ABSTRACT
Quantifying and comparing the amount of adaptive evolution among different species is key to understanding evolutionary processes. Previous studies have shown differences in adaptive evolution across species, however their specific causes remain elusive. Here, we use improved modeling of weakly deleterious mutations and the demographic history of the outgroup species and estimate that 30–34% of nonsynonymous substitutions between humans and outgroup species have been fixed by positive selection. This estimate is much higher than previous estimates, which did not account for the population size of the outgroup species. Next, we directly estimate the proportion and selection coefficients of newly arising strongly beneficial nonsynonymous mutations in humans, mice, and D. melanogaster by examining patterns of polymorphism and divergence. We develop a novel composite likelihood framework to test whether these parameters differ across species. Overall, we reject a model with the same proportion and the same selection coefficients of beneficial mutations across species, and estimate that humans have a higher proportion of beneficial mutations compared to Drosophila and mice. We demonstrate that this result cannot be attributed to biased gene conversion. In summary, we find the proportion of beneficial mutations is higher in humans than in D. melanogaster or mice, suggesting that organismal complexity, which increases the number of steps required in adaptive walks, may be a key predictor of the amount of adaptive evolution within a species.
INTRODUCTION
Since the inception of molecular population genetics, there has been tremendous interest in quantifying the amount of adaptive evolution in different organisms. The neutral theory of molecular evolution postulated that beneficial mutations are rare, and many of the substitutions between species are neutral 1. One early challenge to this theory originated from a comparison of polymorphism and substitutions (also known as divergence) at synonymous sites and nonsynonymous sites in Drosophila 2,3. Under models without positive selection, the ratio of nonsynonymous to synonymous changes should remain equal when comparing polymorphisms and substitutions. In contrast to this prediction, a genome-wide excess of nonsynonymous substitutions between species was observed, a pattern indicative of an abundance of positive selection in Drosophila. More formally, Smith and Eyre-Walker (2002) proposed a statistic, alpha, which is the proportion of nonsynonymous substitutions between species that can be attributed to positive selection. Application of their approach in Drosophila has found that at least 40% of nonsynonymous substitutions have been fixed by positive selection 3.
Since the publication of the original study, alpha has been estimated from different species across the tree of life 4. Estimates of alpha vary tremendously across species, tending to be higher in insects 5,6, but much lower in primates 6,7 and plants 8. In these latter species, formal tests have been unable to reject that alpha is zero (i.e. no positive selection) 6,7,9. It is not clear why alpha varies across species. One possibility is that alpha is higher for species with larger population sizes, which could occur if adaptation is mutation limited, and therefore species with larger population sizes would have more beneficial mutations. The fixation probability of a given beneficial mutation also would be higher in species with larger population size, but this effect is likely to only be important for very weakly beneficial mutations. Evidence indicates that, in some cases, alpha is indeed related to population size. For example, Phifer-Rixey et al. found that estimates of alpha were higher for species of mice that have larger population sizes compared to species with smaller population sizes 10. Further, recent studies have found a positive correlation between alpha and population size when comparing different species of sunflowers 11 and from phylogenetically diverse taxa 12. More recently, Galtier found a positive correlation between alpha and effective population size for 44 animal species 13. Additional evidence that there is more positive selection in larger populations stems from recent analyses of linked selection. Corbett-Detig et al. found increased evidence for linked selection in species with larger population sizes, though the mechanism driving this pattern is not immediately clear 14. Further, Nam et al. have suggested that across primates, species with larger population sizes have had more selective sweeps 15.
While evidence suggests that adaptation could be mutation limited and this could be driving the variation in alpha across species, it is important to note that other factors could be influencing the alpha statistic16. By definition, alpha is the proportion of nonsynonymous substitutions attributable to positive selection. As such, it is heavily influenced by the total number of substitutions and thus the number of substitutions attributable to the fixation of weakly deleterious mutations. For two populations with the same number of beneficial substitutions, the one with a higher number of substitutions due to weakly deleterious mutations will have a lower alpha. Indeed, because the number of weakly deleterious mutations fixed is inversely related to population size, this effect could drive the correlation between alpha and population size. In support of this prediction, Galtier found that the rate of adaptive divergence showed no correlation with population size 13. Similar arguments have been made by Phifer-Rixey et al. 10
A recent conceptual and theoretical investigation of beneficial mutations under Fisher’s geometric model found that population size was a poor predictor of alpha and the rate of adaptive divergence 17. Instead, organismal complexity (here defined as the number of phenotypes under selection) and the rate of environmental changes were better predictors of alpha. They also point out that the distribution of fitness effects (DFE) for newly arising beneficial mutations likely differs with population size. Because small populations likely have had more fixations of weakly deleterious alleles, they are further from the fitness optimum. Thus, small populations then have the potential for more new beneficial mutations compared to larger populations.
In summary, the amount of adaptive evolution in disparate species with varying population sizes remains elusive. Equally unclear is the best metric to quantify the amount of positive selection in distinct species. Boyko et al. found that by assuming some fraction (0 to 1.86%) of new mutations is positively selected, they could better match the frequency spectrum of polymorphisms and the counts of human-chimpanzee differences. Importantly, models with weaker selection coefficients for beneficial mutations tended to have a higher proportion of positively selected mutations than models with stronger selection 7. Further, by fitting a DFE from Fisher’s Geometric model to polymorphism data in humans and Drosophila melanogaster, Huber et al. found a higher proportion (14%) of new weakly beneficial mutations in humans compared to Drosophila (<1%) 18. They attributed this higher estimate of the proportion of new beneficial mutations in humans as compensating for deleterious alleles that became fixed due to the small population size that in turn moved the human population away from the fitness optimum.
