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W4313009195 abstract "Full text Figures and data Side by side Abstract Editor's evaluation eLife digest Introduction Results Discussion Methods Appendix 1 Appendix 2 Data availability References Decision letter Author response Article and author information Metrics Abstract Ancient genome sequencing technologies now provide the opportunity to study natural selection in unprecedented detail. Rather than making inferences from indirect footprints left by selection in present-day genomes, we can directly observe whether a given allele was present or absent in a particular region of the world at almost any period of human history within the last 10,000 years. Methods for studying selection using ancient genomes often rely on partitioning individuals into discrete time periods or regions of the world. However, a complete understanding of natural selection requires more nuanced statistical methods which can explicitly model allele frequency changes in a continuum across space and time. Here we introduce a method for inferring the spread of a beneficial allele across a landscape using two-dimensional partial differential equations. Unlike previous approaches, our framework can handle time-stamped ancient samples, as well as genotype likelihoods and pseudohaploid sequences from low-coverage genomes. We apply the method to a panel of published ancient West Eurasian genomes to produce dynamic maps showcasing the inferred spread of candidate beneficial alleles over time and space. We also provide estimates for the strength of selection and diffusion rate for each of these alleles. Finally, we highlight possible avenues of improvement for accurately tracing the spread of beneficial alleles in more complex scenarios. Editor's evaluation This is an important manuscript that presents an elegant framework to infer the dynamics of beneficial alleles over time and space. The authors present a new method and show, convincingly, its utility and great potential to reconstruct the evolutionary history of beneficial alleles. The method is also applied to loci that likely mediated human genetic adaptations, contributing to our understanding of human recent evolution. The work will be of broad interest to evolutionary biologists who seek to understand the dynamics of beneficial mutations in populations. https://doi.org/10.7554/eLife.73767.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest Analyzing the genomes of our ancient ancestors can reveal how certain traits spread through the human population over the course of evolution. Mutations that make individuals better equipped to survive their environment are more likely to be passed on to the next generation and become more common. For example, a genetic variant that enables adult people to digest sugars in dairy products has become more common in humans over time. Yet evolution does not only happen across time: it transverses space as well. Modeling the geographic spread of such genetic mutations is challenging using existing methods. To overcome this, Muktupavela et al. developed a new computational method that uses modern and ancient human genomes to study the evolution of specific genetic variants across space and time. The tool can determine where certain variants first emerged, how quickly they spread across geographic areas, and how rapidly they became prevalent in human populations. Muktupavela et al. applied their new method, which was based on a previously published framework, to track the spread of two common genetic variations that have previously been reported to be subject to natural selection: one that allows adult humans to digest dairy products, and another associated with skin pigmentation. They found that the mutation that enabled dairy consumption originated around what is now southwestern Russia or eastern Ukraine. The variation then spread westward, becoming increasingly more common over the course of the Holocene. The mutation related to skin pigmentation emerged further south than the dairy-related variation, and then also spread westward. Massive human migrations during the Neolithic and Bronze Age eras may have helped disperse both variants. The model developed by Muktupavela et al. could help scientists track the geographic spread of other genetic variants in human populations, as well as provide new insights into how humans adapt to changing environmental conditions. Incorporating major events into the model, like mass migrations or glacial retreats, may lead to even more insights. Introduction Understanding the dynamics of the spread of a beneficial allele through a population is one of the fundamental problems in population genetics (Ewens, 2012). We are often interested in knowing the location where an allele first arose and the way in which it spread through a population, but this is often unknown, particularly in natural, non-experimental settings where genetic sampling is scarce and uneven. Patterns of