The effect of natural selection on linked sites has been suggested to be a major determinant of genetic diversity. While it is in principle possible to estimate this effect from genome sequence data, interactions between selection, demography and inbreeding are expected to make inference less reliable. Here, we investigate whether the genome-wide reduction in diversity due to background selection (B¯) can be accurately estimated when populations are at demographic non-equilibrium and/or reproduce by partial self-fertilization. We show that the classic-BGS model is surprisingly robust to both demographic non-equilibrium and low rates of selfing, although both processes do lead to biased estimation of the distribution of fitness effects (DFE) of deleterious mutations. A high rate of selfing leads to poor estimation of both B¯ and DFE parameters. We propose an alternative approach where background selection, demography and partial selfing are jointly estimated from windowed site frequency spectra. This approach resolves most of the bias observed under the classic-BGS model and can also generate estimates of past demography that account for the effect of background selection and partial selfing. We apply the approach to genome sequence data from Capsella grandiflora and Capsella orientalis, which have contrasting mating systems and display a forty-fold difference in nucleotide diversity. Our results suggest that background selection has a weak effect on levels of genetic diversity in the outcrosser C. grandiflora (B¯=0.89) and a more substantial effect in the predominantly selfing species C. orientalis (B¯=0.44), but that background selection alone cannot explain their disparity in genetic diversity.

Abstract The signed linkage disequilibrium (LD) among selected mutations plays an important role in theoretical models of the evolution of sex and recombination. Several recent studies have quantified LD among mutations in genomic datasets, often reporting positive LD, particularly among mutations presumed to be less deleterious, such as synonymous variants. In this article, we investigate two potential sources of this positive LD: the focus on rare alleles, as adopted in several previous studies, and errors arising in the mapping of short-read sequences onto a reference genome. Using coalescent simulations, we extend previous theoretical results of the effect of focusing on rare alleles, and show that derived neutral alleles present at similar frequencies tend to be in positive LD, while alleles present at different frequencies tend to be in negative LD. Reanalyzing datasets from Capsella grandiflora and Drosophila melanogaster , we show that LD among synonymous derived alleles vanishes in the absence of any conditioning on frequency, while LD between mutations categorized as potentially deleterious by the SIFT4G program stays positive. However, we show that in both cases, this positive LD may be at least partly caused by the potential mismapping of a small fraction of sequences in some individuals, which could be a consequence of structural variants that are absent from the reference genome. Overall, these results show that average signed LD among mutations can be strongly affected by technical artifacts even if these concern only a minority of variants. Finally, we discuss other possible sources of positive LD among deleterious mutations.

ABSTRACT Eusocial Hymenoptera present the highest known recombination rates among metazoans, which evolved several times independently among bees, ants and wasps. Several hypotheses have been proposed to explain this observation, including stronger selection for recombination caused by coevolving parasites and pathogens, and strong sexual selection among haploid males due to male-biased sex ratios among reproductive individuals. In this article, we explore the effects of haplodiploidy and differential selection between sexes on the evolution of recombination, by analyzing a three-locus model in which selection for recombination stems from negative epistasis between selected loci. Our analytical predictions are compared with the results of individual-based simulations in which deleterious mutations occur along a linear chromosome. Our results show that, at mutation-selection balance for deleterious alleles, increasing the strength of selection against deleterious alleles (due to the effect of male haploidy and/or sexual selection) tends to reduce selection for recombination. However, an increase in the overall magnitude of negative epistasis (which may also be due to male haploidy and/or sexual selection) combined with the fact that recombination only occurs in females may increase selection for recombination substantially. Our model also shows that, in conditions favoring recombination, increasing recombination in meioses leading to parthenogenetic ovules (and male offspring) may yield stronger benefits than in meioses leading to fertilized ovules (and female offspring).

Abstract The evolution of recombination is thought to be influenced by many factors, including the mating system. Here, we provide an experimental test of how self-fertilization (selfing) affects the evolution of a recombination modifier. We used experimental populations of Caenorhabditis elegans segregating for the recombination modifier rec-1 , a mutant that redistributes crossovers from the genetically diverse chromosome arms toward the less diverse central regions. By evolving populations under varying selfing rates, we show that increasing selfing reverses selection acting on the rec-1 mutant, from positive to negative. Simulations show that this reversal can be explained by an expansion of the genomic region over which the modifier remains associated with the genetic combinations it creates. These results demonstrate that selfing can fundamentally alter the evolutionary fate of recombination modifiers and reveal a mechanism not predicted by previous theoretical models of recombination evolution under different mating systems, which assumed uniform recombination landscapes.