However, direct comparison the DFEs of beneficial mutations across species has not been performed rigorously before, and in previous work on estimating alpha, there were unjustified assumptions about the demography of the outgroup species that can have substantial impacts on the inference. Here we directly estimate the proportion and selection coefficients of newly arising strongly beneficial mutations in humans, mice, and D. melanogaster by examining patterns of polymorphism and divergence. We then develop a composite likelihood framework to test whether these parameters differ across species. This approach enables a more direct comparison of the amount of beneficial mutations across different species, and is also less confounded by the fixation of weakly deleterious mutations. Overall, we reject a model with the same proportion and the same selection coefficients of beneficial mutations across species, and estimate that humans have a higher proportion of beneficial mutations compared to Drosophila and mice. Using improved modeling of weakly deleterious mutations and demographic models, particularly correcting for the population size of outgroup species, we estimate that 30–34% of nonsynonymous substitutions between humans and the outgroup is driven by positive selection, much higher than previously thought. In addition, we explore the effect of biased gene conversion (BGC) on our estimates of adaptive evolution by looking at subsets of sites that are unaffected by BGC and find that while BGC influence our estimates of positive selection in a species-specific manner, it cannot account for our main findings that the proportion and strength of beneficial mutations differ across species.
RESULTS
Estimates of alpha for multiple species
We first estimated alpha from coding regions of humans, mice and D. melanogaster. We analyzed published genomic datasets to obtain counts of synonymous and nonsynonymous polymorphisms (PS and PN, respectively) as well as synonymous and nonsynonymous substitutions between species (DS and DN, respectively). In total, 19.1Mb of coding sequence for human, 26.6 Mb of coding sequence for mice and 15.8Mb of coding sequence for D. melanogaster were used in our analysis (see Methods). For computation of alpha in humans, we used chimpanzee and macaque as outgroup species. For mice, we used rat as outgroup, and for D. melanogaster, we used D. simulans as the outgroup species (see Methods).
Alpha was first estimated using an extension of the McDonald-Kreitman (MK) test (Smith and Eyre-Walker 2002b; equation (2); table 1; supplementary table S1). To examine the effect of slightly deleterious mutations on alpha, we also filtered the data with several minor allele frequency (MAF) cutoffs (supplementary table S2). After removing low frequency polymorphisms with MAF less than 20%, the estimated alpha is close to zero for humans when using chimpanzee as outgroup species (table 1), consistent with previous estimates of alpha in humans 6,7. However, when using macaque as the outgroup species, the estimate of alpha is -0.22 (table 1), suggesting that the choice of outgroup species could greatly influence alpha. Nevertheless, these results suggest at most only a very small proportion of nonsynonymous substitutions have been fixed by positive selection in the human lineage. In contrast, for D. melanogaster and mice, the estimated alpha is 49% and 40%, respectively, with MAF filter at 20% (table 1). Both of these estimates of alpha are comparable to those seen in previous studies 5,6,10. These results suggest that the proportion of substitutions fixed by positive selection varies drastically across species, and for species with larger population sizes, like mice and D. melanogaster, adaptive forces may have had a greater contribution to divergence.
Model based inference of alpha
Due to these concerns regarding estimating alpha directly from MK table counts, model-based approaches to quantify alpha have been developed. Boyko et al. and Eyre-Walker et al. estimated alpha as the proportion of the observed nonsynonymous substitutions (DNO) that cannot be explained by models with only neutral and deleterious mutations 6,7. Specifically, they assume a DFE for deleterious and neutral mutations as well as a demographic model, and predicted the expected number of nonsynonymous substitutions (DNE). The excess of DNO compared to the DNE is attributed to fixations driven by positive selection. Here, we have extended the approach of Boyko et al. using prfreq 7 and applied it to data from humans, mice and D. melanogaster (see Methods).
Because a wide range of divergence times were reported in previous studies for each species, we estimate divergence time that best fit our data using the observed DS. We then use prfreq to predict DN using this estimated divergence time, the gamma-distributed DFE, and the demographic model (see Methods). Applying this framework using chimpanzee as the outgroup species, we initially estimated that 15% of the nonsynonymous substitutions between humans and chimp were driven by positive selection (table 1). Our estimate is comparable to the inference by Boyko et al., where authors implemented similar approach and estimated that approximately 10% of human-chimp nonsynonymous substitutions were fixed by positive selection 7.
Interestingly, when using macaque as the outgroup species, we estimate the proportion of nonsynonymous substitutions fixed by positive selection in humans is close to zero, using the aforementioned framework (table 1). While it is possible that this difference could reflect distinct evolutionary events experienced by different outgroups or different periods of history, we consider that it could be an artifact of the modeling assumptions. Specifically, one assumption of prfreq is that the effective population size of the outgroup species is the same as the ancestral population size, which is not the case for the species considered here, especially for humans, chimpanzees, and macaques. The inferred human ancestral size is 7067, which is much smaller than previous estimates of the human-macaque or human-chimp ancestral population sizes in the range of tens of thousands 20–25. Using a population size for the outgroup species that is too small likely biases estimate of alpha because more of the nonsynonymous substitutions could be attributed to the fixation of weakly deleterious mutations, causing alpha to be under-estimated.
