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Adaptive evolution can be described by an uphill walk in a fitness landscape. However, climbing the global peak in a multipeak landscape is improbable because of the high chance of being trapped at a local peak. Nonetheless, over three-quarters of simulated adaptive walks in the fitness landscape of the Escherichia coli dihydrofolate reductase (DHFR) gene were reported to end at the highest 14% of peaks, suggesting that biological systems may be substantially more evolvable than commonly thought. To investigate the cause and generality of this observation, we estimate in empirical and theoretical fitness landscapes the probability of reaching high peaks by adaptive walks (PHP), where high peaks refer to the highest 1, 5, 14, or 25% of all peaks. We find that (i) PHP varies substantially among landscapes, (ii) PHP in empirical landscapes is generally comparable to or smaller than that in same-size Rough Mount Fuji landscapes of similar ruggedness, and (iii) lowering landscape ruggedness boosts PHP. As observed in DHFR, we find in every examined landscape a positive correlation between the fitness of a peak and its basin size, which is the number of genotypes that can reach the peak through adaptive walks. Yet, this correlation does not guarantee a large PHP because of the influences of other factors. We conclude that evolvability depends on the specific fitness landscape and that the large PHP in the DHFR landscape is not a general property of empirical or theoretical fitness landscapes.

Epigenetic modifications, such as DNA methylation or histone modifications, can be transmitted between cellular or organismal generations. However, there are no experiments measuring their role in adaptation, so here we use experimental evolution to investigate how epigenetic variation can contribute to adaptation. We manipulated DNA methylation and histone acetylation in the unicellular green alga Chlamydomonas reinhardtii both genetically and chemically to change the amount of epigenetic variation generated or transmitted in adapting populations in three different environments (salt stress, phosphate starvation, and high CO2) for two hundred asexual generations. We find that reducing the amount of epigenetic variation available to populations can reduce adaptation in environments where it otherwise happens. From genomic and epigenomic sequences from a subset of the populations, we see changes in methylation patterns between the evolved populations over-represented in some functional categories of genes, which is consistent with some of these differences being adaptive. Based on whole genome sequencing of evolved clones, the majority of DNA methylation changes do not appear to be linked to cis-acting genetic mutations. Our results show that transgenerational epigenetic effects play a role in adaptive evolution, and suggest that the relationship between changes in methylation patterns and differences in evolutionary outcomes, at least for quantitative traits such as cell division rates, is complex.

Abstract Understanding the evolutionary factors that impact the genetic architecture of traits is a central goal of evolutionary genetics. Here, we investigate how quantitative trait variation accumulated over time in populations that colonized a novel environment. We compare the genetic architecture of flowering time in Arabidopsis populations from the drought-prone Cape Verde Islands and their closest outgroup population from North Africa. We find that trait polygenicity is severely reduced in the island populations compared to the continental North African population. Further, trait architectures and reconstructed allelic histories best fit a model of strong directional selection in the islands in accord with a Fisher–Orr adaptive walk. Consistent with this, we find that large-effect variants that disrupt major flowering time genes (FRI and FLC) arose first, followed by smaller effect variants, including ATX2 L125F, which is associated with a 4-day reduction in flowering time. The most recently arising flowering time-associated loci are not known to be directly involved in flowering time, consistent with an omnigenic signature developing as the population approaches its trait optimum. Surprisingly, we find no effect in the natural population of EDI-Cvi-0 (CRY2 V367M), an allele for which an effect was previously validated by introgression into a Eurasian line. Instead, our results suggest the previously observed effect of the EDI-Cvi-0 allele on flowering time likely depends on genetic background, due to an epistatic interaction. Altogether, our results provide an empirical example of the effects demographic history and selection has on trait architecture.

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation-limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive-walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.

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.

A fitness landscape is a mapping from a space of discrete genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes connected by single mutational steps. Such a path is said to be accessible if the fitness values of the genotypes encountered along the path increase monotonically. We study accessible paths on random fitness landscapes of the House-of-Cards type, on which fitness values are independent, identically and continuously distributed random variables. The genotype space is taken to be a Cartesian power graph A L , where L is the number of genetic loci and the allele graph A encodes the possible allelic states and mutational transitions on one locus. The probability of existence of accessible paths between two genotypes at a distance linear in L displays a transition from 0 to a positive value at a threshold β c for the fitness difference between the initial and final genotype. We derive a lower bound on β c for general A and show that this bound is tight for a large class of allele graphs. Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs.

We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this population can be modelled as a measure-valued Markov process. Multiple variations of this system have been studied in the simultaneous limit of large populations and rare mutations, where the regime is chosen such that mutations are separated. We consider the deterministic system, resulting from the large population limit, and then let the mutation probability tend to zero. This corresponds to a much higher frequency of mutations, where multiple microscopic types are present at the same time. The limiting process resembles an adaptive walk or flight and jumps between different equilibria of coexisting types. The graph structure on the type space, determined by the possibilities to mutate, plays an important role in defining this jump process. In a variation of the above model, where the radius in which mutants can be spread is limited, we study the possibility of crossing valleys in the fitness landscape and derive different kinds of limiting walks.

It is currently unclear whether the amino acid substitutions that occur during protein evolution are primarily driven by adaptation, or reflect the random accumulation of neutral changes. When estimated from genomic data, the proportion of adaptive amino acid substitutions, called α, was found to vary greatly across species, from nearly zero in humans to above 0.5 in Drosophila. These variations have been interpreted as reflecting differences in effective population size, adaptation being supposedly more efficient in large populations. Here, we investigate the influence of effective population size and other biological parameters on the rate of adaptive evolution by simulating the evolution of a coding sequence under Fisher’s geometric formalism. We explicitly model recurrent environmental changes and the subsequent adaptive walks, followed by periods of stasis during which purifying selection dominates. We show that, under a variety of conditions, the effective population size has only a moderate influence on α, and an even weaker influence on the per generation rate of selective sweeps, modifying the prevalent view in current literature. The rate of environmental change and, interestingly, the dimensionality of the phenotypic space (organismal complexity) affect the adaptive rate more deeply than does the effective population size. We discuss the reasons why verbal arguments have been misleading on that subject and revisit the empirical evidence. Our results question the relevance of the “α” parameter as an indicator of the efficiency of molecular adaptation.

Fisher's geometric model of adaptation (FGM) has been the conceptual foundation for studies investigating the genetic basis of adaptation since the onset of the neo Darwinian synthesis. FGM describes adaptation as the movement of a genotype toward a fitness optimum due to beneficial mutations. To date, one prediction of FGM, the probability of improvement is related to the distance from the optimum, has only been tested in microorganisms under laboratory conditions. There is reason to believe that results might differ under natural conditions where more mutations likely affect fitness, and where environmental variance may obscure the expected pattern. We chemically induced mutations into a set of 19 Arabidopsis thaliana accessions from across the native range of A. thaliana and planted them alongside the premutated founder lines in two habitats in the mid-Atlantic region of the United States under field conditions. We show that FGM is able to predict the outcome of a set of random induced mutations on fitness in a set of A. thaliana accessions grown in the wild: mutations are more likely to be beneficial in relatively less fit genotypes. This finding suggests that FGM is an accurate approximation of the process of adaptation under more realistic ecological conditions.