genetic variation can be used to estimate how strongly natural selection has affected the trajectory of an allele and to fit the parameters of the selection process. The problem of estimating the age of a beneficial allele, for example, has yielded a rich methodological literature (Slatkin and Rannala, 2000), and recent methods have exploited fine-scale haplotype information to produce highly accurate age estimates (Mathieson and McVean, 2014; Platt et al., 2019; Albers and McVean, 2020). In contrast, efforts to infer the geographic origins of beneficial mutations are scarcer. These include Novembre et al., 2005, who developed a maximum likelihood method to model the origin and spread of a beneficial mutation and applied it to the CCR5-Δ32 allele, which was, at the time, considered to have been under positive selection (Stephens et al., 1998; Sabeti et al., 2005; Novembre and Han, 2012). Similarly, Itan et al., 2009 developed an approximate Bayesian computation (ABC) approach using demic simulations, in order to find the geographic and temporal origins of a beneficial allele, based on present-day allele frequency patterns. As ancient genome sequences become more readily available, they are increasingly being used to understand the process of natural selection (see reviews in Malaspinas et al., 2012; Dehasque et al., 2020). However, few studies have used ancient genomes to fit spatial dynamic models of the spread of an allele over a landscape. Most spatiotemporal analyses that included ancient genomes have used descriptive modeling in order to learn the spatiotemporal covariance structure of allele frequencies (Segurel et al., 2020) or hidden ancestry clusters (Racimo et al., 2020b), and then used that structure to hindcast these patterns onto a continuous temporally evolving landscape. In contrast to descriptive approaches, dynamic models have the power to infer interpretable parameters from genomic data and perhaps reveal the ultimate causes for these patterns (Wikle et al., 2019). Dynamic models can also contribute to ongoing debates about the past trajectories of phenotypically important loci. For example, the geographic origin of the rs4988235(T) allele—upstream of the LCT gene and associated with adult lactase persistence in most of Western Eurasia (Enattah et al., 2002)—remains elusive, as is the way in which it spread (an extensive review can be found in Ségurel and Bon, 2017). The allele has been found in different populations, with frequencies ranging from 5% up to almost 100%, and its selection coefficient has been estimated to be among the highest in human populations (Bersaglieri et al., 2004; Enattah et al., 2008; Tishkoff et al., 2007). However, the exact causes for its adaptive advantage are contested (Szpak et al., 2019), and it has been suggested that the selection pressures acting on the allele may have been different in different parts of the continent (Gerbault et al., 2009). Ancient DNA evidence shows that the allele was rare in Europe during the Neolithic (Burger et al., 2007; Gamba et al., 2014; Allentoft et al., 2015; Mathieson et al., 2015) and only became common in Northern Europe after the Iron Age, suggesting a rise in frequency during this period, perhaps mediated by gene flow from regions east of the Baltic where this allele was more common during the onset of the Bronze Age (Krüttli et al., 2014; Margaryan et al., 2020). Itan et al., 2009 deployed their ABC approach to model the spatial spread of the rs4988235(T) allele and estimated that it was first under selection among farmers around 7500 years ago possibly between the Central Balkans and Central Europe. Others have postulated a steppe origin for the allele (Allentoft et al., 2015), given that the rise in frequency appears to have occurred during and after the Bronze Age migration of steppe peoples into Western Eurasia (Haak et al., 2015; Allentoft et al., 2015). However, the allele is at low frequency in genomes of Bronze Age individuals associated with Corded Ware and Bell Beaker assemblages in Central Europe who have high steppe ancestry (Mathieson et al., 2015; Margaryan et al., 2020), complicating the story further (Ségurel and Bon, 2017). The origins and spread dynamics of large-effect pigmentation-associated SNPs in ancient Eurasians have also been intensely studied (Ju and Mathieson, 2020). Major loci of large effect on skin, eye, and hair pigmentation have been documented as having been under recent positive selection in Western Eurasian history (Voight et al., 2006; Sabeti et al., 2007; Pickrell et al., 2009; Lao et al., 2007; Mathieson et al., 2015; Alonso et al., 2008; Hudjashov et al., 2013). These include genes SLC45A2, OCA2, HERC2, SLC24A5, and TYR. While there is extensive evidence supporting the adaptive significance of these alleles, debates around their exact origins and spread are largely driven by comparisons of allele frequency estimates in population groups, which are almost always discretized in time and/or space. Among