Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Fixation probability and time in subdivided populations

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

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.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.     

Recombination and hitchhiking of deleterious alleles

When new advantageous alleles arise and spread within a population, deleterious alleles at neighboring loci can hitchhike alongside them and spread to fixation in areas of low recombination, introducing a fixed mutation load. We use branching processes and diffusion equations to calculate the probability that a deleterious allele hitchhikes and fixes alongside an advantageous mutant. As expected, the probability of fixation of a deleterious hitchhiker rises with the selective advantage of the sweeping allele and declines with the selective disadvantage of the deleterious hitchhiker. We then use computer simulations of a genome with an infinite number of loci to investigate the increase in load after an advantageous mutant is introduced. We show that the appearance of advantageous alleles on genetic backgrounds loaded with deleterious alleles has two potential effects: it can fix deleterious alleles, and it can facilitate the persistence of recombinant lineages that happen to occur. The latter is expected to reduce the signals of selection in the surrounding region. We consider these results in light of human genetic data to infer how likely it is that such deleterious hitchhikers have occurred in our recent evolutionary past.     

Effects of Interference Between Selected Loci on the Mutation Load,Inbreeding Depression,and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.     

Clusters of Identical New Mutations Can Account for the ``overdispersed'''' Molecular Clock

Germ-cell mutations may occur during meiosis, giving rise to independent mutant gametes in a Poisson process, or before meiosis, giving rise to multiple copies of identical mutant gametes at a much higher probability than the Poisson expectation. We report that the occurrence of these early premeiotic clusters of new identical mutant alleles increases the variance-to-mean ratio of mutation rate (R(u) > 1). This leads to an expected variance-to-mean ratio (R(t)) of the molecular clock that is always greater than one and may cover the observed range of R(t) values. Hence, the molecular clock may not be over-dispersed based on this new mutational model that includes clusters. To get a better estimation of R(u) and R(t), one needs measurements of the intrageneration variation of reproductive success (N(i)/N(e(i))), population dynamics (k(i)), and the proportion of new mutations that occur in clusters (r(c)), especially those formed before germ-cell differentiation.     

Fixation of clonal lineages under Muller's ratchet

For clonal lineages of finite size that differ in their deleterious mutational effects, the probability of fixation is investigated by mathematical theory and Monte Carlo simulations. If these fitness effects are sufficiently small in one or both lineages, then the lineage with the less deleterious effects will become fixed with high probability. If, however, in both lineages the deleterious effects are larger than a threshold s(c), then the probability of fixation is independent of the fitness effects and depends only on the initial frequencies of the lineages. This threshold decreases with decreasing genomic mutation rate U and increases with population size N. (For N = 10(5), we have s(c) approximately = 0.1 if U = 1, and s(c) approximately = 0.015 if U = 0.1). Above the threshold, the competition is not driven by the ratio of mean fitnesses of the lineages, but by the relative sizes of the zero-mutation classes, which are independent of the fitness effects of the mutations. After the loss of the zero-mutation class of a lineage, the other lineage will spread to fixation with high probability and within a short time span. If the mutation rates of the lineages differ substantially, the lineage with the lower mutation rate is fixed with very high probability unless the lineage with the larger mutation rate has very slightly deleterious mutational effects. If the mutation rates differ by not more than a few percent, then the lineage with the higher mutation rate and the more deleterious effects can become fixed with appreciable probability for a certain range of parameters. The independence of the fixation probability on the fitness effects in a single population leads to dramatic effects in metapopulations: lineages with more deleterious effects have a much higher fixation probability. The critical value s(c), above which this phenomenon occurs, decreases as the migration rate between the subpopulations decreases.     