To more accurately model the larger outgroup population size in chimpanzees and macaques, we add an additional ancient epoch where the population size is 73,000 individuals before the time of the human-chimpanzee divergence in our initial two-epoch human demographic model (supplementary table S4), which is within the range of estimated population sizes of human-chimpanzee and human-macaque common ancestors (see Methods). This is our three-epoch model. Because this added epoch is ancient, it does not affect the polymorphism pattern within humans (see Methods). Importantly, the larger ancient population size better reflects the effective population size of the outgroup species, thus yielding a more accurate estimate of the number of substitutions between species. Using the modified three-epoch model for humans, we obtain comparable estimates of alpha regardless of our outgroup choice. Specifically, we estimate approximately 33% of human-chimpanzee nonsynonymous substitutions were fixed by positive selection and approximately 30% of human-macaque nonsynonymous substitutions were fixed by positive selection (supplementary table S1). Importantly, our estimates of alpha in humans using the more realistic three-epoch demographic model are much higher than the previously reported estimates 7, implying that there is a greater contribution of positive selection to nonsynonymous substitutions than previously appreciated.
Similarly, we improved the two-epoch models of D. melanogaster and mice to three-epoch models by including an additional ancient epoch at the time of divergence with their outgroup species. Specifically, for D. melanogaster it had been inferred that D. simulans have slightly larger Ne 26, so we added an ancient epoch of 1.5× the current population size at the D. melanogaster and D. simulans split (supplementary table S4). For mice, a previous study estimated that the outgroup rat species has an effective population size about fivefold lower than wild house mice 27. Thus we added an ancient epoch that was 0.2× the current population size of mice (supplementary table S4). Using the three-epoch models for D. melanogaster and mice, we estimated their alpha to be 68% and 38%, respectively (table 1, supplementary table S1) compared with 58% for D. melanogaster and 48% for mice (table 1, supplementary table S1) using the original two-epoch model. The differences between these estimates reflect the importance of accurately modeling the population size of outgroup species for calculations of alpha.
When we apply DFE-alpha to our three species, alpha is estimated to be 24% for humans using chimpanzee as outgroup, 2% for humans using macaque as outgroup, 71% for D. melanogaster, and 51% for mice (table 1). These estimates are all slightly higher compared to estimates from our two-epoch models. However, the estimates of alpha computed for humans differ significantly depending on whether the macaque or chimpanzee is used as the outgroup. We additionally estimate alpha for substitutions that occurred on the human lineage, using the human-macaque alignment to polarize substitutions between human and chimp (see Methods). We estimate that alpha equals 18.3% using the 2-epoch model and 19.7% using the 3-epoch model.
Test whether p+ and s+ differ across species
Thus far we have examined the proportion of nonsynonymous substitutions that have been fixed by positive selection. This is the outcome of the evolutionary process and is a function of the input of beneficial mutations as well as how they are affected by demography and natural selection. Here we take a different approach to quantify the properties of new beneficial mutations. Specifically, we estimate the DFE including new beneficial mutations. Our model of the DFE includes two additional parameters compared to the base model that only includes deleterious mutations. For each species, we estimate the proportion of new mutations that are beneficial (p+) and their selection coefficient (s+). We then test whether these two parameters differ across species.
The number of nonsynonymous substitutions (DN) is Poisson distributed 28, with rate parameter equal to: where G(s) is the DFE of deleterious and neutral mutations, u(s) is the fixation probability of deleterious and neutral mutations, u(s+) is the fixation probability of beneficial mutations, and p+ is the proportion of beneficial mutations. We then use a Poisson log-likelihood function for DN in each species and a series of likelihood ratio tests to determine whether p+ and s+ differ across species (see Methods).
Using this framework, we find that the full model H1, where each species is allowed to have its own p+ and s+, fits DN significantly better than the constrained null model, where p+ and s+ are constrained to be the same across all three species (Likelihood Ratio Test (LRT)) statistic Λ=122,724, df=4, P<10-16; fig. 1; supplementary table S5). Taking the MLEs of p+ and s+ for the full model, we predicted DN between species, which matched the observed DN (supplementary fig. S1). When we used the MLEs for the constrained model, the predicted DN did not match the observed DN (supplementary fig. S1).
We estimate that humans have a higher proportion of strongly beneficial nonsynonymous mutations than Drosophila and mouse (supplementary table S5 and fig. 1). Specifically, we estimate that approximately 2.15% of new nonsynonymous mutations in humans are beneficial with a selection coefficient of approximately 2.45E-05 (outgroup: chimpanzee), approximately 0.0075% of new nonsynonymous mutations in D. melanogaster are beneficial with a selection coefficient of approximately 4.99E-05, and approximately 1.97% of new nonsynonymous mutations in mice are beneficial with a selection coefficient of 1.21E-05 (supplementary table S5). It is important to point out that models with a larger selection coefficient tend to have a lower proportion of positively selected mutations than models with weaker selection. Consequently, the likelihoods of these parameter values can be very close to the likelihoods at the MLEs.
To examine if any two species out of three share the same values of p+ and s+, we performed LRTs comparing each pair of species. In all pairwise tests, the model where each species has its own p+ and s+ fits the observed DN significantly better than a model where p+ and s+ are constrained to be the same in the tested two species (supplementary table S5). These results suggest each species has their own unique values of p+ and s+. This result is robust regardless of outgroup species and demography (supplementary table S5).
We next investigated whether it is possible that either p+ or s+ is the same across species, but the other parameter varies. Specifically, we allowed p+ to differ across species, then explored whether a model with the same s+ could fit all species. This is shown in conditional likelihood plots, where assuming the same s+ for all species, humans would need a higher proportion of beneficial mutations compared to mice and D. melanogaster to match the observed DN (fig. 2A). Similarly, allowing s+ to differ across species, a model with the same p+ across all species could fit the data. When we forced the same p+ for all species, s+ for beneficial mutations in humans would be larger compared to that in mice and D. melanogaster (fig. 2B). However, for the same p+ value, s+ could not be the same in all species. Similarly, for the same s+ value, p+ could not be the same across species.
