Predicting Carriers of Ongoing Selective Sweeps without Knowledge of the Favored Allele
[['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 .'], ['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 .', 'We now consider the dynamics of HAF scores in a population undergoing a selective sweep .', 'To do this , we use data simulated under several scenarios .', 'Fig 2 illustrates the HAF score dynamics in a single simulated population undergoing a hard sweep , with selection coefficient s = 0 . 05 .', 'See ‘Simulations’ in Methods for a detailed description of the simulation parameters .', 'Initially ( leftmost , time 0 ) the HAF scores of carriers and non-carriers of the favored allele are similar .', 'As the sweep progresses ( times 100–450 ) , carrier HAF scores increase to a peak value ( HAF-peak ) .', 'Soon after fixation ( time ∼450 ) , we observe a sharp decline in HAF scores ( HAF-trough ) , followed by slow and steady recovery due to new mutation and drift ( times 500–50000 ) .', 'We observe similar behavior for the HAF score dynamics in an exponentially growing population , and soft sweep scenarios ( S5 and S6 Figs ) .', 'Though soft sweeps can arise under different circumstances , we restrict our attention to soft sweeps arising from standing variation .', 'While the behavior is similar , we note that during a soft sweep , the HAF scores do not have as sharp a decline as in the hard sweep scenarios .', 'Below , we provide a theoretical description of these dynamics , as well as empirical validation using simulations .', 'This allows us to predict HAF scores in', '( a ) the post-fixation trough;', '( b ) the pre-fixation peak; and', '( c ) the rate of growth of HAF scores from pre-sweep to peak value .', 'Our understanding of the dynamics of HAF scores of a haplotype during a selective sweep has many potential applications .', 'For example , we could compare the dynamics of hard and soft sweeps to distinguish between the two events .', 'Second , HAF scores of haplotypes in a region under selection might help predict the future MRCA of a population .', 'Finally , by conditioning on known or deduced selective sweeps in a population sample , we can predict the state ( carrier/non-carrier ) of the favored allele in its haplotypes .', 'Below we explore the last application , leaving the first two to future work .', 'In Fig 4A , we show the distributions of haplotype 1-HAF scores aggregated from 500 simulated populations undergoing a hard selective sweep ( see ‘Simulations’ in Methods for detailed parameter choices ) .', 'Scores were computed for random samples of n = 200 haplotypes taken at regular time intervals .', 'They are stratified by the frequency of the favored allele at the time of sampling .', 'Further , scores are stratified into carrier and non-carrier classes ( of the favored allele ) .', 'As with a single population , HAF scores of carriers and non-carriers diverge as the sweep progresses in frequency .', 'We note , however , that even close to fixation ( frequencies 80–100% ) the distributions of HAF scores between carriers and non-carriers maintain considerable overlap .', 'The high variance in HAF scores makes them only weakly informative of sweep carrier status when comparing across population samples ( or genomic regions within a single population ) .', 'Within a single population sample , however , the HAF scores are highly informative of the carrier status .', 'This is illustrated in Fig 4B , showing the distributions of HAF score percentile rank within their respective samples .', 'We observe that the rank distributions have minimal overlap for carriers and non-carriers of the favored allele .', 'Any remaining overlap in the percentile rank distributions in the final stages of a sweep ( favored allele frequency ≥ 70% ) stems mostly from recombination , which allows the favored allele to recombine onto haplotypes outside the selected clade ( creating low HAF score carriers ) and vice-versa ( creating high HAF score non-carriers ) .', 'The overall strong separation between carriers and non-carriers is further illustrated by the highly significant P-values of Wilcoxon rank sum tests rejecting the null hypothesis of identically distributed HAF scores among carriers and non-carriers within each population sample ( Fig 4C ) .', 'Fig 4 does not show how HAF scores are distributed following fixation of the sweep .', 'Starting at fixation , we see a strong decline in HAF scores owing to the loss of many high frequency derived alleles from the pool of segregating sites .', 'However , crossover events may unlink hitchhiking alleles from the favored allele , and they may remain segregating in the population even after fixation of the favored allele .', 'Therefore , the decline in HAF scores may be abrupt or gradual , depending on the linkage between the favored and hitchhiking alleles .', 'Finally , after reaching a trough , HAF scores gradually recover to their neutral levels over time .', 'The post-fixation dynamics of HAF scores are shown in S7 Fig . To evaluate the effectiveness of PreCIOSS in distinguishing carriers of a selective sweep from non-carriers , we applied it to several genomic regions ( e . g . , [39] ) where', '( i ) there is strong evidence of a selective sweep , and', '( ii ) the favored allele has been characterized .', 'In applying PreCIOSS to