Changes in life history and population size can explain the relative neutral diversity levels on X and autosomes in extant human populations

Significance

All else being equal, the ratio of diversity levels on X and autosomes at selectively neutral sites should mirror the ratio of their numbers in the population and thus equal 3/4. In reality, the ratios observed across human populations differ markedly from 3/4 and from each other. Because, from a population perspective, autosomes spend an equal number of generations in both sexes, while the X spends twice as many generations in females, these departures from the naïve expectations plausibly reflect differences between male and female life histories and their effects on mutation processes. Indeed, we show that the ratios observed across human populations can be explained by demographic history, assuming realistic sex-specific mutation rates, generation times, and reproductive variances.

Abstract

In human populations, the relative levels of neutral diversity on the X and autosomes differ markedly from each other and from the naïve theoretical expectation of 3/4. Here we propose an explanation for these differences based on new theory about the effects of sex-specific life history and given pedigree-based estimates of the dependence of human mutation rates on sex and age. We demonstrate that life history effects, particularly longer generation times in males than in females, are expected to have had multiple effects on human X-to-autosome (X:A) diversity ratios, as a result of male-biased mutation rates, the equilibrium X:A ratio of effective population sizes, and the differential responses to changes in population size. We also show that the standard approach of using divergence between species to correct for male mutation bias results in biased estimates of X:A effective population size ratios. We obtain alternative estimates using pedigree-based estimates of the male mutation bias, which reveal that X:A ratios of effective population sizes are considerably greater than previously appreciated. Finally, we find that the joint effects of historical changes in life history and population size can explain the observed X:A diversity ratios in extant human populations. Our results suggest that ancestral human populations were highly polygynous, that non-African populations experienced a substantial reduction in polygyny and/or increase in the male-to-female ratio of generation times around the Out-of-Africa bottleneck, and that current diversity levels were affected by fairly recent changes in sex-specific life history.

Neutral polymorphism patterns on the X and autosomes reflect a combination of evolutionary forces. Theory predicts that, all else being equal, the ratio of diversity levels on X and autosomes at selectively neutral sites should mirror the ratio of their numbers in the population and thus equal 3/4 (1). A complication, however, is that autosomes spend an equal number of generations in diploid form in both sexes, whereas the X spends twice as many generations in diploid form in females as in haploid form in males. As a result, the X-to-autosome (X:A) diversity ratio can also be shaped by differences in male and female life history and mutation processes, as well as by differences in the effects of demographic history and selection at linked sites on the X and autosomes. The effects of these factors have been studied theoretically (2) and in relation to observations in many species (3–8). Notably, their effects on diversity ratios in human populations have attracted considerable interest over the past decade (9–15).

The impact of selection at linked sites on neutral diversity levels could differ for X and autosomes because of differences in recombination rates, in the density of selected regions, and in the efficacy and modes of selection. Notably, the hemizygosity of the X in males leads to a more rapid fixation of partially or fully recessive beneficial alleles and to a more rapid purging of recessive deleterious ones (16, 17). Considering these effects and accounting for recombination rates suggests that in humans—in mammals more generally—the effects of selection at linked sites should be stronger on the X (ref. 18, but see ref. 3). To evaluate these effects empirically, several studies have examined how diversity levels on the X and autosomes vary with genetic distance from putatively selected regions, for example from coding and conserved noncoding regions (11, 13–15, 19, 20). In most hominids, including humans, such comparisons confirm the theoretical expectation that selection at linked loci reduces X:A diversity ratios (11, 15, 20). They further suggest that the effects are minimal sufficiently far from genes (11, 19), thereby providing an opportunity to examine the effects of other factors shaping X:A diversity ratios in isolation by considering regions that are minimally affected.

Even far from genes, however, the X:A diversity ratios in humans and other hominids differ from the naïve expectation of 3/4 (11, 13, 14). Diversity levels on the X and autosomes are typically divided by divergence from an outgroup (e.g., divergence from orangutan or rhesus macaque is used to normalize diversity levels in humans) in order to control for the effects of higher mutation rates in males and variation in mutation rates along the genome (9). The normalized estimates of X:A diversity ratios in regions far from genes range between 3/4 and 1 among human populations, generally decreasing with the distance from Africa (11, 13, 15). Ratios exceeding 3/4 have also been observed in most other hominids (ref. 14, but see ref. 21).

These departures from 3/4 and differences among populations and species have been attributed in part to the effects of demographic history, in particular to historical changes in population size. If we assume that the effective population size of the X is generally smaller than that of autosomes, then changes in population size will have a different impact on diversity levels on X and autosomes (5, 22–24). Notably, population bottlenecks that occurred sufficiently recently, such as the Out-of-Africa (OoA) bottleneck in human evolution, will have decreased the X:A diversity ratio, because a greater proportion of X-linked lineages will have coalesced during the bottleneck (24). Indeed, simulation studies suggest that historical changes in population size have contributed substantially to decreased X:A diversity ratios with the distance from Africa (15). Historical differences between males and females may have also played a role; for example, male-biased migration or longer male generation times during the OoA bottleneck may have also contributed to the lower X:A ratios in non-Africans (12).

