Predicting Carriers of Ongoing Selective Sweeps without Knowledge of the Favored Allele

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Methods for detecting the genomic signatures of natural selection have been heavily studied, and they have been successful in identifying genomic regions under positive selection. However, methods that detect positive selective sweeps do not typically identify the favored allele, or even the haplotypes carrying the favored allele. The main contribution of this paper is the development and analysis of a new statistic (the HAF score), assigned to individual haplotypes. Using both theoretical analyses and simulations, we describe how the HAF scores differ for carriers and non-carriers of the favored allele, and how they change dynamically during a selective sweep. We also develop an algorithm, PreCIOSS, for separating carriers and non-carriers. Our tool has broad applicability as carriers of the favored allele are likely to contain a future most recent common ancestor. Therefore, identifying them may prove useful in predicting the evolutionary trajectory—for example, in contexts involving drug-resistant pathogen strains or cancer subclones.

Published in the journal: . PLoS Genet 11(9): e32767. doi:10.1371/journal.pgen.1005527
Category: Research Article
doi: https://doi.org/10.1371/journal.pgen.1005527

Summary

Introduction

With genome sequencing, we now have an opportunity to more completely sample genetic diversity in human populations, and probe deeper for signatures of adaptive evolution [1–3]. Genetic data from diverse human populations in recent years have revealed a multitude of genomic regions believed to be evolving under recent positive selection [4–16].

Methods for detecting selective sweeps from DNA sequences have examined a variety of signatures, including patterns represented in variant allele frequencies as well as in haplotype structure. Initially, the problem of detecting selective sweeps was approached primarily by considering variant allele frequencies, exploiting the shift in frequency at ‘hitchhiking’ sites linked to a favored allele relative to non-hitchhiking sites [17, 18]. The site frequency spectrum (SFS) within and across populations is often used as a basis for such inference [4, 6, 19–25]. More recently, methods based on haplotype structure have been developed using a variety of approaches, including the frequency of the most common haplotype [26], the number and diversity of distinct haplotypes [27], the haplotype frequency spectrum [28], and the popular approach of long-range haplotype homozygosity [29–32].

In general, haplotype-based methods seek to characterize the population with summary statistics that capture the frequency and length of different haplotypes. However, the haplotypes are related through a genealogy, and relationships among them are inherently lost in such analyses. In addition, data on the site frequency spectrum can be lost or hidden in analyses focused on haplotype spectra. In this paper, we connect related measures of haplotype frequencies and the site frequency spectrum by merging information describing haplotype relationships with variant allele frequencies. Our main contribution is a statistic that we term the haplotype allele frequency (HAF) score, which captures many of the properties shared by haplotypes carrying a favored allele.

Consider a sample of haplotypes in a genomic region. We assume that all sites are biallelic, and at each site, we denote ancestral alleles by 0 and derived alleles by 1. We also assume that all sites are polymorphic in the sample. The HAF vector of a haplotype h, denoted c, is obtained by taking the binary haplotype vector and replacing non-zero entries (derived alleles carried by the haplotype) with their respective frequencies in the sample (Fig 1A). For parameter ℓ, we define the ℓ-HAF score of c as:

where the sum proceeds over all segregating sites j in the genomic region. The 1-HAF score of a haplotype amounts to the sum of frequencies of all derived alleles carried by the haplotype. The ℓ-HAF score is equivalent to the ℓ-norm of c raised to the ℓ^th power, or ( ‖ c ‖ ℓ ) ℓ. We will show that during a selective sweep, the HAF score of a haplotype serves as a proxy to its relative fitness.

Selective sweeps

The classical model for selection, and the one that has received most attention, is the “hard sweep” model, in which a single mutation conveys higher fitness immediately upon occurrence, and rapidly rises in frequency, eventually reaching fixation [17, 33]. Under this model, we can partition the haplotypes into carriers of the favored allele, and non-carriers. In the absence of recombination, the favored haplotypes form a single clade in the genealogy. As a sweep progresses, HAF scores in the favored clade will rise due to the increasing frequencies of alleles hitchhiking along with the favored allele. HAF scores of non-carrier haplotypes will decrease, as many of the derived alleles they carry become rare (Fig 1B). After fixation of the favored and hitchhiking alleles, HAF scores will decline sharply (Fig 1C), as the selected site and other linked sites are no longer polymorphic. Thus, this reduction in the HAF score results from the sudden loss of many high-frequency derived alleles from the pool of segregating sites [18, 20, 24]. Finally, as the site-frequency spectrum recovers to its neutral state due to new mutations and drift [23], so will the HAF scores.