the datasets , we assumed that the region was known , but did not supply the favored allele to PreCIOSS .', 'In each case , we tested if PreCIOSS could separate the haplotypes that carried the favored allele .', 'We use phased haplotypes from the HapMap project [51] , setting the ancestral allele to that observed in orthologous Chimpanzee sequence [52] .'], ['This paper introduces a new perspective on the genetic signatures of selective sweeps .', 'From identifying and characterizing sweeps in a population sample—the topic of typical studies of selective sweeps—we progress to considering the role of individual haplotypes within an ongoing sweep .', 'Using both simulated and real data , we show that the HAF score is well-correlated with the relative fitness of individual haplotypes , and that our algorithm ( PreCIOSS ) is highly effective at predicting carriers of selective sweeps .', 'The HAF framework has many natural extensions and potential applications .', 'On the theoretical side , we have obtained the expected HAF score in both constant-sized and exponentially growing populations evolving neutrally ( Eqs ( 3 ) and ( 12 ) ) .', 'However , we do not yet know the variance .', 'This quantity would provide a better understanding of the respective distributions , and a means to to statistically test for deviations from neutrality .', 'Moreover , although we have observed in simulation and in practice that our theoretical argument is robust to recombination ( genealogies violating a tree structure ) , a theoretical argument supporting these observations would be valuable .', 'In terms of application , several additional directions are worth investigating .', 'The HAF framework is potentially useful in distinguishing hard from soft sweeps .', 'Intuitively , hard sweep genealogies will likely have a single hitchhiking branch dominating the HAF scores , and leading to near-uniform scores in favored haplotypes .', 'However , soft sweep genealogies may have several hitchhiking branches , potentially leading to distinct HAF score peaks .', 'Even if the different favored clades happen to have similar scores , the haplotypes within them will not form a highly-related group as expected in hard sweeps .', 'Our results on known selective sweeps in humans illustrates this idea already ( Fig 7 ) .', 'A recent study by Peter et al . ( 2012 ) [39] assigned posterior probabilities to hard vs . soft sweeps occurring in the same genes .', 'Peter et al . assigned the highest likelihood of a hard sweep to LCT ( 0 . 99 ) , followed by EDAR ( 0 . 89 ) , ADH1B ( 0 . 78 ) , TRPV ( 0 . 45 ) , and finally PSCA ( 0 . 24 ) .', 'This is in striking concordance with the spread in HAF scores in Fig 7 .', 'The clusters capturing the carriers in LCT and EDAR have tightly distributed HAF scores ( Fig 7A and 7I ) .', 'The cluster for ADH1B ( Fig 7G ) has more variance by comparison , and the variance increases for TRPV6 ( Fig 7C ) and PSCA ( Fig 7E ) , with PSCA showing the highest variance of HAF scores in carriers .', 'Finally , perhaps the highest potential impact of the HAF score could be in predicting the ‘MRCA of the future’ .', 'We know that future haplotypes are more likely similar to favored individuals than to unfavored ones , and that HAF scores correlate well with relative fitness in ongoing selective sweeps .', 'Therefore , high HAF haplotypes are more likely to be similar to future generations .', 'This relationship is particularly valuable when action may be taken based on such predictions .', 'For instance , rapid influenza viral evolution is known to change the strain composition from year to year .', 'The mutations are a mix of favored and deleterious mutations .', 'The fitness and frequency of the current year’s strain have been used to predict the next year’s dominant strain [73] .', 'The HAF score may allow for a careful look at the dynamics of the current strain and possibly offer better insight into the problem .', 'As a second example , tumor cells show great heterogeneity and much variation occurs at the single cell level .', 'This intra-tumor variation allows sub-population of cells to resist therapy and proliferate [74] .', 'Once again , HAF scores of haplotypes in cells undergoing treatment can potentially distinguish between carriers and non-carriers of drug resistance mutations , and thereby improve our insight into mechanisms of drug resistance .'], ['We simulated data for various evolutionary scenarios .', 'Neutral samples and sweep samples were generated using the simulator msms [47] .', 'All simulations generated samples of n ∈ [20 , 400] haplotypes from a larger effective population of N = 20000 haplotypes , each of length 50 kb .', 'A mutation rate of approximately μ = 2 . 4⋅10−8 mutations per bp per generation was used [75 , 76] .', 'For our simulations , we choose a population-scaled mutation rate θ ∈ {24 , 48} .', 'For human recombination events , a population scaled rate of ρ = 1 . 