly increase the amount of weakly deleterious polymorphisms, as a consequence of the longer unconditional sojourn times compared to neutral mutations.     

Influence of random genetic drift on human immunodeficiency virus type 1 env evolution during chronic infection

Human immunodeficiency virus type 1 (HIV-1) has high replication and mutation rates that generate large census populations and high levels of genetic variation. We examined the roles of natural selection, population growth, random genetic drift, and recombination in shaping the variation in 1509 C2-V5 env sequences derived from nine men with chronic HIV-1 infection. These sequences were obtained from clinical visits that reflect the first 6-13.7 years of infection. Pairwise comparisons of nonsynonymous and synonymous distances, Tajima's D test, Fu and Li's D* test, and a test of recurrent mutation revealed evidence for episodes of nonneutral evolution in a total of 22 out of 145 blood samples, representing six of the nine individuals. Using three coalescent-based maximum-likelihood estimators, we found viral effective population sizes in all nine individuals to be approximately 10(3). We also show that a previous estimate of the effective population size of approximately 10(5) based on rare haplotype frequencies decreases to approximately 10(3) upon correcting a biased sampling procedure. We conclude that the genetic variation in these data sets can be explained by a predominance of random genetic drift of neutral mutations with brief episodes of natural selection that were frequently masked by recombination.     

Testing the molecular and evolutionary causes of a 'leapfrog' pattern of geographical variation in coloration

Understanding the mechanisms accounting for the evolution of phenotypic diversity is central to evolutionary biology. We use molecular and phenotypic data to test hypotheses for 'leapfrog' patterns of geographical variation, in which phenotypically similar, disjunct populations are separated by distinct populations of the same species. Phylogenetic reconstructions revealed independent evolution of melanic plumage characters in different populations in the Neotropical avian genus Arremon. Thus, phenotypic similarities between distant populations cannot be explained by close phylogenetic affinity. Nor can they be attributed to recurring mutations in the MC1R gene, a locus involved in melanic pigmentation. A coalescent analysis indicates that plumage traits have become fixed at a faster rate than expected under genetic drift, suggesting that selection underlies their repeated evolution. In contrast to views that genetic drift drives phenotypic differentiation in Neotropical montane birds, our results imply that geographical variation preceding speciation may reflect the action of deterministic selective processes.     

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.     

History can matter: non-Markovian behavior of ancestral lineages

Although most of the important evolutionary events in the history of biology can only be studied via interspecific comparisons, it is challenging to apply the rich body of population genetic theory to the study of interspecific genetic variation. Probabilistic modeling of the substitution process would ideally be derived from first principles of population genetics, allowing a quantitative connection to be made between the parameters describing mutation, selection, drift, and the patterns of interspecific variation. There has been progress in reconciling population genetics and interspecific evolution for the case where mutation rates are sufficiently low, but when mutation rates are higher, reconciliation has been hampered due to complications from how the loss or fixation of new mutations can be influenced by linked nonneutral polymorphisms (i.e., the Hill-Robertson effect). To investigate the generation of interspecific genetic variation when concurrent fitness-affecting polymorphisms are common and the Hill-Robertson effect is thereby potentially strong, we used the Wright-Fisher model of population genetics to simulate very many generations of mutation, natural selection, and genetic drift. This was done so that the chronological history of advantageous, deleterious, and neutral substitutions could be traced over time along the ancestral lineage. Our simulations show that the process by which a nonrecombining sequence changes over time can markedly deviate from the Markov assumption that is ubiquitous in molecular phylogenetics. In particular, we find tendencies for advantageous substitutions to be followed by deleterious ones and for deleterious substitutions to be followed by advantageous ones. Such non-Markovian patterns reflect the fact that the fate of the ancestral lineage depends not only on its current allelic state but also on gene copies not belonging to the ancestral lineage. Although our simulations describe nonrecombining sequences, we conclude by discussing how non-Markovian behavior of the ancestral lineage is plausible even when recombination rates are not low. As a result, we believe that increased attention needs to be devoted to the robustness of evolutionary inference procedures that rely upon the Markov assumption.     

