The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher-Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative fitness effects. We solve the infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number $L$ of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to $L$ in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with $L$ genomic segments.
Many species reproduce both sexually and asexually producing genetically unique and clonal recruits. The relative contribution of sexual and asexual reproduction is mostly considered a consequence of natural selection, for example, disfavouring sexual propagules during invasions. Here, we present a novel model for the invasion of species into a new habitat. The model is fully neutral with respect to the dispersal and the survival of sexual and asexual recruits. In addition to local dispersal through sexual and asexual reproduction, long-distance dispersal is implemented through a non-zero prob…
A comparison of three replication strategies in complex multicellular organisms: Asexual replication, sexual replication with identical gametes, and sexual replication with distinct sperm and egg gametes
In species reproducing both sexually and asexually clones are often more common in recently established populations. Earlier studies have suggested that this pattern arises from natural selection favouring asexual recruitment in young populations. Alternatively, as we show here, this pattern may result from stochastic processes during species-range expansions. We model a dioecious species expanding into a new area in which all individuals are capable of both sexual and asexual reproduction, and all individuals have equal survival rates and dispersal distances. Even under conditions that eventu…
We study the evolution of sexual and asexual populations in general fitness landscapes. We find deep relations between the mathematics of biological evolution and the formalism of quantum mechanics. We give the general structure of the evolution of populations which is in general an off-equilibrium process that can be expressed by path integrals over phylogenies. These phylogenies are sums of linear lineages for asexual populations. For sexual populations instead, each lineage is a tree of branching ratio two and the path integral describing the evolving population is given by a sum over these…
The prevalence of sexual reproduction ("sex") in eukaryotes is an enigma of evolutionary biology. Sex increases genetic variation only tells its long-term superiority in essence. The accumulation of harmful mutations causes an immediate and ubiquitous pressure for organisms. Contrary to the common sense, our theoretical model suggests that reproductive rate can influence initiatively the accumulation of harmful mutations. The interaction of reproductive rate and the integrated harm of mutations causes a critical reproductive rate R*. A population will become irreversibly extinct once the repro…
How self-incompatibility systems are maintained in plant populations is still a debated issue. Theoretical models predict that self-incompatibility systems break down according to the intensity of inbreeding depression and number of S-alleles. Other studies have explored the function of asexual reproduction in the maintenance of self-incompatibility. However, the population genetics of partially asexual, self-incompatible populations are poorly understood and previous studies have failed to consider all possible effects of asexual reproduction or could only speculate on those effects. In this …
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can bring together beneficial alleles from different backgrounds, but tightly linked alleles may still greatly interfere with each other. We show for well-mixed populations that when this interference is strong, the genome can be seen as consisting of many effectively asexual stretches linked together. The rate at which beneficial alleles fix is thus roughly propo…
Muller's ratchet describes the irreversible accumulation of deleterious mutations in asexual populations. In well-mixed populations the speed of fitness decline is exponentially small in the population size, and any positive rate of beneficial mutations is sufficient to reverse the ratchet in large populations. The behavior is fundamentally different in populations with spatial structure, because the speed of the ratchet remains nonzero in the infinite size limit when the deleterious mutation rate exceeds a critical value. Based on the relation between the spatial ratchet and directed percolat…
We show that the Eigen model and the asexual Wright-Fisher model can be obtained as different limit cases of a unique stochastic model. This derivation makes clear which are the exact differences between these two models. The two key concepts introduced with the Eigen model, the error threshold and the quasispecies, are not affected by these differences, so that they are naturally present also in population genetics models. According to this fact, in the last part of the paper, we use the classical diploid mutation-selection equation and the single peak fitness approximation to obtain the erro…