these, selection at the TYR locus is thought to have occurred particularly recently, over the last 5000 years (Stern et al., 2019), driven by a recent mutation (Albers and McVean, 2020) that may have spread rapidly in Western Eurasia. Here, we develop a method to model the spread of a recently selected allele across both space and time, avoiding artificial discretization schemes to more rigorously assess the evidence for or against a particular dispersal process. We begin with the model proposed by Novembre et al., 2005 and adapt it in order to handle ancient low-coverage genomic data and explore more complex models that allow for both diffusion and advection (i.e., directional transport) in the distribution of allele frequencies over space, as well as for a change in these parameters at different periods of time. We apply the method to alleles in two of the aforementioned loci in the human genome, which have been reported to have strong evidence for recent positive selection: LCT/MCM6 and TYR. We focus on Western Eurasia during the Holocene, where ancient genomes are most densely sampled, and infer parameters relevant to the spread of these alleles, including selection, diffusion and advection coefficients. Results Summary of model We based our statistical inference framework on a model proposed by Novembre et al., 2005 to fit allele frequencies in two dimensions to present-day genotype data spread over a densely sampled map. We extend this model in several ways: We incorporate temporally sampled data (ancient genomes) to better resolve changes in frequency distributions over time. We make use of genotype likelihoods and pseudohaploid genotypes to incorporate low-coverage data into the inference framework. We permit more general dynamics by including advection parameters. We allow the selection, advection, and diffusion parameters to be different in different periods of time. Specifically, to reflect changes in population dynamics and mobility before and after the Bronze Age (Loog et al., 2017; Racimo et al., 2020a), we partitioned the model fit into two time periods: before and after 5000 years BP. We explored the performance of two different spread models, which are extensions of the original model by Novembre et al., 2005, hereby called model A. This is a diffusion model containing a selection coefficient s (determining the rate of local allele frequency growth) and a single diffusion term (σ). A more general diffusion model—hereby model B—allows for two distinct diffusion parameters for latitudinal (σy) and longitudinal (σx) spread. Finally, model C is even more general and includes two advection terms (vx and vy), allowing the center of mass of the allele’s frequency to diverge from its origin over time. The incorporation of advection is meant to account for the fact that population displacements and expansions could have led to allele frequency dynamics that are poorly explained by diffusion alone. In order to establish a starting time point for our diffusion process, we used previously published allele age estimates obtained from a nonparametric approach leveraging the patterns of haplotype concordance and discordance around the mutation of interest (Albers and McVean, 2020). In the case of the allele in the LCT/MCM6 region, we also used age estimates based on an approximate Bayesian computation approach (Itan et al., 2009). Performance on deterministic simulations To characterize the accuracy of our inference method under different parameter choices, we first generated deterministic simulations from several types of diffusion models. First, we produced an allele frequency surface map with a specified set of parameters from which we drew 1040 samples matching the ages, locations, and genotype calling format (diploid vs. pseudohaploid) of the 1040 genomes that we analyze below when studying the rs1042602(A) allele. We generated six different simulations with different diffusion coefficients and afterward ran our method assuming model B. The results (simulations B1−B6) are summarized in Figure 1, Figure 1—figure supplements 1–5, and Appendix 2—table 1. Overall, the model is more accurate at correctly inferring the parameters for the time period before 5000 years BP (Figure 1b), with decreased performance when longitudinal diffusion is high (Figure 1—figure supplement 5). Figure 1 with 7 supplements see all Download asset Open asset Comparison of true and inferred allele frequency dynamics for simulation B5. (a) Comparison of true and inferred allele frequency dynamics for a simulation with diffusion and no advection (B5). The green dot corresponds to the origin of the allele. The parameter values used to generate the frequency surface maps are summarized in Appendix 2—table 1. (b) Comparison of true parameter values and model estimates. Whiskers represent 95% confidence intervals. Next, we investigated the performance of model C, which includes advection coefficients. We generated four different simulations