Recombination is a source of ‘noise’ for the properties of the HAF score, predicted under the assumption of a hard sweep and no recombination, as it allows haplotypes to cross into and out of the favored clade. Recombination can lead to (i) haplotypes that carry the favored allele but little of the hitchhiking variation, thus having relatively low HAF scores despite their high fitness, or (ii) haplotypes that do not carry the favored allele but do carry much of the hitchhiking variation, thus having relatively high HAF scores despite their low fitness. By the same logic, recombination adds ‘noise’ after fixation by making the otherwise sharp decline in HAF scores more subtle and gradual. This more gradual decline occurs due to recombination weakening the linkage between the favored allele and hitchhiking variants.

Recently, “soft sweeps” have generated significant interest [34–36]. A soft sweep occurs when multiple sets of hitchhiking alleles in a given region increase in frequency, rather than a single favored haplotype. Soft sweeps may take place by one or more of the following mechanisms: (i) selection from standing variation: a neutral segregating mutation, which exists on several haplotypic backgrounds, becomes favored due to a change in the environment; (ii) recurrent mutation: the favored mutation arises several times on different haplotypic backgrounds; or, (iii) multiple adaptations: multiple favored mutations occur on multiple haplotypic backgrounds. Several methods have been developed for detecting soft sweeps [37, 38], as well as for distinguishing between soft and hard sweeps [39–41]. In soft sweeps, multiple sets of hitchhiking alleles rise to intermediate frequencies as the favored allele fixes. This could cause the pre-fixation peak and post-fixation trough in HAF scores to be less pronounced and to occur more gradually compared to a hard sweep.

We find (see Results) that the properties of the HAF score remain robust to many soft sweep scenarios. Moreover, the HAF score could potentially be used to detect soft sweeps. However, in this paper, we focus on the foundations, developing theoretical analysis and empirical work that predicts the dynamics of the HAF score. We also develop a single application. Recall that most existing methods for characterizing selective sweeps focus on identifying regions under selection. Here, given a region already identified to be undergoing a selective sweep, we ask if we can accurately predict which haplotypes carry the favored allele, without knowledge of the favored site. Successfully doing so may provide insight into the future evolutionary trajectory of a population. Haplotypes in future generations are more likely to be descended from, and therefore to resemble, extant carriers of a favored allele. This predictive perspective is of particular importance when a sweep is undesirable and measures may be taken to prevent it. For instance, consider a set of tumor haplotypes isolated from single cells, some of which are drug-resistant and therefore favored under drug exposure. Given a genetic sample of the tumor haplotypes, the HAF statistic may be applied to identify the resistant haplotypes—carriers of a favored allele—before they clonally expand and metastasize.

Below, we start with a theoretical explanation of the behavior of the HAF score under different evolutionary scenarios, validating our results using simulation. We then develop an algorithm (PreCIOSS: Predicting Carriers of Ongoing Selective Sweeps) to detect carriers of selective sweeps based on the HAF score. We demonstrate the power of PreCIOSS on simulations of both hard and soft sweeps, as well as on real genetic data from well-known sweeps in human populations. While our theoretical derivations make use of coalescent theory, and explicitly use tree-like genealogies, we note that HAF scores can be computed for any haplotype matrix including those with recombination events. Our results on simulated and real data imply that the utility of the HAF score extends to cases with recombination as well as other evolutionary scenarios.

Results

Theoretical and empirical modeling of HAF scores

We consider a sample of n haploid individuals chosen at random from a larger haploid population of size N. Let μ denote the mutation rate per generation per nucleotide, and let θ = 2NμL denote the population-scaled mutation rate in a region of length L bp. We consider both constant-sized and exponentially growing populations. For exponentially growing populations, let N₀ denote the final population size, let r denote the growth rate per generation, and let α = 2 N₀ r the population-scaled growth rate. Let ρ denote the population-scaled recombination rate. In our theoretical calculations, we assume no recombination (ρ = 0), and we derive expressions for the general ℓ-HAF score. We use simulations to demonstrate the concordance of theoretical and empirical values of the ℓ-HAF score, and show that the values are robust to the presence of recombination (see ‘Simulations’ in Methods for parameter choices). Although some of our theoretical calculations below derive expressions for the general ℓ-HAF score, we primarily use 1-HAF in the applied sections. Applications of ℓ-HAF with ℓ > 1 will be explored in future work.

Expected ℓ-HAF score under neutrality, constant population size

First, we assume that the genomic region of interest is evolving neutrally, the population size remains constant at N, and that the ancestral states are known or can be derived. In a sample of size n, let c(v) denote the HAF vector c for the v^th haplotype (v ∈ {1, …, n}). Let ξ_w be the number of sites with derived allele frequency w. We only consider polymorphic sites in the sample, so the frequency is in the range w ∈ {1, …, n − 1}; a mutation present in all or none of the haplotypes in the sample would not be detectable. Each of the ξ_w sites of frequency w contributes w^ℓ to the ℓ-HAF score of each of the w haplotypes with the mutation, and contributes 0^ℓ = 0 for each of the other n − w haplotypes. The mean of the ℓ-HAF scores of all n haplotypes in the sample is

Under the coalescent model, [42, Eq. (22)] shows that

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