Deleterious mutations have multiple effects on the fate of chromosomal inversions. In this article, we use individual-based simulations to estimate the fixation probabilities of neutral inversions under a constant input of deleterious mutations. As shown previously, we find that "lucky" inversions carrying a lower-than-average mutation load are initially favored and tend to selectively spread. Our results also outline the importance of Muller's ratchet caused by the absence of recombination in Y-linked and rare autosomal inversions, reducing their fixation probabilities. Despite the fact that Y-linked inversions are more susceptible to Muller's ratchet, they can more easily fix than autosomal inversions despite initially carrying mutations when these mutations have sufficiently low selection or dominance coefficients (sheltering effect). Similarly, the sheltering of deleterious alleles can increase the fixation probability of inversions capturing a mating-type locus, particularly under intermediate rates of self-fertilization. Overall, our results confirm that when mating is random and for realistic parameter values, the presence of deleterious alleles reduces the average fixation probability of autosomal, sex-linked, or mating type-linked inversions below that of a neutral mutation. Nevertheless, the occasional fixation of a lucky inversion may have important macroevolutionary consequences, potentially contributing to the evolution of recombination arrest on sex chromosomes.

By increasing local genetic drift and generating inbreeding, population spatial structure may have important effects on the evolutionary benefits of sexual reproduction. In this article, we consider a population structured according to the island model, and use two and three-locus analytical models and multilocus simulations to explore the selective forces acting on a modifier locus affecting the rate of sexual reproduction of facultatively sexual organisms, in the presence of recurrent deleterious mutations. The results show that population structure and selection combine to generate a local excess of heterozygotes at selected loci (negative $F_{\mathrm{IS}}$), for both partially recessive and partially dominant deleterious alleles. The linkage disequilibrium between deleterious alleles may be either negative or positive depending on their dominance coefficient, the degree of population structure and the rate of sex. These genetic associations combine with many other ones to generate indirect selection at the sex modifier locus, generally favoring intermediate rates of sex even when sex entails direct fitness costs. Multilocus simulations show that the equilibrium rate of sex increases moderately as the degree of population structure increases. However, population structure may also prevent the irreversible spread of asexual mutants when the cost of sex is strong. ### Competing Interest Statement The authors have declared no competing interest.

Genetic drift is potentially an important component of selection for sex, as it is a source of statistical associations between alleles at selected loci. By increasing local drift, population structure may thus amplify the evolutionary advantage of sex. However, most previous models have focused either on haploid populations or on diploid populations without spatial structure. In this article, we use two- and three-locus analytical models and multilocus simulations to explore selection for sex in a diploid population structured according to the island model, in the presence of recurrent deleterious mutations. Our results show that selection generally favors an intermediate rate of sex that decreases as the direct cost of sex increases and increases moderately as the degree of population structure increases. Selection for sex is generated by multiple effects involving genetic associations within and between loci. When selection occurs at many loci, it is generally dominated by interference effects involving deleterious alleles at different loci, captured by our three-locus model. In our multilocus simulations, we observed an irreversible spread of asexual mutants under strong costs of sex, and when deleterious mutations are partially recessive. However, population structure may prevent this spread of asexual mutants when dispersal rates are sufficiently small.

Meiotic recombination is a central mechanism underlying sexual reproduction among eukaryotes. In many species, the recombination rate is strongly constrained by chromosome size, as the number of crossovers per chromosome generally ranges between one and no more than a few (around three to five). Yet, recombination rates are variable and can evolve between species, in particular when they differ in their reproductive system. According to theory, indirect selection towards higher recombination rates is expected to be stronger in inbred populations, such as selfing species compared with randomly mating species. To test for the impact of the mating system on the evolution of recombination rates, we leveraged a dataset with genetic maps, genome sizes, chromosome numbers, and life history traits in 200 seed plant species. After controlling for the chromosome size effect, the phylogeny, and map quality, we found a joint positive effect of the mating system and longevity on recombination rates, with higher recombination rates in mixed-mating and selfing species. We also found that mixed-mating and selfing species had a significantly higher number of crossovers in larger chromosomes than outcrossing species, suggesting selection for relaxed crossover interference in these former species. Our results point to the mating system as an important factor potentially shaping the evolution of recombination despite mechanical constraints acting on the number of crossovers per chromosome.

Sex chromosomes are involved in three major empirical patterns: (i) Y (or W) chromosomes are often nonrecombining and degenerate; (ii) heterogametic offspring (XY or ZW) from interspecific crosses are more often sterile or inviable compared with homogametic offspring (Haldane's rule); and (iii) the X (or Z) has a disproportionately large effect on reproductive isolation between species compared with autosomes (the large X effect). Each observation has received its own tailored explanation involving multiple genetic and evolutionary causes. In this work, we show that these empirical patterns all emerge from a single theory for sex chromosome evolution incorporating the coevolution of cis- and trans-acting regulators of gene expression and leading to systematic misexpression of dosage-compensated genes in heterogametic F1 hybrids, for both young and old sex chromosomes.

