Summary: 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. Here, we summarize the key theoretical concepts and contrast model predictions with observed patterns in Drosophila, humans, and microbes. 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. 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.

Evolutionary theory has produced two conflicting paradigms for the adaptation of a polygenic trait. While population genetics views adaptation as a sequence of selective sweeps at single loci underlying the trait, quantitative genetics posits a collective response, where phenotypic adaptation results from subtle allele frequency shifts at many loci. Yet, a synthesis of these views is largely missing and the population genetic factors that favor each scenario are not well understood. Here, we study the architecture of adaptation of a binary polygenic trait (such as resistance) with negative epistasis among the loci of its basis. The genetic structure of this trait allows for a full range of potential architectures of adaptation, ranging from sweeps to small frequency shifts. By combining computer simulations and a newly devised analytical framework based on Yule branching processes, we gain a detailed understanding of the adaptation dynamics for this trait. Our key analytical result is an expression for the joint distribution of mutant alleles at the end of the adaptive phase. This distribution characterizes the polygenic pattern of adaptation at the underlying genotype when phenotypic adaptation has been accomplished. We find that a single compound parameter, the population-scaled background mutation rate Θ_bg, explains the main differences among these patterns. For a focal locus, Θ_bg measures the mutation rate at all redundant loci in its genetic background that offer alternative ways for adaptation. For adaptation starting from mutation-selection-drift balance, we observe different patterns in three parameter regions. Adaptation proceeds by sweeps for small Θ_bg ≲ 0.1, while small polygenic allele frequency shifts require large Θ_bg ≳ 100. In the large intermediate regime, we observe a heterogeneous pattern of partial sweeps at several interacting loci. It is still an open question how complex traits adapt to new selection pressures. While population genetics champions the search for selective sweeps, quantitative genetics proclaims adaptation via small concerted frequency shifts. To date the empirical evidence of clear sweep signals is more scarce than expected, while subtle shifts remain notoriously hard to detect. In the current study we develop a theoretical framework to predict the expected adaptive architecture of a simple polygenic trait, depending on parameters such as mutation rate, effective population size, size of the trait basis, and the available genetic variability at the onset of selection. For a population in mutation-selection-drift balance we find that adaptation proceeds via complete or partial sweeps for a large set of parameter values. We predict adaptation by small frequency shifts for two main cases. First, for traits with a large mutational target size and high levels of genetic redundancy among loci, and second if the starting frequencies of mutant alleles are more homogeneous than expected in mutation-selection-drift equilibrium, e.g. due to population structure or balancing selection.

Great care is needed when interpreting claims about the genetic basis of human variation based on data from genome-wide association studies.

Recent research shows that introgression between closely-related species is an important source of adaptive alleles for a wide range of taxa. Typically, detection of adaptive introgression from genomic data relies on comparative analyses that require sequence data from both the recipient and the donor species. However, in many cases, the donor is unknown or the data is not currently available. Here, we introduce a genome-scan method—VolcanoFinder—to detect recent events of adaptive introgression using polymorphism data from the recipient species only. VolcanoFinder detects adaptive introgression sweeps from the pattern of excess intermediate-frequency polymorphism they produce in the flanking region of the genome, a pattern which appears as a volcano-shape in pairwise genetic diversity. Using coalescent theory, we derive analytical predictions for these patterns. Based on these results, we develop a composite-likelihood test to detect signatures of adaptive introgression relative to the genomic background. Simulation results show that VolcanoFinder has high statistical power to detect these signatures, even for older sweeps and for soft sweeps initiated by multiple migrant haplotypes. Finally, we implement VolcanoFinder to detect archaic introgression in European and sub-Saharan African human populations, and uncovered interesting candidates in both populations, such as TSHR in Europeans and TCHH-RPTN in Africans. We discuss their biological implications and provide guidelines for identifying and circumventing artifactual signals during empirical applications of VolcanoFinder. The process by which beneficial alleles are introduced into a species from a closely-related species is termed adaptive introgression. We present an analytically-tractable model for the effects of adaptive introgression on non-adaptive genetic variation in the genomic region surrounding the beneficial allele. The result we describe is a characteristic volcano-shaped pattern of increased variability that arises around the positively-selected site, and we introduce an open-source method VolcanoFinder to detect this signal in genomic data. Importantly, VolcanoFinder is a population-genetic likelihood-based approach, rather than a comparative-genomic approach, and can therefore probe genomic variation data from a single population for footprints of adaptive introgression, even from a priori unknown and possibly extinct donor species.