Sex: differences in mutation, recombination, selection, gene flow, and genetic drift

In many instances, there are large sex differences in mutation rates, recombination rates, selection, rates of gene flow, and genetic drift. Mutation rates are often higher in males, a difference that has been estimated both directly and indirectly. The higher male mutation rate appears related to the larger number of cell divisions in male lineages but mutation rates also appear gene- and organism-specific. When there is recombination in only one sex, it is always the homogametic sex. When there is recombination in both sexes, females often have higher recombination but there are many exceptions. There are a number of hypotheses to explain the sex differences in recombination. Sex-specific differences in selection may result in stable polymorphisms or for sex chromosomes, faster evolutionary change. In addition, sex-dependent selection may result in antagonistic pleiotropy or sexually antagonistic genes. There are many examples of sex-specific differences in gene flow (dispersal) and a number of adaptive explanations for these differences. The overall effective population size (genetic drift) is dominated by the lower sex-specific effective population size. The mean of the mutation, recombination, and gene flow rates over the two sexes can be used in a population genetics context unless there are sex-specific differences in selection or genetic drift. Sex-specific differences in these evolutionary factors appear to be unrelated to each other. The evolutionary explanations for sex-specific differences for each factor are multifaceted and, in addition, explanations may include chance, nonadaptive differences, or mechanistic, nonevolutionary factors.     

Cumulant dynamics of a population under multiplicative selection, mutation, and drift

We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation, and drift. The number of beneficial alleles in a multilocus system can be considered a trait under exponential selection. Equations of motion are derived for the cumulants of the trait distribution in the diffusion limit and under the assumption of linkage equilibrium. Because of the additive nature of cumulants, this reduces to the problem of determining equations of motion for the expected allele distribution cumulants at each locus. The cumulant equations form an infinite dimensional linear system and in an authored appendix Adam Prügel-Bennett provides a closed form expression for these equations. We derive approximate solutions which are shown to describe the dynamics well for a broad range of parameters. In particular, we introduce two approximate analytical solutions: (1) Perturbation theory is used to solve the dynamics for weak selection and arbitrary mutation rate. The resulting expansion for the system's eigenvalues reduces to the known diffusion theory results for the limiting cases with either mutation or selection absent. (2) For low mutation rates we observe a separation of time-scales between the slowest mode and the rest which allows us to develop an approximate analytical solution for the dominant slow mode. The solution is consistent with the perturbation theory result and provides a good approximation for much stronger selection intensities.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Species selection and random drift in macroevolution

Species selection resulting from trait‐dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth‐death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype‐dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species‐level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny.     

The mitochondrial genome: mutation, selection and recombination

Within an individual, mitochondria must function in a range of tissue specific environments that are largely governed by expression of a particular suite of nuclear genes. Furthermore, mitochondrial proteins form large complexes with nuclear-encoded proteins to form the electron-transport system. These dynamics between mitochondrial and nuclear genomes have important implications in studies of within and among species genetic variation, and interpretation of disease phenotypes. Experimentally disrupting naturally occurring combinations of nuclear and mitochondrial genomes should provide insights into the coevolutionary dynamics among genomes.     

Sexual selection,germline mutation rate and sperm competition

Background  

An important component of sexual selection arises because females obtain viability benefits for their offspring from their mate choice. Females choosing extra-pair fertilization generally favor males with exaggerated secondary sexual characters, and extra-pair paternity increases the variance in male reproductive success. Furthermore, females are assumed to benefit from 'good genes' from extra-pair sires. How additive genetic variance in such viability genes is maintained despite strong directional selection remains an evolutionary enigma. We propose that sexual selection is associated with elevated mutation rates, changing the balance between mutation and selection, thereby increasing variance in fitness and hence the benefits to be obtained from good genes sexual selection. Two hypotheses may account for such elevated mutation: (1) Increased sperm production associated with sperm competition may increase mutation rate. (2) Mutator alleles increase mutation rates that are revealed by the expression of condition-dependent secondary sexual characters used by choosy females during their mate choice. M Petrie has independently developed the idea that mutator alleles may account for the maintenance of genetic variation in viability despite strong directional selection.     

The distribution of allelic effects under mutation and selection

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.     

