Brian Charlesworth’s research while affiliated with University of Edinburgh and other places

A new approach to modeling the effects of Hill-Robertson interference on levels of adaptation and patterns of variability in a non-recombining genome or genomic region is described. The model assumes a set of L diallelic sites subject to reversible mutations between beneficial and deleterious alleles, with the same selection coefficient at each site. The assumption of reversibility allows the system to reach a stable statistical equilibrium with respect to the frequencies of deleterious mutations, in contrast to many previous models that assume irreversible mutations to deleterious alleles. The model is therefore appropriate for understanding the long-term properties of non-recombining genomes such as Y chromosomes, and is applicable to haploid genomes or to diploid genomes when there is intermediate dominance with respect to the effects of mutations on fitness. Approximations are derived for the equilibrium frequencies of deleterious mutations, the effective population size that controls the fixation probabilities of mutations at sites under selection, the nucleotide site diversity at neutral sites located within the non-recombining region, and the site frequency spectrum for segregating neutral variants. The approximations take into account the effects of linkage disequilibrium on the genetic variance at sites under selection. Comparisons with published and new computer simulation results show that the approximations are sufficiently accurate to be useful, and can thus provide insights into a wider range of parameter sets than is accessible by simulation. The relevance of the findings to data on non-recombining genome regions is discussed. Summary We describe a new model to study how Hill-Robertson interference affects adaptation and genetic variation in non-recombining genome regions, such as Y chromosomes. Unlike many previous models that assumed mutations to deleterious alleles were irreversible, this model allows for reversible mutations, enabling the system to stabilize statistically. It provides calculations for several genetic dynamics, including the equilibrium frequencies of detrimental mutations and the effects of genetic linkage on diversity. This model, validated against simulations, offers a practical tool to examine genetic patterns in non-recombining genomic areas, offering insights that extend beyond what can be achieved through simulation alone.

In their most extreme form, sex chromosomes exhibit a complete lack of genetic recombination along much of their length in the heterogametic sex. Some recent models explain the evolution of such suppressed recombination by the “sheltering” of deleterious mutations by chromosomal inversions that prevent recombination around a polymorphic locus controlling sex. This sheltering hypothesis is based on the following reasoning. An inversion that is associated with the male-determining allele (with male heterogamety) is present only in the heterozygous state. If such an inversion carries a lower-than-average number of deleterious mutations, it will accrue a selective advantage, and will be sheltered from homozygosity for any mutations that it carries due to the enforced heterozygosity for the inversion itself. It can therefore become fixed among all carriers of the male-determining allele. Recent population genetics models of this process are discussed. It is shown that, except under the unlikely scenario of a high degree of recessivity of most deleterious mutations, inversions of this type that lack any other fitness effects will have at best a modest selective advantage; they will usually accumulate on proto-Y chromosomes at a rate close to, or less than, the neutral expectation. While the existence of deleterious mutations does not necessarily prevent the spread of Y-linked inversions, it is unlikely to provide a significant selective advantage to them.

Inversions restrict recombination when heterozygous with standard arrangements, but often have few noticeable phenotypic effects. Nevertheless, there are several examples of inversions that can be maintained polymorphic by strong selection under laboratory conditions. A long-standing model for the source of such selection is divergence between arrangements with respect to recessive or partially recessive deleterious mutations, resulting in a selective advantage to heterokaryotypic individuals over homokaryotypes. This paper uses a combination of analytical and numerical methods to investigate this model, for the simple case of an autosomal inversion with multiple independent nucleotide sites subject to mildly deleterious mutations. A complete lack of recombination in heterokaryotypes is assumed, as well as constancy of the frequency of the inversion over space and time. It is shown that a significantly higher mutational load will develop for the less frequent arrangement. A selective advantage to heterokaryotypes is only expected when the two alternative arrangements are nearly equal in frequency, so that their mutational loads are very similar in size. The effects of some Drosophila pseudoobscura polymorphic inversions on fitness traits seem to be too large to be explained by this process, although it may contribute to some of the observed effects. Several population genomic statistics can provide evidence for signatures of a reduced efficacy of selection associated with the rarer of two arrangements, but there is currently little published data that are relevant to the theoretical predictions.

An interesting new model has recently been proposed for the evolution of suppressed recombination between newly evolving X and Y chromosomes, where males are heterozygous for a locus determining sex and females are homozygous (the same principles apply to systems with female heterogamety, with the role of the two sexes reversed). The model appeals to the selective advantage that accrues to a recombination suppressor (e.g., an inversion), which arises on a male-determining haplotype that carries a smaller number of deleterious mutations than average and remains completely associated with the sex determining locus. The underlying logic of the model rests on the idea that, because such an inversion cannot become homozygous, it is "sheltered" from selection against any deleterious recessive mutations it may carry, in contrast to an autosomal inversion. It has been claimed that computer simulations of this process show that the probability that a new inversion becomes fixed within the population of Y chromosomes is substantially higher than expected under selective neutrality, and higher than that for a comparable autosomal inversion. However, analytical population genetic models of some special cases cast doubt on the magnitude of the selective advantage claimed for Y-linked inversions under this process, demanding re-evaluation of the simulation results. The published estimates of fixation probabilities of Y-linked inversions were in fact calculated after excluding inversions that were lost in the first 20 generations. This generates a substantial bias towards high fixation probabilities and obscures comparisons with neutrality. If all simulation runs are included, most parameter sets yield estimates of fixation probabilities that are close to neutral expectation, unless deleterious mutations are close to being completely recessive. The proposed sheltering mechanism is unlikely to provide a robust selective advantage to inversions suppressing recombination between evolving X and Y (or Z and W) chromosomes.