including advection (simulations C1−C4: Figure 2, Figure 1—figure supplements 1–3, and Appendix 2—table 2). We found that our method is generally able to estimate the selection coefficient accurately. However, in some of the simulations, we found discrepancies between the estimated and true diffusion and advection coefficients, often occurring because of a misestimated origin forcing the other parameters to adjust in order to better fit the allele frequency distribution in later stages of the allele’s spread (Figure 2). Despite the disparities between the true and inferred parameter values, the resulting surface plots become very similar as we approach the present, suggesting that different combinations of parameters can produce similar present-day allele frequency distributions. Figure 2 with 3 supplements see all Download asset Open asset Comparison of true and inferred allele frequency dynamics for simulation C4. (a) Comparison of true and inferred allele frequency dynamics for one of the simulations including advection (C4). The green dot corresponds to the origin of the allele. The parameter values used to generate the frequency surface maps are summarized in Appendix 2—table 2. (b) Comparison of true parameter values and model estimates. Whiskers represent 95% confidence intervals. Advection model applied to non-advection simulations We assessed model performance when we apply model C, which includes advection coefficient estimates, to simulations generated without advection (see Figure 1—figure supplements 6 and 7). We can observe that the advection coefficients are inferred to be non-zero (Figure 1—figure supplements 6b and 7b); however, the inferred allele frequency dynamic plots closely resemble the ones obtained with true parameter values (Figure 1—figure supplements 6a and 7a). This shows that complex interactions between the diffusion and advection coefficients can result in similar outcomes even when only diffusion is considered in the model. The inference of the origin of the allele also differs when we compare results when using models B and C. In order to understand better how the model estimates the allele origin, we highlighted the first individual in simulations B1 and B4 that contains the derived allele. We can see that in the case of simulation B1 the inferred origin of the allele is close to the first observance of the derived allele in the model that includes advection. In contrast when the advection is not included, the origin of the allele is inferred to be closer to where it is initially rising in frequency (Figure 1—figure supplements 1a and 4a). However, this is not always the case. For instance, if we look at the results from the advection model on simulation B4, we can see that the origin of the allele is inferred relatively far from the sample known to have carried the first instance of the derived allele. Therefore, if there is a relatively large interval between the time when the allele originated and when the first ancient genomes are available, the beneficial allele can spread widely, but as this spread is not captured by any of the data points, inference of the precise origin of the selected allele is nearly impossible. Impact of sample clustering on parameter estimates We evaluated the impact of different sampling and clustering schemes on our inferences that could potentially arise by aggregating aDNA data from studies with different sampling schemes. We used a deterministic simulation to create three different degrees of clustering, which we will refer to as ‘homogeneous,’ ‘intermediate,’ or ‘extreme’ by varying the area from which we sample individuals to be used in our inferences (Figure 3—figure supplement 1). Additionally, we also tested the impact of biased temporal sampling in the periods before and after 5000 years BP by oversampling in the ancient period (75%/25%), equally sampling in the two periods (50%/50%), and oversampling in the recent period (25%/75%). Because we evaluated this temporal bias for each of the three spatial clustering sampling scenarios, this resulted in a total of nine different sampling scenarios. We note that the third ‘extreme’ spatial clustering scenario is completely unrealistic and one would not expect inferences of any degree of accuracy from it, but we believe it gives a good idea of the behavior of our method in the limiting case of extremely restricted spatial sampling. A comparison of allele frequency maps generated using true parameter values and using parameter estimates from the different sampling schemes is shown in Figure 3—figure supplements 2–9. In Figure 3 we show the allele frequency map generated using the ‘intermediate 75%/25%’ clustering scheme. Parameter estimates used to generate all these figures are summarized in Appendix 2—table 3. Overall we can see that the allele frequency maps inferred from these scenarios closely resemble the maps generated using the true parameter values, despite the challenges in finding accurate values