Chromosome inversions, local adaptation and speciation

We study the evolution of inversions that capture locally adapted alleles when two populations are exchanging migrants or hybridizing. By suppressing recombination between the loci, a new inversion can spread. Neither drift nor coadaptation between the alleles (epistasis) is needed, so this local adaptation mechanism may apply to a broader range of genetic and demographic situations than alternative hypotheses that have been widely discussed. The mechanism can explain many features observed in inversion systems. It will drive an inversion to high frequency if there is no countervailing force, which could explain fixed differences observed between populations and species. An inversion can be stabilized at an intermediate frequency if it also happens to capture one or more deleterious recessive mutations, which could explain polymorphisms that are common in some species. This polymorphism can cycle in frequency with the changing selective advantage of the locally favored alleles. The mechanism can establish underdominant inversions that decrease heterokaryotype fitness by several percent if the cause of fitness loss is structural, while if the cause is genic there is no limit to the strength of underdominance that can result. The mechanism is expected to cause loci responsible for adaptive species-specific differences to map to inversions, as seen in recent QTL studies. We discuss data that support the hypothesis, review other mechanisms for inversion evolution, and suggest possible tests.     

Mating systems and the efficacy of selection at the molecular level

Mating systems are thought to play a key role in molecular evolution through their effects on effective population size (N(e)) and effective recombination rate. Because of reduced N(e), selection in self-fertilizing species is supposed to be less efficient, allowing fixation of weakly deleterious alleles or lowering adaptation, which may jeopardize their long-term evolution. Relaxed selection pressures in selfers should be detectable at the molecular level through the analyses of the ratio of nonsynonymous and synonymous divergence, D(n)/D(s), or the ratio of nonsynonymous and synonymous polymorphism, pi(n)/pi(s). On the other hand, selfing reveals recessive alleles to selection (homozygosity effect), which may counterbalance the reduction in N(e). Through population genetics models, this study investigates which process may prevail in natural populations and which conditions are necessary to detect evidence for relaxed selection signature at the molecular level in selfers. Under a wide range of plausible population and mutation parameters, relaxed selection against deleterious mutations should be detectable, but the differences between the two mating systems can be weak. At equilibrium, differences between outcrossers and selfers should be more pronounced using divergence measures (D(n)/D(s) ratio) than using polymorphism data (pi(n)/pi(s) ratio). The difference in adaptive substitution rates between outcrossers and selfers is much less predictable because it critically depends on the dominance levels of new advantageous mutations, which are poorly known. Different ways of testing these predictions are suggested, and implications of these results for the evolution of self-fertilizing species are also discussed.     

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.     

Spatial heterogeneity in the strength of selection against deleterious alleles and the mutation load

According to current estimates of genomic deleterious mutation rates (which are often of the order 0.1-1) the mutation load (defined as a reduction in the average fitness of a population due to the presence of deleterious alleles) may be important in many populations. In this paper, I use multilocus simulations to explore the effect of spatial heterogeneity in the strength of selection against deleterious alleles on the mutation load (for example, it has been suggested that stressful environments may increase the strength of selection). These simulations show contrasted results: in some situations, spatial heterogeneity may greatly reduce the mutation load, due to the fact that migrants coming from demes under stronger selection carry relatively few deleterious alleles, and benefit from a strong advantage within demes under weaker selection (where individuals carry many more deleterious alleles); in other situations, however, deleterious alleles accumulate within demes under stronger selection, due to migration pressure from demes under weaker selection, leading to fitness erosion within those demes. This second situation is more frequent when the productivity of the different demes is proportional to their mean fitness. The effect of spatial heterogeneity is greatly reduced, however, when the response to environmental differences is inconsistent across loci.     

Genetics of postzygotic isolation in Eucalyptus: whole-genome analysis of barriers to introgression in a wide interspecific cross of Eucalyptus grandis and E. globulus