Inversions are structural mutations that reverse the sequence of a chromosome segment and reduce the effective rate of recombination in the heterozygous state. They play a major role in adaptation, as well as in other evolutionary processes such as speciation. Although inversions have been studied since the 1920s, they remain difficult to investigate because the reduced recombination conferred by them strengthens the effects of drift and hitchhiking, which in turn can obscure signatures of selection. Nonetheless, numerous inversions have been found to be under selection. Given recent advances in population genetic theory and empirical study, here we review how different mechanisms of selection affect the evolution of inversions. A key difference between inversions and other mutations, such as single nucleotide variants, is that the fitness of an inversion may be affected by a larger number of frequently interacting processes. This considerably complicates the analysis of the causes underlying the evolution of inversions. We discuss the extent to which these mechanisms can be disentangled, and by which approach. Abstract Inversions often play key roles in adaptation and speciation, but the processes that direct their evolution are obscured by the characteristic that makes them so unique (reduced recombination between arrangements). In this review, we examine how different mechanisms can impact inversion evolution, weaving together both theoretical and empirical studies. We emphasize that most patterns are overdetermined (i.e. can be caused by multiple processes), but we highlight new technologies that provide a path forward towards disentangling these mechanisms.

Inversions restrict recombination when heterozygous with standard arrangements, but often have few noticeable phenotypic effects. Nevertheless, there are several examples of inversions that can be maintained polymorphic by strong selection under laboratory conditions. A long-standing model for the source of such selection is divergence between arrangements with respect to recessive or partially recessive deleterious mutations, resulting in a selective advantage to heterokaryotypic individuals over homokaryotypes. This paper uses a combination of analytical and numerical methods to investigate this model, for the simple case of an autosomal inversion with multiple independent nucleotide sites subject to deleterious mutations. A complete lack of recombination in heterokaryotypes is assumed, as well as constancy of the frequency of the inversion over space and time. It is shown that a significantly higher mutational load will develop for the less frequent arrangement. A selective advantage to heterokaryotypes is only expected when the two alternative arrangements are nearly equal in frequency, so that their mutational loads are very similar in size. The effects of some Drosophila pseudoobscura polymorphic inversions on fitness traits seem to be too large to be explained by this process, although it may contribute to some of the observed effects. Several population genomic statistics can provide evidence for signatures of a reduced efficacy of selection associated with the rarer of two arrangements, but there is currently little published data that are relevant to the theoretical predictions.

The strong reduction in the frequency of recombination in heterozygotes for an inversion and a standard gene arrangement causes the arrangements to become partially isolated genetically, resulting in sequence divergence between them and changes in the levels of neutral variability at nucleotide sites within each arrangement class. Previous theoretical studies on the effects of inversions on neutral variability have either assumed that the population is panmictic or that it is divided into two populations subject to divergent selection. Here, the theory is extended to a model of an arbitrary number of demes connected by migration, using a finite island model with the inversion present at the same frequency in all demes. Recursion relations for mean pairwise coalescent times are used to obtain simple approximate expressions for diversity and divergence statistics for an inversion polymorphism at equilibrium under recombination and drift, and for the approach to equilibrium following the sweep of an inversion to a stable intermediate frequency. The effects of an inversion polymorphism on patterns of linkage disequilibrium are also examined. The reduction in effective recombination rate caused by population subdivision can have significant effects on these statistics. The theoretical results are discussed in relation to population genomic data on inversion polymorphisms, with an emphasis on Drosophila melanogaster. Methods are proposed for testing whether or not inversions are close to recombination-drift equilibrium, and for estimating the rate of recombinational exchange in heterozygotes for inversions; difficulties involved in estimating the ages of inversions are also discussed.

The strong reduction in the frequency of recombination in heterozygotes for an inversion and a standard gene arrangement causes inversion and standard haplotypes to become partially isolated, resulting in sequence divergence between them and to changes in the levels of neutral variability at nucleotide sites within each arrangement class, as is also the case for other types of balanced polymorphisms. Previous theoretical studies have either assumed that the population is panmictic or that it is divided into two populations subject to divergent selection. Here, the theory is extended to a model of an arbitrary number of demes connected by migration, using a finite island. Recursion relations for mean pairwise coalescent times are used to obtain simple approximate expressions for diversity and divergence statistics relevant to an inversion polymorphism at equilibrium under recombination and drift, and for the approach to equilibrium following the sweep of an inversion to a stable intermediate frequency. The effects of an inversion polymorphism on patterns of linkage disequilibrium are also examined. The reduction in effective recombination rate caused by population subdivision can have significant effects on these statistics, and hence on estimates of the ages of inversions. The theoretical results are discussed in relation to population genomic data on inversion polymorphisms, with an emphasis on Drosophila melanogaster . Methods are proposed for testing whether or not inversions are close to recombination-drift equilibrium, and for estimating the rate of recombinational exchange in heterozygotes for inversions; difficulties involved in estimating the ages of inversions are also discussed.

It has recently been proposed that lower mutation rates in gene bodies compared with upstream and downstream sequences in Arabidopsis thaliana are the result of an "adaptive" modification of the rate of beneficial and deleterious mutations in these functional regions. This claim was based both on analyses of mutation accumulation lines and on population genomics data. Here we show that several questionable assumptions were used in the population genomics analyses. In particular, we demonstrate that the difference between gene bodies and less selectively constrained sequences in the magnitude of Tajima's D can in principle be explained by the presence of sites subject to purifying selection, and does not require lower mutation rates in regions experiencing selective constraints.