POSITIVE SELECTION DRIVES FASTER‐Z EVOLUTION IN SILKMOTHS

Genes linked to X or Z chromosomes, which are hemizygous in the heterogametic sex, are predicted to evolve at different rates than those on autosomes. This “faster‐X effect” can arise either as a consequence of hemizygosity, which leads to more efficient selection for recessive beneficial mutations in the heterogametic sex, or as a consequence of reduced effective population size of the hemizygous chromosome, which leads to increased fixation of weakly deleterious mutations due to genetic drift. Empirical results to date suggest that, while the overall pattern across taxa is complicated, systems with male heterogamy show a faster‐X effect attributable to more efficient selection, whereas the faster‐Z effect in female‐heterogametic taxa is attributable to increased drift. To test the generality of the faster‐Z pattern seen in birds and snakes, we sequenced the genome of the lepidopteran silkmoth Bombyx huttoni. We show that silkmoths experience faster‐Z evolution, but unlike in birds and snakes, the faster‐Z effect appears to be attributable to more efficient positive selection. These results suggest that female heterogamy alone is unlikely to explain the reduced efficacy of selection on vertebrate Z chromosomes. It is likely that many factors, including differences in overall effective population size, influence Z chromosome evolution.     

The Evolutionarily Stable Distribution of Fitness Effects

The distribution of fitness effects (DFE) of new mutations is a key parameter in determining the course of evolution. This fact has motivated extensive efforts to measure the DFE or to predict it from first principles. However, just as the DFE determines the course of evolution, the evolutionary process itself constrains the DFE. Here, we analyze a simple model of genome evolution in a constant environment in which natural selection drives the population toward a dynamic steady state where beneficial and deleterious substitutions balance. The distribution of fitness effects at this steady state is stable under further evolution and provides a natural null expectation for the DFE in a population that has evolved in a constant environment for a long time. We calculate how the shape of the evolutionarily stable DFE depends on the underlying population genetic parameters. We show that, in the absence of epistasis, the ratio of beneficial to deleterious mutations of a given fitness effect obeys a simple relationship independent of population genetic details. Finally, we analyze how the stable DFE changes in the presence of a simple form of diminishing-returns epistasis.     

Heterosis is common and inbreeding depression absent in natural populations of Arabidopsis thaliana

The importance of genetic drift in shaping patterns of adaptive genetic variation in nature is poorly known. Genetic drift should drive partially recessive deleterious mutations to high frequency, and inter‐population crosses may therefore exhibit heterosis (increased fitness relative to intra‐population crosses). Low genetic diversity and greater genetic distance between populations should increase the magnitude of heterosis. Moreover, drift and selection should remove strongly deleterious recessive alleles from individual populations, resulting in reduced inbreeding depression. To estimate heterosis, we crossed 90 independent line pairs of Arabidopsis thaliana from 15 pairs of natural populations sampled across Fennoscandia and crossed an additional 41 line pairs from a subset of four of these populations to estimate inbreeding depression. We measured lifetime fitness of crosses relative to parents in a large outdoor common garden (8,448 plants in total) in central Sweden. To examine the effects of genetic diversity and genetic distance on heterosis, we genotyped parental lines for 869 SNPs. Overall, genetic variation within populations was low (median expected heterozygosity = 0.02), and genetic differentiation was high (median F_ST = 0.82). Crosses between 10 of 15 population pairs exhibited significant heterosis, with magnitudes of heterosis as high as 117%. We found no significant inbreeding depression, suggesting that the observed heterosis is due to fixation of mildly deleterious alleles within populations. Widespread and substantial heterosis indicates an important role for drift in shaping genetic variation, but there was no significant relationship between fitness of crosses relative to parents and genetic diversity or genetic distance between populations.