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

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

The effects of recombination,mutation and selection on the evolution of the Rp1 resistance genes in grasses

Plant immune genes, or resistance genes, are involved in a co‐evolutionary arms race with a diverse range of pathogens. In agronomically important grasses, such R genes have been extensively studied because of their role in pathogen resistance and in the breeding of resistant cultivars. In this study, we evaluate the importance of recombination, mutation and selection on the evolution of the R gene complex Rp1 of Sorghum, Triticum, Brachypodium, Oryza and Zea. Analyses show that recombination is widespread, and we detected 73 independent instances of sequence exchange, involving on average 1567 of 4692 nucleotides analysed (33.4%). We were able to date 24 interspecific recombination events and found that four occurred postspeciation, which suggests that genetic introgression took place between different grass species. Other interspecific events seemed to have been maintained over long evolutionary time, suggesting the presence of balancing selection. Significant positive selection (i.e. a relative excess of nonsynonymous substitutions (d_N/d_S>1)) was detected in 17–95 codons (0.42–2.02%). Recombination was significantly associated with areas with high levels of polymorphism but not with an elevated d_N/d_S ratio. Finally, phylogenetic analyses show that recombination results in a general overestimation of the divergence time (mean = 14.3%) and an alteration of the gene tree topology if the tree is not calibrated. Given that the statistical power to detect recombination is determined by the level of polymorphism of the amplicon as well as the number of sequences analysed, it is likely that many studies have underestimated the importance of recombination relative to the mutation rate.     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

Ribozyme motif structure mapped using random recombination and selection

Isolating the core functional elements of an RNA is normally performed during the characterization of a new RNA in order to simplify further biochemical analysis. The removal of extraneous sequence is challenging and can lead to biases that result from the incomplete sampling of deletion variants. An impartial solution to this problem is to construct a library containing a large number of deletion constructs and to select functional RNA isolates that are at least as efficient as their full-length progenitors. Here, we use nonhomologous recombination and selection to isolate the catalytic core of a pyrimidine nucleotide synthase ribozyme. A variable-length pool of approximately 10(8) recombinant molecules that included deletions, inversions, and translocations of a 271-nucleotide-long ribozyme isolate was constructed by digesting and randomly religating its DNA genome. In vitro selection for functional ribozymes was then performed in a size-dependent and a size-independent manner. The final pools had nearly equivalent catalytic rates even though their length distributions were completely different, indicating that a diverse range of deletion constructs were functionally active. Four short sequence islands, requiring as little as 81 nt of sequence, were found within all of the truncated ribozymes and could be folded into a secondary structure consisting of three helix-loops. Our findings suggest that nonhomologous recombination is a highly efficient way to isolate a ribozyme's core motif and could prove to be a useful method for evolving new ribozyme functions from pre-existing sequences in a manner that may have played an important role early in evolution.     

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

Establishment and maintenance of adaptive genetic divergence under migration, selection, and drift

There is a long tradition in population genetics of exploring the maintenance of variation under migration-selection balance using deterministic models that assume infinite population size. With finite population size, stochastic dynamics can greatly reduce the potential for the maintenance of polymorphism, but this has yet to be explored in detail. Here, classical two-patch models are extended to predict: (1) the probability of a locally beneficial mutation rising in frequency in the patch where it is favored and (2) the critical threshold migration rate above which the maintenance of polymorphism is much less likely. Individual-based simulations show that these approximations provide accurate predictions across a wide range of parameter space.     

The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates

We analyze a decoupled Moran model with haploid population size N, a biallelic locus under mutation and drift with scaled forward and backward mutation rates θ₁=μ₁N and θ₀=μ₀N, and directional selection with scaled strength γ=sN. With small scaled mutation rates θ₀ and θ₁, which is appropriate for single nucleotide polymorphism data in highly recombining regions, we derive a simple approximate equilibrium distribution for polymorphic alleles with a constant of proportionality. We also put forth an even simpler model, where all mutations originate from monomorphic states. Using this model we derive the sojourn times, conditional on the ancestral and fixed allele, and under equilibrium the distributions of fixed and polymorphic alleles and fixation rates. Furthermore, we also derive the distribution of small samples in the diffusion limit and provide convenient recurrence relations for calculating this distribution. This enables us to give formulas analogous to the Ewens-Watterson estimator of θ for biased mutation rates and selection. We apply this theory to a polymorphism dataset of fourfold degenerate sites in Drosophila melanogaster.     

Sexual selection effects on the evolution of senescence

Although the basic theories concerning evolution of senescence have been generally accepted for a half-century, interpretation of this paradigm has been constrained by an over-reliance on mortality as both the cause and the measure of senescence. Consideration of both survival and fecundity as components of reproductive value, and integration of sexual selection theory with senescence theory allows reconciliation of long-standing, as well as recent, discrepancies between data and theory. This approach demonstrates that sexual selection on males in polygynous mating systems can have significant effects on the evolution of senescence that could overshadow the selection effects of mortality rates among such animals.     

Group selection, individual selection, and the evolution of genetic drift.

In a subdivided population, genetic drift affects variation between groups, and thus it can have an important effect on the outcome of evolution (Wright, 1978). The rate of genetic drift is determined, in part, by the behaviour of population members. This paper presents three mathematical models in which behavioural traits that affect the rate of genetic drift are allowed to coevolve with traits that are under selection at the group and individual levels. The results show that if group selection is strong relative to individual selection, then behavioural traits that enhance the rate of genetic drift will tend to increase in frequency. The strength of this effect depends, in part, on the way in which vacant sites are colonized.