Test whether gamma+ and p+ differ across species
Humans, D. melanogaster, and mice have drastically different population sizes. These different population sizes can influence the efficacy of selection within each species. Thus, we next examined whether the selection coefficient scaled by current population size (gamma+=2Ns+) and p+ differ across species.
We find the model (Full model H1) where each species has its own different gamma+ and p+ fits the observed DN significantly better than a model (constrained model H0) where gamma+ and p+ are constrained to be the same across all three species (LRT statistic Λ=30,061; df=4, P<10-16, fig. 3 and supplementary table S5). Taking the MLEs of gamma+ and p+ for the full model, we predict DN between species, which matches the observed DN. When using the MLEs for the constrained model, the predicted DN does not match the observed data (supplementary fig. S1).
Under the full model, we estimate that approximately 1% of new nonsynonymous mutations in humans are beneficial with gamma+ of 1.38, approximately 2% of new nonsynonymous mutations in D. melanogaster are beneficial with gamma+ of 1.95, and approximately 4% of new nonsynonymous mutations in mice are beneficial with gamma+ of 4.8 (supplementary table S5). Similarly, models with stronger gamma+ tended to have a lower proportion of positively selected mutations than models with weaker selection, and the likelihoods can be very close to those at the MLEs. The current population sizes are 16539, 7616700, 488948 for humans, D. melanogaster and mice, respectively. As a result, we are searching for p+ within the same range of gamma+ (see Methods), but markedly different ranges of s+ for these three species. Thus, the relative ordering of the MLEs of p+ across species considering gamma+ is not necessarily the same as that for the s+ results described above.
To examine if any two species out of three may share the same values of gamma+ and p+, we performed LRTs comparing each pair of species. We find that the model where each species has its own different gamma+ and p+ fit the observed DN significantly better than a model where gamma+ and p+ are constrained to be the same in the tested two species (supplementary table S5). Thus each species likely has its unique gamma+ and p+. This result is generally robust regardless of outgroup species. However, when using the human two-epoch model, we cannot reject the hypothesis that human and Drosophila have the same gamma+ and p+ (supplementary table S5). One must note that the difference in chimpanzee population size with human ancestor population size is well established in literature 20–25, so the two-epoch model makes unrealistic assumptions and thus, this comparison is not meaningful.
We next investigated whether it is possible that either gamma+ or p+ is the same across species, while the other parameter varies. The results are shown in conditional likelihood plots, where with the same gamma+ for all species, humans would need a lower proportion of beneficial mutations compared to mice and Drosophila to fit the observed DN (supplementary fig. S2A). Similarly, allowing gamma+ to differ across species, a model with the same p+ could fit all species. When we force the same p+ for all species, humans have smaller gamma+ for beneficial mutations (supplementary fig. S2B). However, for the same p+ value, gamma+ cannot be the same in all species. Similarly, for the same gamma+ value, p+ cannot be the same across species.
Effects of biased gene conversion
Biased gene conversion (BGC) is the preferred transmission of G/C alleles (S: strong alleles) at the expense of A/T alleles (W: weak alleles). This process is common in mammals, including two of our three targeted species: humans and mice. BGC could impact patterns of genetic diversity significantly 29–31 and bias estimates of rate of positive selection32, especially when comparing between species with BGC and species without BGC, i.e. D. melanogaster 33.
To test whether BGC drives the observed pattern of positive selection across species, we filtered the human and mouse data to keep only strong to strong or weak to weak mutations (herein called SSWW mutations), which are not affected by BGC. For humans, the filtered SSWW polymorphisms have a similar SFS as the full dataset (supplementary fig. S3A). Thus we use the demographic and DFE parameters estimated from the full data. We used the observed number of synonymous SSWW polymorphisms to estimate the mutation rate of human SSWW mutations to be 3.14E-09, which is comparable to the previous estimates 30,34. Following the method used on the full data, we re-estimate the human-chimpanzee divergence time that fits best to the observed SSWW DS. We then use prfreq to predict the SSWW DN using this new estimated divergence time, DFE, and demographic models (supplementary table S1). We estimate that under the two-epoch demographic model and the improved three-epoch model, approximately 17.1% or approximately 34.3% of the observed SSWW DN in humans using chimpanzee as outgroup was driven by positive selection, respectively (table 1). These estimates of alpha from SSWW sites are slightly elevated but are comparable to the estimates from the full dataset (table 1).
For mice, however, the SFS of SSWW polymorphism has a very different shape compared to the SFS from the full dataset (supplementary fig. S3B). Thus, we re-estimated the demographic and DFE parameters for mice SSWW mutations (supplementary table S3; see Methods).
We then estimate that under the two-epoch demographic model and the improved three-epoch model, approximately 33.4% and 19.2% of the observed SSWW DN in mice was driven by positive selection, respectively (table 1, supplementary table S1). These estimates of proportion of positive selection from SSWW mutations are much lower than those estimated from the full dataset (table 1). This suggests that biased gene conversion may account for some of the nonsynonymous substitutions between mouse and rat.
