Sweeps in time: leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here, we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome.

Polygenic adaptation: From sweeps to subtle frequency shifts

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.

Linking genome signatures of selection and adaptation in non-model plants: exploring potential and limitations in the angiosperm Amborella

Selective sweeps may be caused by environmental conditions that select for a gene function or trait at one locus, causing reduced variation at neighboring sites due to linkage, with specific non-selected variants being swept along with the selected variant. For many species, genomic and environmental data are available to test hypotheses that environmental conditions are correlated with selected regions. Most genomic studies relating selection to environment use model organisms or crop species; typically, these studies have genomic data from large numbers of individuals and extensive environmental data. Here, we review studies associating selective sweeps with environment and consider the impediments to successful application of these methods to non-model species. We present an initial investigation into linking genomic regions of selection to environmental conditions in the narrowly distributed, non-model plant Amborella trichopoda (Amborellaceae), the sister species to all other living flowering plants and one of over 2500 plant species endemic to New Caledonia.

A Coalescent Model for a Sweep of a Unique Standing Variant

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical "hard sweep" hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.

The genetics of speciation: are complex incompatibilities easier to evolve?

Reproductive isolation can evolve readily when genotypes containing incompatible alleles are connected by chains of fit intermediates. Experimental crosses show that such Dobzhansky-Muller incompatibilities (DMIs) are often complex (involving alleles at three or more loci) and asymmetrical (such that reciprocal introgressions have very different effects on fitness). One possible explanation is that asymmetrical and complex DMIs are 'easier to evolve', because they block fewer of the possible evolutionary paths between the parental genotypes. To assess this argument, we model evolutionary divergence in allopatry and calculate the delays to divergence caused by DMIs of different kinds. We find that the number of paths is sometimes, though not always, a reliable predictor of the time to divergence. In particular, we find limited support for the idea that symmetrical DMIs take longer to evolve, but this applies largely to two-locus symmetrical DMIs (which leave no path of fit intermediates). Symmetrical complex DMIs can also delay divergence, but only in a limited region of parameter space. In most other cases, the presence and form of DMIs have little influence on times to divergence, and so we argue that ease of evolution is unlikely to be important in explaining the experimental data.

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep

A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076-1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and ̂σ(2)(D), a quantity introduced by Ohta and Kimura (Genetics 63(1):229-238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.

Recent and recurrent selective sweeps of the antiviral RNAi gene Argonaute-2 in three species of Drosophila

Antagonistic host–parasite interactions can drive rapid adaptive evolution in genes of the immune system, and such arms races may be an important force shaping polymorphism in the genome. The RNA interference pathway gene Argonaute-2 (AGO2) is a key component of antiviral defense in Drosophila, and we have previously shown that genes in this pathway experience unusually high rates of adaptive substitution. Here we study patterns of genetic variation in a 100-kbp region around AGO2 in three different species of Drosophila. Our data suggest that recent independent selective sweeps in AGO2 have reduced genetic variation across a region of more than 50 kbp in Drosophila melanogaster, D. simulans, and D. yakuba, and we estimate that selection has fixed adaptive substitutions in this gene every 30–100 thousand years. The strongest signal of recent selection is evident in D. simulans, where we estimate that the most recent selective sweep involved an allele with a selective advantage of the order of 0.5–1% and occurred roughly 13–60 Kya. To evaluate the potential consequences of the recent substitutions on the structure and function of AGO2, we used fold-recognition and homology-based modeling to derive a structural model for the Drosophila protein, and this suggests that recent substitutions in D. simulans are overrepresented at the protein surface. In summary, our results show that selection by parasites can consistently target the same genes in multiple species, resulting in areas of the genome that have markedly reduced genetic diversity.