Modifiers of recombination rates have been described but the selective pressures acting on them and their effect on adaptation to novel environments remain unclear. We performed experimental evolution in the nematode Caenorhabditis elegans using alternative rec-1 alleles modifying the position of meiotic crossovers along chromosomes without detectable direct fitness effects. We show that adaptation to a novel environment is impaired by the allele that decreases recombination rates in the genomic regions containing fitness variation. However, the allele that impairs adaptation is indirectly favored by selection, because it increases recombination rates and reduces the associations among beneficial and deleterious variation located in its chromosomal vicinity. These results validate theoretical expectations about the evolution of recombination but suggest that genome-wide polygenic adaptation is of little consequence to indirect selection on recombination rate modifiers.

Whether partially recessive deleterious mutations should favor the spread of chromosomal inversions extending permanently heterozygous sex determining regions (SDR) has led to some debate. In this article, we use individual-based simulations to estimate fixation probabilities of inversions arising on autosomes and sex chromosomes under a wide range of parameter values. As shown previously, ‘lucky’ inversions carrying a lower-than-average mutation load are initially favored and tend to spread. Our results show that linkage to a permanently heterozygous SDR (on a Y or W chromosome) or to a mating-type locus hinders the spread of inversions when Ns is high (where N is population size and s the strength of selection against deleterious alleles), as the absence of recombination leads to mutation accumulation. However, it may help the spread of inversions when Ns is lower and/or when the dominance coefficient of deleterious alleles is low, by allowing the fixation of inversions that initially carry deleterious alleles, despite the fact that they eventually become deleterious (‘sheltering’ effect). Finally, we show that partial selfing may either help or hinder the spread of inversions capturing a mating-type locus, as they benefit from the masking of deleterious alleles, but also suffer from a higher equilibrium mutation load. ### Competing Interest Statement The authors have declared no competing interest.

Beneficial mutations drive the within-host adaptation of viral populations and can prolong the duration of host infection. Yet, most mutations are not adaptive and the increase of the mean fitness of viral populations is hampered by deleterious and lethal mutations. Because of this ambivalent role of mutations, it is unclear if a higher mutation rate boosts or slows down viral adaptation. Here, we study the interplay between selection, mutation, genetic drift and within-host dynamics of viral populations. We obtain good approximations for the transient evolutionary epidemiology of viral adaptation under the assumption that the mutation rate is high and the effects of nonlethal mutations remain small. We use measures of fitness effects of mutations for a range of viruses to predict the critical mutation rate required to drive viral extinction. This analysis questions the feasibility of lethal mutagenesis because the fold increase of viral mutation rates induced by available mutagenic drugs is not high enough to reach the critical mutation rate predicted by our model.

Meiotic crossover positions are uneven along eukaryotic chromosomes, giving rise to heterogeneous recombination rate landscapes. Genetic modifiers of local and genome-wide crossover positions have been described, but the selective pressures acting on them and their potential effect on adaptation in already-recombining populations remain unclear. We performed experimental evolution using a mutant that modifies the position of crossovers along chromosomes in the nematode Caenorhabditis elegans, without any detectable direct fitness effect. Our results show that when the recombination landscape is fixed, adaptation is facilitated by the modifier allele that, on average, increases recombination rates in genomic regions containing heritable fitness variation. However, in polymorphic populations containing both the wild-type and mutant modifier alleles, the allele that facilitates adaptation tends to decrease in frequency. This is likely because the allele that reduces recombination between selected loci at the genome-wide scale increases recombination in its chromosomal vicinity, and may thus benefit from local associations it establishes with beneficial genotype combinations. These results demonstrate that indirect selection acting on a recombination modifier mainly depends on its local effect, which may be decoupled from its consequences on genome-wide polygenic adaptation. ### Competing Interest Statement The authors have declared no competing interest.

Beneficial mutations drive the within-host adaptation of viral populations and can prolong the duration of host infection. Yet, most mutations are not adaptive and the increase of the mean fitness of viral populations is hampered by deleterious and lethal mutations. Because of this ambivalent role of mutations, it is unclear if a higher mutation rate boosts or slows down viral adaptation. Here we study the interplay between selection, mutation, genetic drift and within-host dynamics of viral populations. We obtain good approximations for the transient evolutionary epidemiology of viral adaptation under the assumption that the mutation rate is high and the effects of non-lethal mutations remains small. We use this theoretical framework to discuss the feasibility of lethal mutagenesis to treat viral infections.### Competing Interest StatementThe authors have declared no competing interest.