Removing the effect of BGC in humans and mice by using only the SSWW changes in these two species and the full dataset of D. melanogaster, we again quantify and compare the strength and proportion of new beneficial mutations across all three species. Using the same composite likelihood framework as above, we find that the model where each species has its own p+ and s+ fits the observed DN significantly better than a model where p+ and s+ are constrained to be the same across all three species (LRT statistic Λ=3,213, df=4, P<10-16; fig. 4; supplementary table S5). Models comparing each pair of species suggest that each species has its own unique p+ and s+, regardless of outgroup and demography (supplementary table S4). Allowing p+ to differ across species, a model with the same s+ across all species could fit the data, and vice versa. When we force the same s+ for all species, humans still have the highest proportion of new beneficial mutations, D. melanogaster has the smallest proportions of new beneficial mutations, and mice have an intermediate proportion of beneficial mutations (fig. 4). When we force the same p+ for all species, humans have the largest selection coefficient, D. melanogaster has the weakest selection coefficient, and mice have an intermediate selection coefficient (fig. 4).
Lastly, we find that the model where each species has its own p+ and gamma+ fits the observed DN significantly better than a model where p+ and gamma+ are constrained to be the same across all three species (LRT Λ=1,114, df=4, P<10-16; supplementary fig. S4; supplementary table S5). For pairwise comparisons, however, we cannot reject the null hypothesis that D. melanogaster and mice have the same p+ and gamma+ (supplementary table S5). Only under uncorrected demographic scenarios (i.e. human two-epoch), sometimes we cannot reject humans and D. melanogaster, or humans and mice having the same p+ and gamma+ supplementary table S5). These results are also reflected in the conditional likelihood plots. Allowing p+ to differ across species, a model with the same gamma+ across all species could fit the data, and vice versa. When we force the same gamma+ for all species, humans have the smallest proportion of new mutations being beneficial, while D. melanogaster and mice both have higher proportions of beneficial mutations than humans. But D. melanogaster and mice could have the same or different proportions, depending on the gamma+ (supplementary fig. S4). When we force the same p+ for all species, humans have the lowest gamma+, and D. melanogaster and mice both have a higher gamma+, but their relative strength with each other depends on p+ (supplementary fig. S4).
DISCUSSION
Here we used novel composite likelihood procedures to show that the amount of adaptive evolution and the DFE of newly arising beneficial mutations differ across species. We find that the species with smaller population size (i.e. humans) has stronger and/or more abundant new beneficial mutations than the other two species with much larger population sizes (i.e. mice and D. melanogaster). Our findings are consistent with predictions made in Lourenço et al 17. Namely they used Fisher’s geometric model to argue that a smaller population will have more fixations of weakly deleterious mutations pushing it further away from the fitness optimum, thus creating more opportunities of beneficial compensatory mutations. We also find that alpha varies in a complex way across species. Indeed, alpha is the result of an intricate interplay between the DFE, demography, and population size. Importantly, our model-based alpha estimate for humans is approximately 30%, which is much higher than all previous estimates 6,7, and this result is robust to the choice of different outgroups and BGC. In addition, although our estimates indicate a higher alpha in D. melanogaster and mice than in humans, the difference between mice and humans is small (38% vs. 33%). Interestingly, when taking BGC into account, mice have a smaller alpha (19%) than human (34%), which goes in the opposite direction seen when not controlling for BGC. After removing the potentially confounding effects of BGC, alpha is no longer correlated with population size.
One major improvement of our method over previous similar approaches from Boyko et al and DFE-alpha 6,7 is that we take into account the difference in outgroup population size. In Boyko et al., the outgroup population size is assumed to be the same as that found in the ancestral in-group population. DFE-alpha allows for inference of demographic parameters of one-to three-epoch models, and the outgroup population size is assumed to be the same as the ancestral in-group population. When considering species like humans in relation to other primates, like chimpanzee or macaque, this assumption almost certainly does not hold as primate species have population sizes at least several fold larger than the estimated ancestral human population size of approximately 8,000 individuals. The size of the outgroup population matters because it affects the fixation probability of weakly deleterious alleles1. As such, the amount of nonsynonymous substitutions attributed to weakly deleterious mutations is highly affected by the population size of the outgroup. Consequently, estimates of alpha are then affected as well. Our approach includes an additional population size change, such that the outgroup can have a more realistic population size. By using more realistic population sizes in the outgroup species, the alpha estimates we obtained for human are similar when using the chimpanzee or macaque as outgroup species. This is strong evidence that our method is more accurate as all the other methods give drastically different estimates of alpha using these two different outgroups. Interestingly, Eyre-Walker and Keightley also suggested that alpha in human could be as high as 0.31 if the effective population size of humans and macaques was much higher than 10,000 until very recently 6, agreeing with our current estimates. Future studies should carefully consider outgroup population size and should use statistical methods that allow for additional size changes.
Huber et al. found 15% of nonsynonymous mutations in humans are weakly beneficial, consistent with Fisher’s geometric model. This proportion of weakly beneficial mutations is much higher than that in D. melanogaster that have a larger population size. Because strongly beneficial mutations are thought to become fixed rapidly, they are not observed in polymorphism data. Thus, the Huber et al. study does not include these strongly beneficial mutations. Here, taking advantage of the availability of large genome sequences of several relative species, we can estimate the proportion of strongly beneficial mutations that are fixed between species. Thus, the results presented here in terms of p+ refer to strongly beneficial (s+>1E-5) mutations. In our method, the weakly beneficial mutations are already accounted for using the DFE from Huber et al. as many weakly beneficial mutations are likely segregating as polymorphisms. Intriguingly, we find that humans have a higher proportion of strongly beneficial mutations than Drosophila. This finding is in the same direction as what was found for weakly beneficial mutations in Huber et al.
