A population can adapt to a rapid environmental change or habitat expansion in two ways. It may adapt either through new beneficial mutations that subsequently sweep through the population or by using alleles from the standing genetic variation. We use diffusion theory to calculate the probabilities for selective adaptations and find a large increase in the fixation probability for weak substitutions, if alleles originate from the standing genetic variation. We then determine the parameter regions where each scenario-standing variation vs. new mutations-is more likely. Adaptations from the standing genetic variation are favored if either the selective advantage is weak or the selection coefficient and the mutation rate are both high. Finally, we analyze the probability of "soft sweeps," where multiple copies of the selected allele contribute to a substitution, and discuss the consequences for the footprint of selection on linked neutral variation. We find that soft sweeps with weaker selective footprints are likely under both scenarios if the mutation rate and/or the selection coefficient is high.

In the classical model of molecular adaptation, a favored allele derives from a single mutational origin. This ignores that beneficial alleles can enter a population recurrently, either by mutation or migration, during the selective phase. In this case, descendants of several of these independent origins may contribute to the fixation. As a consequence, all ancestral haplotypes that are linked to any of these copies will be retained in the population, affecting the pattern of a selective sweep on linked neutral variation. In this study, we use analytical calculations based on coalescent theory and computer simulations to analyze molecular adaptation from recurrent mutation or migration. Under the assumption of complete linkage, we derive a robust analytical approximation for the number of ancestral haplotypes and their distribution in a sample from the population. We find that so-called "soft sweeps," where multiple ancestral haplotypes appear in a sample, are likely for biologically realistic values of mutation or migration rates.

Summary1. The tempo and mode of adaptive evolution determine how natural selection shapes patterns of genetic diversity in DNA polymorphism data. While slow mutation-limited adaptation leads to classical footprints of 'hard' selective sweeps, these patterns are different when adaptation responds quickly to a novel selection pressure, acting either on standing genetic variation or on recurrent new mutation. In the past decade, corresponding footprints of 'soft' selective sweeps have been described both in theoretical models and in empirical data. 2. Here, we summarize the key theoretical concepts and contrast model predictions with observed patterns in Drosophila, humans, and microbes. 3. Evidence in all cases shows that 'soft' patterns of rapid adaptation are frequent. However, theory and data also point to a role of complex adaptive histories in rapid evolution. 4. While existing theory allows for important implications on the tempo and mode of the adaptive process, complex footprints observed in data are, as yet, insufficiently covered by models. They call for in-depth empirical study and further model development.Key-words: adaptation, Drosophila, genetic hitch-hiking, HIV, lactase, malaria, selective sweep Hard and soft selective sweeps

Polymorphism data can be used to identify loci at which a beneficial allele has recently gone to fixation, given that an accurate description of the signature of selection is available. In the classical model that is used, a favored allele derives from a single mutational origin. This ignores the fact that beneficial alleles can enter a population recurrently by mutation during the selective phase. In this study, we present a combination of analytical and simulation results to demonstrate the effect of adaptation from recurrent mutation on summary statistics for polymorphism data from a linked neutral locus. We also analyze the power of standard neutrality tests based on the frequency spectrum or on linkage disequilibrium (LD) under this scenario. For recurrent beneficial mutation at biologically realistic rates, we find substantial deviations from the classical pattern of a selective sweep from a single new mutation. Deviations from neutrality in the level of polymorphism and in the frequency spectrum are much less pronounced than in the classical sweep pattern. In contrast, for levels of LD, the signature is even stronger if recurrent beneficial mutation plays a role. We suggest a variant of existing LD tests that increases their power to detect this signature.