32θ has been proposed ( e . g . [77] ) .', 'We use simulations either with no recombination , or with ρ ∈ {25 , 50} in a 50 kb region to approximate human rates .', 'For exponential growth , we used N = 20000 as the size of the final ( current ) population .', 'Let r denote the growth rate per generation , so that at t generations prior to the current generation , the population size was N ( t ) = Ne−rt .', 'Define the scaled growth rate α = 2Nr .', 'We set α to a range of values in [200 , 1600] .', 'For selective sweeps , we used forward simulations assuming a diploid population with recombination and mutation parameters as described above .', 'While diploid populations were simulated to incorporate recombination , we used phased haplotypes for our analysis .', 'We assumed a single favored allele under selection coefficient s ∈ [0 . 005 , 0 . 050] and heterozygosity 0 . 5 ( haploid carriers get half the fitness advantage of diploid carriers ) .', 'When s is ‘low’ ( 0 . 001 ≤ s ≤ 0 . 01 ) , the available tests do not detect a selective sweep with reasonable power [21 , 23] .', 'Selection with s ≥ 0 . 08 is considered ‘high’ ( e . g . , see [21] ) .', 'For high values of s , the carrier haplotypes are identical or very similar in simulations , making the problem of detecting carriers easy .', 'Therefore , we chose intermediate values ( s ∈ [0 . 005 , 0 . 050] ) in our simulations .', 'Soft sweeps can arise either due to standing variation or due to multiple favored alleles .', 'Here , we focus on the former , where the favored allele is present in at least one carrier in the population ( ν0 ∈ [1/N , 1] ) , and drifting at the onset of selection .', 'In our simulations , we set ν0 at the beginning of the sweep to ν0 = 1/N = 5⋅10−5 for hard sweeps and ν0 ∈ {0 . 001 , 0 . 02} for soft sweeps , corresponding to 20–400 carrier haplotypes at the onset of selection .', 'In comparing the performance of PreCIOSS against iHS , we used the software selscan [78] to compute iHS scores .', 'To investigate the performance of HAF scores on human populations , we used a popular demographic model ( S11 Fig ) with parameters suggested from Gravel et al . ( 2011 ) [50] .', 'Among the different properties , the model assumes an out-of-Africa migration at 51 kya , and a European , East Asian split 23 kya .', 'The European Asian split was accompanied by a bottleneck event that reduced the effective population sizes of the European and Asian populations , and was followed by an exponential growth in these populations .', 'We used msms to simulate populations according to this model .', 'In modeling selection , we partitioned the onset of selection into two epochs: ‘pre-bottleneck’ events between 51 kya and 23 kya , and 23 kya , and ‘post-bottleneck’ epoch between 23 kya , and the current generation .', 'For each epoch , we picked 10000 times for onset of selection chosen uniformly from the time interval , and performed forward simulations with a sample size of n = 200 .', 'Samples were chosen during the sweeps , and partitioned according to carrier allele frequency , with 200 samples randomly chosen for each bin .', 'Samples in the pre-bottleneck epoch were simulated with s = 0 . 005 to reduce the chance of fixation , and s = 0 . 02 in the post-bottleneck epoch .', 'The balanced accuracy measurements were done independently for the two epochs .', 'We downloaded pre-phased haplotype data from the HapMap [51] project website .', 'Both HapMap 3 [51] and HapMap 2 [79] project data were used depending on whether the causal allele was sampled or not .', 'For LCT ( rs4988235 ) , we used 88 CEU individuals haplotypes from HapMap 3; for PSCA ( rs2294008 ) , we used 60 YRI individuals from HapMap 2; for TRPV6 , 88 CEU individuals from HapMap 3; for ADH1B ( rs1229984 ) , 90 CHB+JPT individuals from HapMap 2; and , for EDAR ( rs3827760 ) , we chose 90 CHB+JPT individuals from HapMap 2 .', 'The number of phased haplotypes was twice the number of individuals in each case .', 'We downloaded Chimpanzee genome alignments [52] to identify the ancestral allele .', 'A total of ∼93% of the sites analyzed had were covered by the Chimpanzee data .', 'For these sites , we set the ancestral allele to the Chimpanzee allele , and we discarded sites that were not covered .', 'The PreCIOSS software is available from the website http://bix . ucsd . edu/projects/precioss/ .']]
['Introduction', 'Results', 'Discussion', 'Methods']
['Methods for detecting the genomic signatures of natural selection have been heavily studied , and they have been successful in identifying many selective sweeps .', 'For most of these sweeps , the favored allele remains unknown , making it difficult to distinguish carriers of the sweep from non-carriers .', 'In an ongoing selective sweep , 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 .', 'The main contribution of this paper is the development and analysis of a new statistic , the Haplotype Allele Frequency ( HAF ) score .', 'The HAF score , assigned to individual haplotypes in a sample , naturally captures many of the properties shared by haplotypes carrying a favored allele .', 'We provide a theoretical framework for computing expected HAF scores under different evolutionary scenarios , and we validate the theoretical predictions with simulations .', 'As an application of HAF score computations , we develop an algorithm ( PreCIOSS: Predicting Carriers of Ongoing Selective Sweeps ) to identify carriers of the favored allele in selective sweeps , and we demonstrate its power on simulations of both hard and soft sweeps , as well as on data from well-known sweeps in human populations .']
['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 .']
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