How much gene flow is needed to inhibit speciation by the accumulation of Dobzhansky-Muller incompatibilities (DMIs) in a structured population? Here, we derive these limits in a classical migration-selection model with two haploid or diploid loci and unidirectional gene flow from a continent to an island. We discuss the dependence of the maximum gene-flow rate on ecological factors (exogeneous selection), genetic factors (epistasis, recombination), and the evolutionary history. Extensive analytical and numerical results show the following: (1) The maximum rate of gene flow is limited by exogeneous selection. In particular, maintenance of neutral DMIs is impossible with gene flow. (2) There are two distinct mechanisms that drive DMI evolution in parapatry, selection against immigrants in a heterogeneous environment and selection against hybrids due to the incompatibility. (3) Depending on the mechanism, opposite predictions result concerning the genetic architecture that maximizes the rate of gene flow a DMI can sustain. Selection against immigrants favors evolution of tightly linked DMIs of arbitrary strength, whereas selection against hybrids promotes the evolution of strong unlinked DMIs. In diploids, the fitness of the double heterozygotes is the decisive factor to predict the pattern of DMI stability.T HE (Bateson-) Dobzhansky-Muller model (DMM) (Bateson 1909; Dobzhansky 1936; Muller 1942) is the standard model to explain the evolution of intrinsic postzygotic isolation. A variety of theoretical studies show the plausibility of this model (reviewed in Coyne and Orr 2004; Gavrilets 2004), and numerous empirical studies report DobzhanskyMuller incompatibilities (DMIs) across several species of animals and plants (see reviews by Lowry et al. 2008 and Presgraves 2010).The appeal of the DMM is its generality: Speciation happens as a by-product of divergence without the need of special selection scenarios or complex adaptations to cross fitness valleys (cf. Orr 1995). The sole, but crucial, assumption is sufficient evolutionary time to let the process unfold and the spatial separation of the incipient species during this phase. The plausibility of the DMM as a mechanism for speciation and the widespread belief in the prevalence of allopatric speciation (Mayr 1942; Coyne and Orr 2004) go hand in hand. However, given that even tiny amounts of gene flow (of the order of a single migrant per generation) can have substantial effects on divergence (Slatkin 1987), it is clear that the assumption of strict allopatry is an idealization. This poses the question of the relevance of the DMM in parapatry and thus whether DMIs can originate or be maintained in the presence of gene flow. It has been suggested that the accumulation of DMIs in parapatry is possible (e.g., Gavrilets 1997Gavrilets , 2004 Porter and Johnson 2002; Kondrashov 2003; Agrawal et al. 2011; Nosil and Flaxman 2011). However, usually only the limit of weak migration has been studied. In contrast, we focus on the maximum rates of gene flow th...
The challenge of distinguishing genetic drift from selection remains a central focus of population genetics. Time-sampled data may provide a powerful tool for distinguishing these processes, and we here propose approximate Bayesian, maximum likelihood, and analytical methods for the inference of demography and selection from time course data. Utilizing these novel statistical and computational tools, we evaluate whole-genome datasets of an influenza A H1N1 strain in the presence and absence of oseltamivir (an inhibitor of neuraminidase) collected at thirteen time points. Results reveal a striking consistency amongst the three estimation procedures developed, showing strongly increased selection pressure in the presence of drug treatment. Importantly, these approaches re-identify the known oseltamivir resistance site, successfully validating the approaches used. Enticingly, a number of previously unknown variants have also been identified as being positively selected. Results are interpreted in the light of Fisher's Geometric Model, allowing for a quantification of the increased distance to optimum exerted by the presence of drug, and theoretical predictions regarding the distribution of beneficial fitness effects of contending mutations are empirically tested. Further, given the fit to expectations of the Geometric Model, results suggest the ability to predict certain aspects of viral evolution in response to changing host environments and novel selective pressures.