It is important to emphasize that we quantify adaptive evolution from two different perspectives. First, we estimate the DFE of newly arising beneficial mutations, i.e. p+ and s+. Our method and the method of Boyko et al. aim to understand the properties of new beneficial mutations, the beginning point where beneficial mutation appear and enter the population. Second, we estimate the proportion of adaptive nonsynonymous substitutions between species, alpha. This latter statistic is the end point where a number of factors such as demography, genetic drift, and natural selection all come into play. The results of how the DFE for the newly arising beneficial mutations varies across species could be in the opposite direction to what has been found considering fixed differences. This is expected as these two approaches measure distinct quantities and different aspects of adaptive evolution.
Our estimate of alpha for human lineage is 18.3% using 2-epoch model and 19.7% using 3-epoch model, which is comparable to the estimate of human-lineage alpha by Urrichio et al., despite the use of different analytical approaches. Alpha is expected to be lower on the human lineage as compared to the chimp or macaque lineage due to the higher proportion of weakly deleterious amino acid substitutions on the human lineage to their smaller population size.
One previous explanation for varying estimates of alpha across species was that adaptation is mutation limited and there are more beneficial mutations in organisms with larger population sizes. This view was not supported by a simulation study by Lourenço et al. that considered a changing DFE over time in the context of Fisher’s geometric model 16. Instead, they found that the population size only weakly related to alpha, and the rate at which the environment changed was an important predictor of the amount of adaptive evolution, as environmental shifts moved the population from the fitness optimum, creating the opportunity for new beneficial mutations. However, Connallon and Clark found that environmental heterogeneity reduces the fraction of beneficial mutations by inflating the standardized mutation size in Fisher’s geometric model 35. Lourenco et al. also found that organismal complexity, here defined as the number of phenotypes under selection, was a key predictor of the amount of adaptive evolution within species. Through a “cost of complexity”, more complex organisms have a harder time adapting to new environmental conditions due to the additional constraints imposed by the increased number of traits under selection. As such, adaptive walks require more beneficial mutations.
Our results presented here are in broad agreement with this conceptual model. Specifically, we do not find that species with larger population sizes (i.e. D. melanogaster) have more beneficial mutations. Instead, we find that p+ is higher in humans than in D. melanogaster or mice. Second, while it is hard to precisely define organismal complexity, previous work has found more protein-protein interactions in humans than in D. melanogaster 36,37, suggesting that humans may be more complex than flies. If this is the case, then our findings of a higher p+ in humans than flies and mice supports the arguments from Lourenco et al. 16 that adaptive walks after an environmental shift are less efficient and require more steps (i.e. beneficial mutations) in more complex organisms, leading to higher p+ in complex organisms. Lastly, while it is hard to say which species has experienced more environmental shifts, changing environments may also be contributing to the disparate estimates of p+ across species.
METHODS
Polymorphism and divergence data sets for humans, mice, and D. melanogaster
For humans, we used polymorphism data from 112 individuals from Yoruba in Ibadan, Nigeria (YRI) from the 1000 genomes project 38. Published genome alignments of human and chimpanzee (hg19/pantro4), and human and Macaca mulatta (hg19/rheMac3) were downloaded from UCSC (http://hgdownload.soe.ucsc.edu/goldenPath/hg19/). For D. melanogaster, polymorphism data were from 197 African D. melanogaster lines from the Drosophila Population Genomics Project phase 3 data of samples from Zambia, Africa 39. For divergence, D. melanogaster and D. simulans genic alignments (Dmel v5/Dsim v2) were extracted from the multi-species alignments from 40. Only autosomal regions were used in our analysis. Human and Drosophila polymorphism data were filtered and down-sampled to 100 chromosomes as described in Huber et al. 17
For mice, raw data (fastq) was downloaded for 10 M. m. castaneus individuals that were collected in the northwest Indian state of Himachal Pradesh 41,42. Reads were mapped against mouse genome mm9 using bwa 43 and stampy 44, duplicate reads were marked using Picard, and further pre-processing was done following GATK Best Practice guidelines 45. Variants were called using the GATK UnifiedGenotyper and filtered using the GATK VQSR using Affymetrix Mouse Diversity Genotyping Array sites 46. We further filtered the dataset to only retain sites with a sample size of at least 16 chromosomes and down-sampled all sites with larger sample size to a sample size of 16 chromosomes using the hypergeometric probability distribution. Published genome alignments of mice and rat (mm9/rn5) were downloaded from UCSC (http://hgdownload.soe.ucsc.edu/goldenPath/mm9/vsRn5/axtNet/). For each species, polymorphism data and divergence data were intersected, and only coding regions shared by both datasets were used in our analysis.
In total, 19.1Mb of coding sequences for human, 26.6 Mb of coding sequences for mice and 15.8Mb of coding sequences for D. melanogaster were included. The nonsynonymous and synonymous total sequence lengths (LNS, LS) were estimated using multipliers of LNS = 2.85 × LS in Drosophila, and LNS = 2.31 × LS in humans and mice from Huber et al 17. In these filtered coding sequences, we annotated synonymous and nonsynonymous sites in both polymorphism and substitution data for each species. Human variants were annotated using the SeattleSeq Annotation pipeline (http://snp.gs.washington.edu/SeattleSeqAnnotation138/). Mice and Drosophila variants were annotated using SnpEeff v3.6 using the mice NCBIM37.66 annotation database and the D. melanogaster BDGP5.75 annotation database, respectively. Sites that are annotated as near-splice, or loss of function were removed. The ratio of nonsynonymous/synonymous differences between human and chimp sequences in our dataset is about 0.65, which is consistent with several previous reports from different datasets 47–49.
