Effects of dominance on the probability of fixation of a mutant allele

We consider whether the fixation probability of an allele in a two-allele diploid system is always a monotonic function of the selective advantage of the allele. We show that while this conjecture is correct for intermediate dominance, it is not correct in general for either overdominant or underdominant alleles, and that for some parameter ranges the fixation probability can initially decrease and then increase as a function of the amount of selection. We have partial results that characterize the ranges of parameters for which this happens.      

Meiotic drive and evolution of female choice.

As a special version of the good-genes hypothesis, it was recently proposed that females could benefit from choosing drive-resistant males in a meiotic drive system. Here, we examine with a three-locus, six-allele population genetic model whether female choice for drive resistance can evolve. An allele leading to female preference for drive-resistant males was introduced at low frequency into a population polymorphic for meiotic drive and drive resistance. Our simulations show that female choice of drive-resistant males is disadvantageous when resistance is Y-linked. This disadvantage occurs because, at equilibrium, drive-resistant males have lower reproductive success than drive-susceptible males. Thus, female choice of drive-susceptible males can evolve when resistance is Y-linked. When resistance is autosomal, selection on female choice for drive resistance is less strong and depends on the frequency of choice: female preference of resistant males is favoured when choice is rare and disadvantageous when choice is frequent, leading to a stable equilibrium at a low frequency of the choice allele. Independent of the location of drive resistance alleles, males with the non-driving allele always have above average reproductive success. Female choice is therefore beneficial when choosy females prefer males with the non-driving allele.     

Convergence of genotypic frequencies for differential selfing and positive assortative mating at a biallelic locus

For a biallelic model of differential self-fertilization and differential positive assortative mating based on genotype, it is shown that the genotypic frequencies converge for all sets of mating system parameters. Overdominance and underdominance with respect to the parameters are necessary but not sufficient conditions for global convergence to a polymorphic equilibrium and local attractiveness of both the fixation states, respectively. There are cases of overdominance and underdominance for which one fixation state is globally attractive. The relationship of the result to those known from the classical viability selection model are briefly discussed. For the multiallelic version, it is shown that after the first generation all of the homozygote frequencies are always in excess of the corresponding Hardy-Weinberg proportions if at least one homozygote rate of self-fertilization or assortment probability is positive.     

Fixation of advantageous alleles in partially self-fertilizing populations. The effect of different selection modes

The expected fixation probability of an advantageous allele was examined in a partially self-fertilizing hermaphroditic plant species using the diffusion approximation. The selective advantage of the advantageous allele was assumed to be increased viability, increased fecundity, or an increase in male fitness. The mode of selection, as well as the selfing rate, the population size, and the dominance of the advantageous allele, affect the fixation probability of the allele. In general it was found that increases in selfing rate decrease the fixation probability under male sexual selection, increase fixation probability under fecundity selection, and increase when recessive and decrease when dominant under viability selection. In some cases the highest fixation probability of advantageous alleles under fecundity or under male sexual selection occurred at an intermediary selfing rate. The expected mean fixation times of the advantageous allele were also examined using the diffusion approximation.     

A Simulation Study of Truncation Selection for a Quantitative Trait Opposed by Natural Selection

A quantitative character controlled at one locus with two alleles was submitted to artificial (mass) selection and to three modes of opposing natural selection (directional selection, overdominance and underdominance) in a large random-mating population. The selection response and the limits of the selective process were studied by deterministic simulation. The lifetime of the process was generally between 20 and 100 generations and did not appear to depend on the mode of natural selection. However, depending on the values of the parameters (initial gene frequency, selection intensity, ratio of the effect of the gene to the environmental standard deviation, fitness values) the following outcomes of selection were observed: fixation of the allele favored by artificial selection, stable nontrivial equilibrium, unstable equilibrium and loss of the allele favored by artificial selection. Finally, the results of the simulation were compared to the results of selection experiments.     