The genetic architecture of hybrid fitness characters can provide valuable insights into the nature and evolution of postzygotic reproductive barriers in diverged species. We determined the genome-wide distribution of barriers to introgression in an F(1) hybrid of two Eucalyptus tree species, Eucalyptus grandis (W. Hill ex Maiden.) and E. globulus (Labill.). Two interspecific backcross families (N = 186) were used to construct comparative, single-tree, genetic linkage maps of an F(1) hybrid individual and two backcross parents. A total of 1354 testcross AFLP marker loci were evaluated in the three parental maps and a substantial proportion (27.7% average) exhibited transmission ratio distortion (alpha = 0.05). The distorted markers were located in distinct regions of the parental maps and marker alleles within each region were all biased toward either of the two parental species. We used a Bayesian approach to estimate the position and effect of transmission ratio distorting loci (TRDLs) in the distorted regions of each parental linkage map. The relative viability of TRDL alleles ranged from 0.20 to 0.72. Contrary to expectation, heterospecific (donor) alleles of TRDLs were favored as often as recurrent alleles in both backcrosses, suggesting that positive and negative heterospecific interactions affect introgression rates in this wide interspecific pedigree.     

Heterozygosity-fitness correlations among wild populations of European tree frog (Hyla arborea) detect fixation load

Quantifying the impacts of inbreeding and genetic drift on fitness traits in fragmented populations is becoming a major goal in conservation biology. Such impacts occur at different levels and involve different sets of loci. Genetic drift randomly fixes slightly deleterious alleles leading to different fixation load among populations. By contrast, inbreeding depression arises from highly deleterious alleles in segregation within a population and creates variation among individuals. A popular approach is to measure correlations between molecular variation and phenotypic performances. This approach has been mainly used at the individual level to detect inbreeding depression within populations and sometimes at the population level but without consideration about the genetic processes measured. For the first time, we used in this study a molecular approach considering both the interpopulation and intrapopulation level to discriminate the relative importance of inbreeding depression vs. fixation load in isolated and non-fragmented populations of European tree frog (Hyla arborea), complemented with interpopulational crosses. We demonstrated that the positive correlations observed between genetic heterozygosity and larval performances on merged data were mainly caused by co-variations in genetic diversity and fixation load among populations rather than by inbreeding depression and segregating deleterious alleles within populations. Such a method is highly relevant in a conservation perspective because, depending on how populations lose fitness (inbreeding vs. fixation load), specific management actions may be designed to improve the persistence of populations.     

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.     

Genomic Evidence of Rapid and Stable Adaptive Oscillations over Seasonal Time Scales in Drosophila

In many species, genomic data have revealed pervasive adaptive evolution indicated by the fixation of beneficial alleles. However, when selection pressures are highly variable along a species'' range or through time adaptive alleles may persist at intermediate frequencies for long periods. So called “balanced polymorphisms” have long been understood to be an important component of standing genetic variation, yet direct evidence of the strength of balancing selection and the stability and prevalence of balanced polymorphisms has remained elusive. We hypothesized that environmental fluctuations among seasons in a North American orchard would impose temporally variable selection on Drosophila melanogaster that would drive repeatable adaptive oscillations at balanced polymorphisms. We identified hundreds of polymorphisms whose frequency oscillates among seasons and argue that these loci are subject to strong, temporally variable selection. We show that these polymorphisms respond to acute and persistent changes in climate and are associated in predictable ways with seasonally variable phenotypes. In addition, our results suggest that adaptively oscillating polymorphisms are likely millions of years old, with some possibly predating the divergence between D. melanogaster and D. simulans. Taken together, our results are consistent with a model of balancing selection wherein rapid temporal fluctuations in climate over generational time promotes adaptive genetic diversity at loci underlying polygenic variation in fitness related phenotypes.     

The evolutionary consequences of niche construction: a theoretical investigation using two-locus theory

This paper addresses the joint evolution of environment-altering (niche constructing) traits, and traits whose fitness depends on alterable sources of natural selection in environments. We explore the evolutionary consequences of this niche construction using a two-locus population genetic model. The novel conclusions are that niche construction can (1) cause evolutionary inertia and momentum, (2) lead to the fixation of otherwise deleterious alleles, (3) support stable polymorphisms where none are expected, (4) eliminate what would otherwise be stable polymorphisms, and (5) influence disequilibrium. The results suggest that the changes that organisms bring about in their niche can themselves be an important source of natural selection pressures, and imply that evolution may proceed in cycles of selection and niche construction.