From the down-sampled polymorphism data, we calculated the synonymous and nonsynonymous SFS, and used the folded SFS for all further inferences to avoid misidentification of the ancestral state.
Calculation of alpha
For each species, alpha was calculated using an extension of the McDonald-Kreitman test formulated in Smith and Eyre-Walker 18:
Here, DS is the number of synonymous substitutions, DN is the number of nonsynonymous substitutions, PS is the number of synonymous polymorphisms, and PN is the number of nonsynonymous polymorphisms.
Demographic and DFE inferences for mice
We used methods established in Huber et al to infer demography and DFE of neutral and deleterious mutations from the mouse polymorphism data 17. In short, we first used the synonymous SFS to infer demographic parameters for a two epoch-model using ∂a∂i 28,50. Then, we used a Poisson likelihood function to estimate the parameters of a gamma-distributed DFE of new neutral and deleterious nonsynonymous mutations using the nonsynonymous SFS, conditional on the estimated demographic parameters 7,51.
prfreq estimates of alpha
To implement the prfreq approach to estimate alpha, for each species, we need a demographic model and a DFE for neutral and deleterious mutations to predict the DNE that is accounted for by neutral and deleterious forces. For humans and D. melanogaster, we use demographic and DFE parameters from Huber et al. (supplementary table S3) 17. For mice, we conduct our own inference of these parameters by summarizing the polymorphism data by the folded site frequency spectrum (SFS; see Methods). For mice, using the synonymous SFS, we infer that the ancestral population size is approximately 206,500 which expanded 2.4-fold 293,000 generations ago (supplementary table S3). Conditional on this demographic model, we estimate the DFE for new nonsynonymous mutations in mice. We assume that the DFE follows a gamma distribution and estimate its shape parameter alpha to be 0.21 and scale parameter beta to be 0.083 (supplementary table S3). These estimates are within the same magnitude of previous estimates from Huber et al., which used a much smaller dataset (<0.1% of the total sites used in our study). For both the two-epoch models and the three-epoch models, we first found the demographic parameters (supplementary table S4) that fit the observed number of synonymous substitutions using prfreq. Here the number of synonymous substitutions equals 2 × divergence time × mutation rate. We estimated the divergence time (tdiv) for each model and species using this method because there is a wide range of divergence times from the literature for each species. Second, using this divergence time, demography, and DFE inferred from Huber et al., or as described above for mice, we estimated the expected number nonsynonymous substitutions (Dne) using prfreq according to Sawyer and Hartl eqn 13 (Sawyer and Hartl 1992; Boyko et al. 2008). Then, alpha is calculated as where DNo is the observed number of nonsynonymous substitutions.
DFE-alpha
Data files and the program v2.15 were downloaded from the following link: http://www.homepages.ed.ac.uk/pkeightl//dfe_alpha/download-dfe-alpha.html. Folded synonymous and nonsynonymous SFS were used as input in the inferences. est_alpha_omega program was used to estimate the proportion of adaptive divergence, i.e. alpha.
Coalescent simulations to compare human two-epoch and three-epoch models
To evaluate whether patterns of neutral polymorphism would be predicted to be different under the human two-epoch and three-epoch demographic models, we conducted coalescent simulations under these models using ms 52. Specifically, we simulated 1000 replicates for each scenario and calculated the mean number of synonymous segregating sites across replicates. Both models showed similar numbers of neutral segregating sites (34075 for two-epoch model and 33810 for three-epoch model), suggesting that using population sizes more appropriate for the outgroup population will not affect polymorphism data in the in-group sample.
Composite likelihood approach for testing whether p+ and s+ differ across species
We first used prfreq to numerically solve the forward diffusion equation of allele frequency change for the specified demographic model and mutation rate to generate a look-up table for the expected number of nonsynonymous substitutions for a range of s+ (10-5-10-2) for each species. We focused on this range to capture strongly advantageous mutations. For each species, we then did a grid search of log10(s+) (-5 to -2) and p+(0–7.5%). We are interested in this range of strong s+ because weakly beneficial mutations still segregating in polymorphisms should be taken into account by the DFE being fit to the SFS. We use a Poisson log-likelihood function to calculate the log-likelihood (LL) for each combination of s+ and p+. We find the MLE of s+ and p+ for each species under each demographic model that maximizes the LL and best fit the observed DN. This is the full model (H1) where each species is allowed to have its own s+ and p+. Our H0 hypothesis is the constrained model, where two or three species under certain demographic scenario have the same s+ and p+. The LL of the constrained model is the sum of LL for each s+ and p+ for each species under comparison. We then find the MLE for the constrained model and calculate the likelihood ratio between H1 and H0.
Composite likelihood approach for testing whether p+ and gamma+ differ across species
Similarly, we used prfreq to generate a look-up table for the expected number of nonsynonymous substitutions for a range of gamma+ (1–103) for each species under each demographic model. For each species, we performed a grid search of log10(gamma+) (0-3) and p+(0-7.5%). Note, because effective population sizes differ over several orders of magnitude across our three species, we are searching across drastically different ranges of s+ as compared to our previous inference described above. We again use a Poisson log-likelihood function to calculate the LL for each combination of gamma+ and p+. We find the MLE of gamma+ and p+ for each species under each demographic model that best fit our observed nonsynonymous divergences. This is the full model (H1) where each species is allowed to have its own gamma+ and p+. Our H0 hypothesis is the constrained model, where two or three species under certain demographic scenarios have the same gamma+ and p+. The LL of the constrained model is the sum of LL for each gamma+ and p+ for each species under comparison. We then find the MLE for the constrained model and calculate the likelihood ratio between H1 and H0.