for the individual point estimates of some of the parameters, highlighting that various combinations of diffusion and advection coefficients can produce similar underlying frequency maps (as discussed in the section ‘Performance on deterministic simulations’). This suggests that the joint spatiotemporal information encoded in the inferred maps (not just the individual parameters estimates) should be used in interpreting model outputs, particularly when it comes to the advection and diffusion parameters. The selection coefficient estimates are inferred highly accurately, regardless of the sampling scheme chosen, and lie close to the true value, with only a slight underestimation in the time period after 5000 years BP (with the exception of the ‘extreme 25%/75%’). Figure 3 with 9 supplements see all Download asset Open asset Comparison of true allele frequency map and map generated using ‘intermediate 75%/25%’ clustering scheme. Left: allele frequency map generated using true parameter values. Right: allele frequency map generated using parameter estimates for ‘intermediate 75%/25%’ clustering scheme. Parameter values used to generate the maps are summarized in Appendix 2—table 3. Spatially explicit forward simulations In addition to drawing simulated samples from a diffusion model, we used SLiM (Haller and Messer, 2019) to perform spatially explicit individual-based forward-in-time simulations of selection acting on a beneficial allele by leveraging an R interface for spatial population genetics now implemented in the R package slendr (Petr, 2021). We introduced a single beneficial additive mutation in a single individual and let it evolve across the European landscape. Before applying our method on the simulated data, we sampled 1040 individuals whose ages were log-uniformly distributed to ensure that there were more samples closer to the present, as in the real data. We transformed the diploid genotypes to pseudohaploid genotypes by assigning a heterozygous individual an equal probability of carrying the ancestral or the derived genotype. The parameter values estimated by our model to the simulations described in this section are summarized in Appendix 2—table 4. We can see that the origin of the allele inferred by the model closely corresponds to the first observation of the derived allele in the simulation (Figure 4). The inferred selection coefficient is only slightly higher than the true value from the simulation (0.0366 vs. 0.030). In general, the model accurately captures the spread of the allele centered in Central Europe, though we observe some discrepancies due to differences between the model assumed in the simulation (which, e.g., accounts for local clustering of individuals, Figure 4—figure supplement 1), and that assumed by our diffusion-based inference. Figure 4 with 1 supplement see all Download asset Open asset Comparison of an individual-based simulation and allele frequency dynamics inferred by the diffusion model. (A) Individual-based simulation of an allele that arose in Central Europe 15,000 years ago with a selection coefficient of 0.03. Each dot represents a genotype from a simulated genome. To avoid overplotting, only 1000 out of the total 20,000 individuals in the simulation in each time point are shown for each genotype category. (B) Allele frequency dynamics inferred by the diffusion model on the individual-based simulation to the left, after randomly sampling 1040 individuals from the simulation and performing pseudohaploid genotype sampling on them. The ages of sampled individuals were log-uniformly distributed. The estimated parameter values of the fitted model are shown in Appendix 2—table 4. Dynamics of the rs4988235(T) allele Having tested the performance of our method on simulated data, we set out to infer the allele frequency dynamics of the rs4988235(T) allele (associated with adult lactase persistence) in ancient Western Eurasia. For our analysis, we used a genotype dataset compiled by Segurel et al., 2020, which amounts to 1434 genotypes from ancient Eurasian genomes individuals, and a set of 36,659 genotypes from present-day Western and Central Eurasian genomes (Ségurel and Bon, 2017; Heyer et al., 2011; Marchi et al., 2018; Liebert et al., 2017; Gallego Romero et al., 2012; Itan et al., 2010; Charati et al., 2019). After filtering out individuals falling outside of the range of the geographic boundaries considered in this study, we retained 1332 ancient individuals. The locations of ancient and present-day individuals used in the analysis to trace the spread of rs4988235(T) are shown in Figure 5. Figure 5 Download asset Open asset Locations of samples used to model the spread of the rs4988235(T) allele. The upper panel shows the spatiotemporal locations of ancient individuals, and the bottom panel represents the locations of present-day individuals. We used a two-period scheme by allowing the model to have two sets of estimates for the selection coefficient and the diffusion and