Sperm should evolve to make female meiosis fair

Genomic conflicts arise when an allele gains an evolutionary advantage at a cost to organismal fitness. Oögenesis is inherently susceptible to such conflicts because alleles compete for inclusion into the egg. Alleles that distort meiosis in their favor (i.e., meiotic drivers) often decrease organismal fitness, and therefore indirectly favor the evolution of mechanisms to suppress meiotic drive. In this light, many facets of oögenesis and gametogenesis have been interpreted as mechanisms of protection against genomic outlaws. That females of many animal species do not complete meiosis until after fertilization, appears to run counter to this interpretation, because this delay provides an opportunity for sperm‐acting alleles to meddle with the outcome of female meiosis and help like alleles drive in heterozygous females. Contrary to this perceived danger, the population genetic theory presented herein suggests that, in fact, sperm nearly always evolve to increase the fairness of female meiosis in the face of genomic conflicts. These results are consistent with the apparent sperm dependence of the best characterized female meiotic driversin animals. Rather than providing an opportunity for sperm collaboration in female meiotic drive, the “fertilization requirement” indirectly protects females from meiotic drivers by providing sperm an opportunity to suppress drive.     

Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.     

Evolution of the segregation ratio: modification of gene conversion and meiotic drive

We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximinize mean fitness to the generation of such associations.     

Coevolutionary dynamics of polyandry and sex‐linked meiotic drive

Segregation distorters located on sex chromosomes are predicted to sweep to fixation and cause extinction via a shortage of one sex, but in nature they are often found at low, stable frequencies. One potential resolution to this longstanding puzzle involves female multiple mating (polyandry). Because many meiotic drivers severely reduce the sperm competitive ability of their male carriers, females are predicted to evolve more frequent polyandry and thereby promote sperm competition when a meiotic driver invades. Consequently, the driving chromosome's relative fitness should decline, halting or reversing its spread. We used formal modeling to show that this initially appealing hypothesis cannot resolve the puzzle alone: other selective pressures (e.g., low fitness of drive homozygotes) are required to establish a stable meiotic drive polymorphism. However, polyandry and meiotic drive can strongly affect one another's frequency, and polyandrous populations may be resistant to the invasion of rare drive mutants.     

Sperm competition and the dynamics of X chromosome drive: stability and extinction

Several empirical studies of sperm competition in populations polymorphic for a driving X chromosome have revealed that Sex-ratio males (those carrying a driving X) are at a disadvantage relative to Standard males. Because the frequency of the driving X chromosome determines the population-level sex ratio and thus alters male and female mating rates, the evolutionary consequences of sperm competition for sex chromosome meiotic drive are subtle. As the SR allele increases in frequency, the ratio of females to males also increases, causing an increase in the male mating rate and a decrease in the female mating rate. While the former change may exacerbate the disadvantage of Sex-ratio males during sperm competition, the latter change decreases the incidence of sperm competition within the population. We analyze a model of the effects of sperm competition on a driving X chromosome and show that these opposing trends in male and female mating rates can result in two coexisting locally stable equilibria, one corresponding to a balanced polymorphism of the SR and ST alleles and the second to fixation of the ST allele. Stochastic fluctuations of either the population sex ratio or the SR frequency can then drive the population away from the balanced polymorphism and into the basin of attraction for the second equilibrium, resulting in fixation of the SR allele and extinction of the population.     

Probability of fixation in a heterogeneous environment

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

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.     

The robustness of Hamilton's rule with inbreeding and dominance: kin selection and fixation probabilities under partial sib mating

Assessing the validity of Hamilton's rule when there is both inbreeding and dominance remains difficult. In this article, we provide a general method based on the direct fitness formalism to address this question. We then apply it to the question of the evolution of altruism among diploid full sibs and among haplodiploid sisters under inbreeding resulting from partial sib mating. In both cases, we find that the allele coding for altruism always increases in frequency if a condition of the form rb>c holds, where r depends on the rate of sib mating alpha but not on the frequency of the allele, its phenotypic effects, or the dominance of these effects. In both examples, we derive expressions for the probability of fixation of an allele coding for altruism; comparing these expressions with simulation results allows us to test various approximations often made in kin selection models (weak selection, large population size, large fecundity). Increasing alpha increases the probability of fixation of recessive altruistic alleles (h<1/2), while it can increase or decrease the probability of fixation of dominant altruistic alleles (h>1/2).     