The vast majority of mutations are deleterious, and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet turns into a mutational "meltdown" leading to a rapid degradation of population fitness. Evidently, the long term stability of an asexual population requires an influx of beneficial mutations that continuously compensa…
Analytical results on the Muller's ratchet effect in growing populations
Fontanari等人介绍了[Phys. Rev. Lett. 91，218101（2003）]的一个模型，用于研究穆勒的棘轮现象在不断增长的无性种群。他们研究了两种情况，包括或不包括每个新生儿的死亡概率，但只能在无衰变的情况下找到解析（递归）表达式。在本文中，一个分支过程的形式主义是用来找到recorrence方程，除了确认有趣的效果，他们的模拟显示，推广的分析结果的原始文件。
The rate of recombination affects the mode of molecular evolution. In high-recombining sequence, the targets of selection are individual genetic loci; under low recombination, selection collectively acts on large, genetically linked genomic segments. Selection under linkage can induce clonal interference, a specific mode of evolution by competition of genetic clades within a population. This mode is well known in asexually evolving microbes, but has not been traced systematically in an obligate sexual organism. Here we show that the Drosophila genome is partitioned into two modes of evolution:…
Failure of the fittest: limits on asexual adaptation to changing environments
Univ. Brest, CNRS UMR 6205, Laboratoire de Mathematiques de Bretagne Atlantique（布雷斯特大学）；BioSP, INRAE（法国国家农业食品与环境研究院）；Department of Ecology & Evolutionary Biology, University of Toronto（多伦多大学）
Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptati…
The evolution of microbial and viral organisms often generates clonal interference, a mode of competition between genetic clades within a population. In this paper, we show that interference strongly constrains the genetic and phenotypic complexity of evolving systems. Our analysis uses biophysically grounded evolutionary models for an organism's quantitative molecular phenotypes, such as fold stability and enzymatic activity of genes. We find a generic mode of asexual evolution called phenotypic interference with strong implications for systems biology: it couples the stability and function o…
In sexual populations, selection operates neither on the whole genome, which is repeatedly taken apart and reassembled by recombination, nor on individual alleles that are tightly linked to the chromosomal neighborhood. The resulting interference between linked alleles reduces the efficiency of selection and distorts patterns of genetic diversity. Inference of evolutionary history from diversity shaped by linked selection requires an understanding of these patterns. Here, we present a simple but powerful scaling analysis identifying the unit of selection as the genomic "linkage block" with a c…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimum phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or …
Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population dynamics, and the genetic elements determining survival and reproduction are under different selective forces throughout an organism lifespan. Here we develop a highly versatile numerical model of genome evolution --- both asexual and sexual --- for a population of virtual individuals with overlapping generations, where the genetic elements affecting survival and …
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the context of invasions, when considering the evolution of a heritable trait that encodes the dispersive ability of individuals, the trait distribution develops a particular spatial structure that leads to the acceleration of the front propagation. That phenomenon is known as spatial sorting. Many biological examples can be cited like the bush cricket in Britain…
We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. In [Neukirch, Bovier, 2016] it is proved that sexual reproduction allows unfit alleles to survive in individuals with mixed genotype much longer than they would in populations reproducing asexually. In the present paper we prove that this indeed opens the possibility that individuals with a pure genotype can reinvade in the population after the appearance of further mutations. We thus expose a formal descr…
我们发现Jan，Stauffer和Moseley [Theory in Biosc.，119，166（2000）]对于性的进化，即设计出逃避由于太多有害突变而导致的灭绝的策略，对于在有限种群内成功进化有性个体的稳态种群是足够的，但不是必需的。只要允许每一代中有一个有限的转化为有性生殖的概率，就可以产生一个稳定的有性生殖群体，因为每个个体的有害突变数量有一个上限。对于这个概率的大值，我们发现一个相变到一个间歇性的，多稳定的制度。另一方面，在极慢驱动的限制下，另一个过渡发生到不同的稳态分布，在无性群体中具有较少的有害突变。
It has been a puzzling question why some organisms reproduce sexually. Fisher and Muller hypothesized that reproducing by sex can speed up the evolution. They explained that in the sexual reproduction, recombination can combine beneficial alleles that lie on different chromosomes, which speeds up the time that those beneficial alleles spread to the entire population. We consider a population model of fixed size $N$, in which we will focus on two loci on a chromosome. Each allele at each locus can mutate into a beneficial allele at rate $μ_N$. The individuals with 0, 1, and 2 beneficial alleles…
Natural Averaging May Complement Known Biological Constraints in Bi-parental Reproduction's Advantages Over Mono-parental in Conserving Species Quantitative Traits
Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans, and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or…