Y and W chromosomes often stop recombining and degenerate. Most work on recombination suppression has focused on the mechanisms favoring recombination arrest in the short term. Yet, the long-term maintenance of recombination suppression is critical to evolving degenerate sex chromosomes. This long-term maintenance has been little investigated. In the long term, recombination suppression may be maintained for selective reasons (e.g., involving the emergence of nascent dosage compensation), or due to mechanistic constraints preventing the reestablishment of recombination, for instance when complex chromosomal rearrangements evolve on the Y. In this paper, we investigate these 'constraint' theories. We show that they face a series of theoretical difficulties: they are not robust to extremely low rates of recombination restoration; they would rather cause population extinction than Y degeneration; they are less efficient at producing a non-recombining and degenerate Y than scenarios adding a selective pressure against recombination, whatever the rate of recombination restoration. Finally, whether such very high constraints exist is questionable. Very low rates of recombination reestablishment are sufficient to prevent Y degeneration, given the large fitness advantage to recover a non-degenerate Y or W for the heterogametic sex. The assumption of a lack of genetic variation to restore recombination seems also implausible given known mechanisms to restore a recombining pair of sex chromosomes.

Sex and recombination can affect the dynamics of transposable elements (TEs) in various ways: while sex is expected to help TEs to spread within populations, the deleterious effect of ectopic recombination among transposons represents a possible source of purifying selection limiting their number. Furthermore, recombination may also increase the efficiency of selection against TEs by reducing selective interference among loci. In order to better understand the effects of recombination and reproductive systems on TE dynamics, this article provides analytical expressions for the linkage disequilibrium among TEs in a classical model in which TE number is stabilized by synergistic purifying selection. The results show that positive linkage disequilibrium is predicted in infinite populations despite negative epistasis, due to the effect of the transposition process. Positive linkage disequilibrium may substantially inflate the variance in the number of elements per genome in the case of partially selfing or partially clonal populations. Finite population size tends to generate negative linkage disequilibrium (Hill-Robertson effect), the relative importance of this effect increasing with the degree of linkage among loci. The model is then extended in order to explore how TEs may affect selection for recombination. While positive linkage disequilibrium generated by transposition generally disfavors recombination, the Hill-Robertson effect may represent a non-negligible source of indirect selection for recombination when TEs are abundant. However, the direct fitness cost imposed by ectopic recombination among elements generally drives the population towards low-recombination regimes, at which TEs cannot be maintained at a stable equilibrium.

Species diversity can vary dramatically across lineages due to differences in speciation and extinction rates. Here, we explore the effects of several plant traits on diversification, finding that most traits have opposing effects on diversification. For example, outcrossing may increase the efficacy of selection and adaptation but also decrease mate availability, two processes with contrasting effects on lineage persistence. Such opposing trait effects can manifest as differences in diversification rates that depend on ecological context, spatiotemporal scale, and associations with other traits. The complexity of pathways linking traits to diversification suggests that the mechanistic underpinnings behind their correlations may be difficult to interpret with any certainty, and context dependence means that the effects of specific traits on diversification are likely to differ across multiple lineages and timescales. This calls for taxonomically and context-controlled approaches to studies that correlate traits and diversification.

Cytological data from flowering plants suggest that the evolution of recombination rates is affected by the mating system of organisms, as higher chiasma frequencies are often observed in self-fertilizing species compared with their outcrossing relatives. Understanding the evolutionary cause of this effect is of particular interest, as it may shed light on the selective forces favoring recombination in natural populations. While previous models showed that inbreeding may have important effects on selection for recombination, existing analytical treatments are restricted to the case of loosely linked loci and weak selfing rates, and ignore the stochastic effect of genetic interference (Hill-Robertson effect), known to be an important component of selection for recombination in randomly mating populations. In this article, we derive general expressions quantifying the stochastic and deterministic components of selection acting on a mutation affecting the genetic map length of a whole chromosome along which deleterious mutations occur, valid for arbitrary selfing rates. The results show that selfing generally increases selection for recombination caused by interference among mutations as long as selection against deleterious alleles is sufficiently weak. While interference is often the main driver of selection for recombination under tight linkage or high selfing rates, deterministic effects can play a stronger role under intermediate selfing rates and high recombination, selecting against recombination in the absence of epistasis, but favoring recombination when epistasis is negative. Individual-based simulation results indicate that our analytical model often provides accurate predictions for the strength of selection on recombination under partial selfing.

Current theory proposes that degenerated sex chromosomes—such as the mammalian Y—evolve through three steps: (i) recombination arrest, linking male-beneficial alleles to the Y chromosome; (ii) Y degeneration, resulting from the inefficacy of selection in the absence of recombination; and (iii) dosage compensation, correcting the resulting low expression of X-linked genes in males. We investigate a model of sex chromosome evolution that incorporates the coevolution of cis and trans regulators of gene expression. We show that the early emergence of dosage compensation favors the maintenance of Y-linked inversions by creating sex-antagonistic regulatory effects. This is followed by degeneration of these nonrecombining inversions caused by regulatory divergence between the X and Y chromosomes. In contrast to current theory, the whole process occurs without any selective pressure related to sexual dimorphism.