Quasispecies Theory for Horizontal Gene Transfer and Recombination

We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic recombination on the steady-state mean fitness and distribution of individuals in the population, through an analytic field theoretic mapping. We investigate both horizontal gene transfer from a population and recombination between pairs of individuals. Somewhat surprisingly, these nonlinear generalizations of quasi-species theory to modern biology are analytically solvable. For two-parent recombination, we find two selected phases, one of which is spectrally rigid. We present exact analytical formulas for the equilibrium mean fitness of the population, in terms of a maximum principle, which are generally applicable to any permutation invariant replication rate function. For smooth fitness landscapes, we show that when positive epistatic interactions are present, recombination or horizontal gene transfer introduces a mild load against selection. Conversely, if the fitness landscape exhibits negative epistasis, horizontal gene transfer or recombination introduce an advantage by enhancing selection towards the fittest genotypes. These results prove that the mutational deterministic hypothesis holds for quasi-species models. For the discontinuous single sharp peak fitness landscape, we show that horizontal gene transfer has no effect on the fitness, while recombination decreases the fitness, for both the parallel and the Eigen models. We present numerical and analytical results as well as phase diagrams for the different cases.Comment: 54 pages; 8 figures; 12 tables; some typos corrected; to appear in Phys. Rev.

The statistical mechanics of a polygenic characterunder stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as 5 loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.Comment: 35 pages, 8 figure

Analytical study of the effect of recombination on evolution via DNA shuffling

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the model allows us to obtain a full analytical treatment of both its dynamical and equilibrium properties, for the case of an infinite population. We also briefly discuss finite population size corrections

Duplication and Gene Conversion in the Drosophila melanogaster Genome

Using the genomic sequences of Drosophila melanogaster subgroup, the pattern of gene duplications was investigated with special attention to interlocus gene conversion. Our fine-scale analysis with careful visual inspections enabled accurate identification of a number of duplicated blocks (genomic regions). The orthologous parts of those duplicated blocks were also identified in the D. simulans and D. sechellia genomes, by which we were able to clearly classify the duplicated blocks into post- and pre-speciation blocks. We found 31 post-speciation duplicated genes, from which the rate of gene duplication (from one copy to two copies) is estimated to be 1.0×10−9 per single-copy gene per year. The role of interlocus gene conversion was observed in several respects in our data: (1) synonymous divergence between a duplicated pair is overall very low. Consequently, the gene duplication rate would be seriously overestimated by counting duplicated genes with low divergence; (2) the sizes of young duplicated blocks are generally large. We postulate that the degeneration of gene conversion around the edges could explain the shrinkage of “identifiable” duplicated regions; and (3) elevated paralogous divergence is observed around the edges in many duplicated blocks, supporting our gene conversion–degeneration model. Our analysis demonstrated that gene conversion between duplicated regions is a common and genome-wide phenomenon in the Drosophila genomes, and that its role should be especially significant in the early stages of duplicated genes. Based on a population genetic prediction, we applied a new genome-scan method to test for signatures of selection for neofunctionalization and found a strong signature in a pair of transporter genes

Cryptic Variation between Species and the Basis of Hybrid Performance

Studies on natural variation in gene expression and its phenotypic effects provide fresh insights into the origins of vigour and sterility in species hybrids

Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans

Background: The accumulation of deleterious mutations can drastically reduce population mean fitness. Self-fertilization is thought to be an effective means of purging deleterious mutations. However, widespread linkage disequilibrium generated and maintained by self-fertilization is predicted to reduce the efficacy of purging when mutations are present at multiple loci. Methodology/Principal Findings: We tested the ability of self-fertilizing populations to purge deleterious mutations at multiple loci by exposing obligately self-fertilizing populations of Caenorhabditis elegans to a range of elevated mutation rates and found that mutations accumulated, as evidenced by a reduction in mean fitness, in each population. Therefore, purging in obligate selfing populations is overwhelmed by an increase in mutation rate. Surprisingly, we also found that obligate and predominantly self-fertilizing populations exposed to very high mutation rates exhibited consistently greater fitness than those subject to lesser increases in mutation rate, which contradicts the assumption that increases in mutation rate are negatively correlated with fitness. The high levels of genetic linkage inherent in self-fertilization could drive this fitness increase. Conclusions: Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. Th

Mutation Accumulation in a Selfing Population: Consequences of Different Mutation Rates between Selfers and Outcrossers