advection coefficients in two different periods of time: before and after 5000 years ago, reflecting the change in population dynamics and mobility before and after the Bronze Age transition (Loog et al., 2017; Racimo et al., 2020a). We used two allele age estimates as input: a relatively young one (7441 years ago) obtained by using the estimated start of selection onset from Itan et al., 2009 (though we note this is necessarily a lower bound of the age of mutation origin), and a relatively old one (20,106 years ago) obtained from the age estimate from Albers and McVean, 2020. The results obtained for fitting the model on rs4988235(T) are summarized in Appendix 2—table 5 and Appendix 2—table 6, and in Figure 6b (younger age) and Figure 6—figure supplement 1 (older age). Figure 6 with 9 supplements see all Download asset Open asset Allele frequency dynamics of rs4988235(T). (a) Top: pseudohaploid genotypes of ancient samples at the rs4988235 SNP in different periods. Yellow corresponds to the rs4988235(T) allele. Bottom: allele frequencies of present-day samples represented as pie charts. The size of the pie charts corresponds to the number of available sequences in each region. (b) Inferred allele frequency dynamics of rs4988235(T). The green dot indicates the inferred geographic origin of the allele. Assuming the mutation age estimate is equivalent to the start of selection onset from Itan et al., 2009, the origin of the allele is estimated to be north of the Caucasus, around what is now southwestern Russia and eastern Ukraine (Figure 6b). Given that this age is relatively young, our method fits a very strong selection coefficient (≈0.1) during the first period in order to accommodate the early presence of the allele in various points throughout Eastern Europe, and a weaker (but still strong) selection coefficient (≈0.03) in the second period. We also estimate stronger diffusion in the second period than in the first, to accommodate the rapid expansion of the allele throughout Western Europe, and a net westward advection parameter, indicating movement of the allele frequency’s center of mass to the west as we approach the present. Assuming the older age estimate from Albers and McVean, 2020, the origin of the allele is estimated to be in the northeast of Europe (Figure 6—figure supplement 1), which is at a much higher latitude than the first occurrence of the allele, in Ukraine. Due to the deterministic nature of the model, the frequency is implicitly imposed to expand in a region where there are no actual observed instances of the allele. The model compensates for this by placing the origin in an area with a lower density of available aDNA data and thus avoiding an overlap of the increasing allele frequencies with individuals who do not carry the derived rs4988235(T) allele (see Figure 6a). As the model expands rapidly in the southern direction (Appendix 2—table 6) it eventually reaches the sample carrying the derived variant in Ukraine. Dynamics of the rs1042602(A) allele Next, we investigated the spatiotemporal dynamics of the spread of an allele at a pigmentation-associated SNP in the TYR locus (rs1042602(A)), which has been reported to be under recent selection in Western Eurasian history (Stern et al., 2019). For this purpose, we applied our method to the Allen Ancient DNA Resource data (Reich and Mallick, 2019), which contains randomly sampled pseudohaploid genotypes from 1513 published ancient Eurasian genomes (listed in Supplementary file 1), from which we extracted those that had genotype information at this locus in Western Eurasia. We merged this dataset with diploid genotype information from high-coverage present-day West Eurasian genomes from the Human Genome Diversity Panel (HGDP) (Bergström et al., 2020), which resulted in a total of 1040 individuals with genotype information at rs1042602, which were used as input to our analysis. Geographic locations of individuals in the final dataset are shown in Figure 7. Figure 7 Download asset Open asset Spatiotemporal sampling locations of sequences used to model the rs1042602(A) allele in Western Eurasia. Upper panel: ancient individuals dated as older than 10,000 years ago. Middle panel: ancient individuals dated as younger than 10,000 years ago. Bottom panel: present-day individuals from the Human Genome Diversity Panel (HGDP). Similarly to our analysis of the spread of the allele in rs4988235(T), we inferred the dynamics of the rs1042602(A) allele separately for the time periods before and after 5000 years BP and assuming the age of the allele to be 26,361 years (Albers and McVean, 2020). The inferred parameters for both time periods are summarized in" @default.
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W4313009195 title "Editor's evaluation: Modeling the spatiotemporal spread of beneficial alleles using ancient genomes" @default.
W4313009195 doi "https://doi.org/10.7554/elife.73767.sa0" @default.
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