The role of adaptation in the evolutionary process has been contentious for decades. At the heart of the century-old debate between neutralists and selectionists lies the distribution of fitness effects (DFE)—that is, the selective effect of all mutations. Attempts to describe the DFE have been varied, occupying theoreticians and experimentalists alike. New high-throughput techniques stand to make important contributions to empirical efforts to characterize the DFE, but the usefulness of such approaches depends on the availability of robust statistical methods for their interpretation. We here present and discuss a Bayesian MCMC approach to estimate fitness from deep sequencing data and use it to assess the DFE for the same 560 point mutations in a coding region of Hsp90 in Saccharomyces cerevisiae across six different environmental conditions. Using these estimates, we compare the differences in the DFEs resulting from mutations covering one-, two-, and three-nucleotide steps from the wild type—showing that multiple-step mutations harbor more potential for adaptation in challenging environments, but also tend to be more deleterious in the standard environment. All observations are discussed in the light of expectations arising from Fisher’s geometric model.
The role of adaptation in molecular evolution has been contentious for decades. Here, we shed light on the adaptive potential in Saccharomyces cerevisiae by presenting systematic fitness measurements for all possible point mutations in a region of Hsp90 under four environmental conditions. Under elevated salinity, we observe numerous beneficial mutations with growth advantages up to 7% relative to the wild type. All of these beneficial mutations were observed to be associated with high costs of adaptation. We thus demonstrate that an essential protein can harbor adaptive potential upon an environmental challenge, and report a remarkable fit of the data to a version of Fisher's geometric model that focuses on the fitness trade-offs between mutations in different environments.
The study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with next-generation sequencing (NGS) methods enable accurate and extensive studies of the fitness effects of mutations, allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape and its implications for the predictability and repeatability of evolution. Here, we present a uniquely large multiallelic fitness landscape comprising 640 engineered mutants that represent all possible combinations of 13 amino acid-changing mutations at 6 sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multiallelic fitness landscape. Using subsets of the data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino acid-specific epistatic hotspots and that inference is additionally confounded by the nonrandom choice of mutations for experimental fitness landscapes.evolution | adaptation | epistasis | fitness landscape | mutagenesis S ince first proposed by Sewall Wright in 1932 (1), the idea of a fitness landscape relating genotype (or phenotype) to the reproductive success of an individual has inspired evolutionary biologists and mathematicians alike (2-4). With the advancement of molecular and systems biology toward large and accurate datasets, the fitness landscape concept has received increasing attention across other subfields of biology (5-9). The shape of the fitness landscape carries information on the repeatability and predictability of evolution, the potential for adaptation, the importance of genetic drift, the likelihood of convergent and parallel evolution, and the degree of optimization that is (theoretically) achievable (4). Unfortunately, the dimensionality of a complete fitness landscape of an organism-that is, a mapping of all possible combinations of mutations to their respective fitness effects-is much too high to be assessed experimentally. With the development of experimental approaches that allow for the assessment of full fitness landscapes of tens to hundreds of mutations, there is growing interest in statistics that capture the features of the landscape and that relate an experimental landscape to theoretical landscapes of similar architecture, which have been studied extensively (10). It is, however, unclear whether this categorization allows for an extrapolation to unknown parts of the landscape, which would be the first step toward quantifying predictability-an advancement that would yield impacts far beyond the field of evolutionary biology, in particular for the clinical study of drug-resistan...
Mutations are the source of evolutionary variation. The interactions of multiple mutations can have important effects on fitness and evolutionary trajectories. We have recently described the distribution of fitness effects of all single mutations for a nine-amino-acid region of yeast Hsp90 (Hsp82) implicated in substrate binding. Here, we report and discuss the distribution of intragenic epistatic effects within this region in seven Hsp90 point mutant backgrounds of neutral to slightly deleterious effect, resulting in an analysis of more than 1,000 double mutants. We find negative epistasis between substitutions to be common, and positive epistasis to be rare--resulting in a pattern that indicates a drastic change in the distribution of fitness effects one step away from the wild type. This can be well explained by a concave relationship between phenotype and genotype (i.e., a concave shape of the local fitness landscape), suggesting mutational robustness intrinsic to the local sequence space. Structural analyses indicate that, in this region, epistatic effects are most pronounced when a solvent-inaccessible position is involved in the interaction. In contrast, all 18 observations of positive epistasis involved at least one mutation at a solvent-exposed position. By combining the analysis of evolutionary and biophysical properties of an epistatic landscape, these results contribute to a more detailed understanding of the complexity of protein evolution.
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