Currently existing theories predict that because deleterious mutations accumulate at a higher rate, selfing populations suffer from more intense genetic degradation relative to outcrossing populations. This prediction may not always be true when we consider a potential difference in deleterious mutation rate between selfers and outcrossers. By analyzing the evolutionary stability of selfing and outcrossing in an infinite population, we found that the genome-wide deleterious mutation rate would be lower in selfing than in outcrossing organisms. When this difference in mutation rate was included in simulations, we found that in a small population, mutations accumulated more slowly under selfing rather than outcrossing. This result suggests that under frequent and intense bottlenecks, a selfing population may have a lower risk of genetic extinction than an outcrossing population

Fitness Consequences of Advanced Ancestral Age over Three Generations in Humans

A rapid rise in age at parenthood in contemporary societies has increased interest in reports of higher prevalence of de novo mutations and health problems in individuals with older fathers, but the fitness consequences of such age effects over several generations remain untested. Here, we use extensive pedigree data on seven pre-industrial Finnish populations to show how the ages of ancestors for up to three generations are associated with fitness traits. Individuals whose fathers, grandfathers and great-grandfathers fathered their lineage on average under age 30 were ~13% more likely to survive to adulthood than those whose ancestors fathered their lineage at over 40 years. In addition, females had a lower probability of marriage if their male ancestors were older. These findings are consistent with an increase of the number of accumulated de novo mutations with male age, suggesting that deleterious mutations acquired from recent ancestors may be a substantial burden to fitness in humans. However, possible non-mutational explanations for the observed associations are also discussed

Accelerated inbreeding depression suggests synergistic epistasis for deleterious mutations in Drosophila melanogaster

Epistasis may have important consequences for a number of issues in quantitative genetics and evolutionary biology. In particular, synergistic epistasis for deleterious alleles is relevant to the mutation load paradox and the evolution of sex and recombination. Some studies have shown evidence of synergistic epistasis for spontaneous or induced deleterious mutations appearing in mutation-accumulation experiments. However, many newly arising mutations may not actually be segregating in natural populations because of the erasing action of natural selection. A demonstration of synergistic epistasis for naturally segregating alleles can be achieved by means of inbreeding depression studies, as deleterious recessive allelic effects are exposed in inbred lines. Nevertheless, evidence of epistasis from these studies is scarce and controversial. In this paper, we report the results of two independent inbreeding experiments carried out with two different populations of Drosophila melanogaster. The results show a consistent accelerated inbreeding depression for fitness, suggesting synergistic epistasis among deleterious alleles. We also performed computer simulations assuming different possible models of epistasis and mutational parameters for fitness, finding some of them to be compatible with the results observed. Our results suggest that synergistic epistasis for deleterious mutations not only occurs among newly arisen spontaneous or induced mutations, but also among segregating alleles in natural populationsWe acknowledge the support by Uvigo Marine Research Centre funded by the “Excellence in Research (INUGA)” Programme from the Regional Council of Culture, Education and Universities, with co-funding from the European Union through the ERDF Operational Programme Galicia 2014-2020. This work was funded by Agencia Estatal de Investigación (AEI) (CGL2016-75904-C2-1-P), Xunta de Galicia (ED431C 2016-037) and Fondos Feder: “Unha maneira de facer Europa.” SD was founded by a predoctoral (FPI) grant from Ministerio de Economía y Competitividad, SpainS

The Ups and Downs of Mutation Frequencies during Aging Can Account for the Apert Syndrome Paternal Age Effect

Apert syndrome is almost always caused by a spontaneous mutation of paternal origin in one of two nucleotides in the fibroblast growth factor receptor 2 gene (FGFR2). The incidence of this disease increases with the age of the father (paternal age effect), and this increase is greater than what would be expected based on the greater number of germ-line divisions in older men. We use a highly sensitive PCR assay to measure the frequencies of the two causal mutations in the sperm of over 300 normal donors with a wide range of ages. The mutation frequencies increase with the age of the sperm donors, and this increase is consistent with the increase in the incidence rate. In both the sperm data and the birth data, the increase is non-monotonic. Further, after normalizing for age, the two Apert syndrome mutation frequencies are correlated within individual sperm donors. We consider a mathematical model for germ-line mutation which reproduces many of the attributes of the data. This model, with other evidence, suggests that part of the increase in both the sperm data and the birth data is due to selection for mutated premeiotic cells. It is likely that a number of other genetic diseases have similar features