Conditional likelihoods
To examine whether all three species could have the same s+ or p+, we examine the conditional likelihoods. To make the conditional likelihood curve for p+, for each s+ value, we look for the p+ that maximizes the likelihood as well as the p+ values that have a likelihood within three LL of this maximum LL for this s+ (i.e. p+|s+). To make the conditional likelihood curve for s+, for each p+ value, we look for the s+ that maximizes the likelihood as well as the s+ values that have a LL within three LL units of this maximum LL for this p+ (i.e. s+|p+).
Similarly, we examine whether all three species could have the same gamma+ or p+. To make the conditional likelihood curve for p+, for each gamma+ value, we look for the p+ that maximizes the likelihood as well as the p+ values that have a likelihood within three LL of this maximum LL for this gamma+ (i.e. p+|gamma+). To make the conditional likelihood curve for gamma+, for each p+ value, we look for the gamma+ that maximizes the likelihood as well as the gamma+ values that have a LL within three LL units of this maximum LL for this p+ (i.e. gamma+|p+).
Estimating alpha on the human lineage
Human-chimp substitutions were polarized by the macaque sequence. Substitutions were assigned to human lineage if the bases differ between human and macaque, but were the same between chimpanzee and macaque in the pairwise genome alignments. Substitutions that are in regions where the human and macaque sequences were un-alignable and substitutions that differ among human, chimp and macaque cannot be polarized (3.8% total) and were filtered out. The total length of coding regions was scaled by this filter accordingly.
To estimate the expected number of substitutions on human lineage, we follow the method described in section prfreq estimates of alpha, with several modifications. Specifically, 1) we use prfreq to compute the expected DS count for both human and chimp lineages; 2) we use prfreq to compute the expected DS.outgroup count for a population with constant size (i.e. 7067 for 2-epoch model, and 73,000 for 3-epoch model), with a split time equal to the one previously estimated from Ds between human-chimp, 3) we divide DS.outgroup by 2 to find the number of nonsynonymous substitutions fixed on the chimp lineage. Then we subtract that number from the expected DS count from both lineages. This reminder should be the expected synonymous divergence on the human lineage. 4) we adjust tdiv to match the expected synonymous divergence on the human lineage with the observed synonymous divergence on the human lineage. 5) With the adjusted tdiv, we similarly estimate the expected nonsynonymous divergence on the human lineage using the same approach as for synonymous divergence described in step 3, except we include the DFE of deleterious mutations. 6) alpha is calculated using equation (3).
Filtering to only include sites not affected by biased gene conversion
Full polymorphism and substitution datasets of humans and mice were filtered to keep only SSWW mutations that were not affected by BGC. This includes only A to T, T to A, C to G and G to C changes. These changes are only a small subset of all variable sites. The nonsynonymous and synonymous sequence lengths (LNS, LS) depend on the transition/transversion ratio and the CpG mutational bias. SSWW mutations are all transversions and do not included any CpG mutations, leading to a multiplier of LNS = 5.21 x LS in both humans and mice. To compute this: 1) we used numbers of 0-, 2-, 3- and 4-fold sites in human from Veeraham 53; 2) we consider all 2-fold sites to be nonsynonymous (because SSWW mutations are all transversions); and 3) we do not consider a mutational bias of CpG sites (because CpG sites are not included in the SSWW set). In addition, because SSWW mutations are only a small subset of all mutations, mutation rates need to be scaled down to the SSWW specific mutation rate. To estimate the demographic parameters and DFE for SSWW polymorphisms in mice, first, we used the observed number of synonymous SSWW polymorphisms to estimate the mutation rate for mice SSWW mutations to be 5.99E-10. Then, using the SFS for SSWW synonymous polymorphisms, we inferred that the ancestral population size is approximately 246,256 which expanded 1.7-fold approximately 262,000 generations ago (supplementary table S3). Conditional on this demographic model, we estimated the DFE for new nonsynonymous SSWW mutations in mice. We assume that the DFE follows a gamma distribution and estimate its shape parameter alpha to be 0.21 and scale parameter beta to be 0.050 (supplementary table S3). These estimates are within the same magnitude of the estimates from the full dataset and a previous study 17. We re-estimated the mouse-rat divergence time that fits best with the observed SSWW DS. We then re-inferred p+ and s+/ gamma+ as done previously, using the filtered data, new mutation rates, and new values of LNS.
Data availability
The datasets analyzed during the current study are available in these published reference articles 38–40 as described in Methods section.
Author contributions
K.E.L conceived of and supervised the study. Y.Z. carried out all analyses of alpha. C.D.H carried demographic and gamma-DFE inference based on the SFS. R.W.D. processed mice raw data to genotypes. Y.Z. generated all figures. Y.Z., C.D.H., R.W.D and K.E.L. all participated in manuscript preparation.
Competing interests
The authors declare no competing interests.
Acknowledgements
We thank Lawrence Uricchio and David Enard for advice, discussions, and sharing their manuscript, and Tanya Phung, Jazlyn Mooney, Clare Marsden and Jesse Garcia for helpful comments on our manuscript. This work was supported by a Searle Scholars Fellowship and NIH Grant R35GM119856 (to K.E.L.). We acknowledge support from a QCB Collaboratory Postdoctoral Fellowship to Y.Z. and the QCB Collaboratory Community directed by Matteo Pellegrini.