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.     

Allele frequency distribution under recurrent selective sweeps

The allele frequency of a neutral variant in a population is pushed either upward or downward by directional selection on a linked beneficial mutation ("selective sweeps"). DNA sequences sampled after the fixation of the beneficial allele thus contain an excess of rare neutral alleles. This study investigates the allele frequency distribution under selective sweep models using analytic approximation and simulation. First, given a single selective sweep at a fixed time, I derive an expression for the sampling probabilities of neutral mutants. This solution can be used to estimate the time of the fixation of a beneficial allele from sequence data. Next, I obtain an approximation to mean allele frequencies under recurrent selective sweeps. Under recurrent sweeps, the frequency spectrum is skewed toward rare alleles. However, the excess of high-frequency derived alleles, previously shown to be a signature of single selective sweeps, disappears with recurrent sweeps. It is shown that, using this approximation and multilocus polymorphism data, genomewide parameters of directional selection can be estimated.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Using underdominance to bi-stably transform local populations

Underdominance refers to natural selection against individuals with a heterozygous genotype. Here, we analyze a single-locus underdominant system of two large local populations that exchange individuals at a certain migration rate. The system can be characterized by fixed points in the joint allele frequency space. We address the conditions under which underdominance can be applied to transform a local population that is receiving wildtype immigrants from another population. In a single population, underdominance has the benefit of complete removal of genetically modified alleles (reversibility) and coexistence is not stable. The two population system that exchanges migrants can result in internal stable states, where coexistence is maintained, but with additional release of wildtype individuals the system can be reversed to a fully wildtype state. This property is critically controlled by the migration rate. We approximate the critical minimum frequency required to result in a stable population transformation. We also concentrate on the destabilizing effects of fitness and migration rate asymmetry. Practical implications of our results are discussed in the context of utilizing underdominance to genetically modify wild populations. This is of importance especially for genetic pest management strategies, where locally stable and potentially reversible transformations of populations of disease vector species are of interest.     

Stability properties of underdominance in finite subdivided populations

IN ISOLATED populations underdominance leads to bistable evolutionary dynamics: below a certain mutant allele frequency the wildtype succeeds. Above this point, the potentially underdominant mutant allele fixes. In subdivided populations with gene flow there can be stable states with coexistence of wildtypes and mutants: polymorphism can be maintained because of a migration-selection equilibrium, i.e., selection against rare recent immigrant alleles that tend to be heterozygous. We focus on the stochastic evolutionary dynamics of systems where demographic fluctuations in the coupled populations are the main source of internal noise. We discuss the influence of fitness, migration rate, and the relative sizes of two interacting populations on the mean extinction times of a group of potentially underdominant mutant alleles. We classify realistic initial conditions according to their impact on the stochastic extinction process. Even in small populations, where demographic fluctuations are large, stability properties predicted from deterministic dynamics show remarkable robustness. Fixation of the mutant allele becomes unlikely but the time to its extinction can be long.     

Soft sweeps II--molecular population genetics of adaptation from recurrent mutation or migration

In the classical model of molecular adaptation, a favored allele derives from a single mutational origin. This ignores that beneficial alleles can enter a population recurrently, either by mutation or migration, during the selective phase. In this case, descendants of several of these independent origins may contribute to the fixation. As a consequence, all ancestral haplotypes that are linked to any of these copies will be retained in the population, affecting the pattern of a selective sweep on linked neutral variation. In this study, we use analytical calculations based on coalescent theory and computer simulations to analyze molecular adaptation from recurrent mutation or migration. Under the assumption of complete linkage, we derive a robust analytical approximation for the number of ancestral haplotypes and their distribution in a sample from the population. We find that so-called "soft sweeps," where multiple ancestral haplotypes appear in a sample, are likely for biologically realistic values of mutation or migration rates.