Sex differences in life history traits are also likely to have had substantial effects on X:A diversity ratios. The most straightforward of these effects arises from sex differences in the variance of offspring numbers, which, for brevity, we refer to as “reproductive variance.” Higher reproductive variance in males than in females causes higher coalescence rates on autosomes and thus increases X:A diversity ratios (2, 9). This increase is theoretically bounded by a factor of $3/2$ (2). Although probably much lower in reality, a greater male reproductive variance is observed in extant hunter-gatherers and hominid species (25), indicating that it plausibly contributed to differences in X:A diversity ratios among populations, as well as to their departure from $3/4$.

Longer generation time in males may have also had substantial yet underappreciated effects (2, 26). Theory indicates that longer generation times in males reduce coalescence rates per generation on autosomes compared to the X and thus the X:A ratio of effective population sizes (26). In addition, the paternal and maternal mutation rates in humans—and likely in mammals more generally—depend on male and female generation times (27). Consequently, male and female generation times affect the ratio of male-to-female mutation rates, often called male mutation bias and denoted by $\alpha$, which in turn affects the mutation rates on the X relative to autosomes (28). As we detail below, normalizing diversity estimates by divergence to an outgroup does not fully account for this mutational effect if, as is likely, the male mutation bias, $\alpha$, evolves over phylogenetic time scales (29–31). Moreover, because a longer generation time in males implies fewer generations on autosomes relative to the X since the species split, normalizing diversity estimates by divergence also absorbs a nonmutational, generation time effect on X:A divergence ratios (31, 32). Thus, male and female generation times can in principle affect X:A diversity ratios in multiple ways, which should be considered jointly.

Here we examine these effects, and those of life history more generally, on diversity ratios in humans. We begin with general considerations about the effects in populations of constant size, the effects in response to changes in population size, and the biases introduced by normalizing diversity ratios by divergence to an outgroup. We then estimate X:A diversity ratios in six human populations in which historical changes in population size were inferred previously and show that considering these effects jointly can explain the observed ratios.

Results

Life History Effects in Populations of Constant Size.

In a parallel paper (26), we derive expressions for neutral X:A diversity ratios in a panmictic population of constant size, under a model that captures quite general life history effects. The model assumes that the population is divided into sex-specific age classes, with female and male proportions ${\gamma }_F$ and ${\gamma }_M$ at birth, respectively $\left({\gamma }_F+{\gamma }_M=1\right)$, and that the (constant) sizes of subsequent age classes of each sex decline with age, reflecting sex- and age-specific mortality. Fecundity also depends on sex and age and incorporates sex-specific reproductive variances and correlations between the numbers of offspring at different ages. Generation times in females, $G_F$, and in males, $G_M$, are defined as the expectations of maternal and paternal ages at birth. Mutation rates can vary with sex and age, with their per-generation rates in females, ${\mu }_F$, and in males, ${\mu }_M$, defined as expectations over parental ages. The expected number of offspring of each sex necessarily equals 1, but female and male reproductive variances, $V_F$ and $V_M$, respectively, may differ due to sex- and age-dependent mortality and fecundity.

We show that the X:A ratio of effective population sizes $\left(N_e\right)$, defined as half the inverse of the coalescence rates, is

$$N_e^X/N_e^A=\frac{3}{4}\cdot \frac{f\left(G_M/G_F\right)}{f\left(\frac{{\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M}{{\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F}\right)},$$ [1]

where $f\left(x\right)=\frac{2x+4}{3x+3}$. We also show that the X:A ratio of expected diversity levels (i.e., heterozygosities) is

$$\frac{E\left({\pi }_X\right)}{E\left({\pi }_A\right)}=\frac{3}{4}\frac{f\left({\mu }_M/{\mu }_F\right)\cdot f\left(G_M/G_F\right)}{f\left(\frac{{\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M}{{\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F}\right)}.$$ [2]

When the mutation rates, generation times, numbers of newborns, and reproductive variance are identical in both sexes, the diversity and $N_e$ ratios reduce to the naïve neutral expectation of 3/4. When these factors differ between sexes and covary, Eq. 2 provides a simple expression for the effect of each factor. Notably, the effects of sex-specific age and reproductive structure reduce to the effects of male-to-female ratios of mutation rates $\left(\alpha ={\mu }_M/{\mu }_F\right)$, generation times $\left(G_M/G_F\right)$, and terms combining reproductive variances and sex proportions $\left(\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/\left({\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\right)\right)$. We note that the ratio combining reproductive variances and sex proportions is invariant to measuring these parameters at any given age, so long as this age is the same for all parameters and precedes reproductive age. For brevity, we refer to this ratio as the ratio of reproductive variances henceforth.

All three ratios in Eq. 2 are male-biased in humans, and in many other mammals (33–36). Across human populations, slightly more births are male than female, with typical values of ${\gamma }_M\approx 0.513$ and ${\gamma }_F\approx 00.487$, and with greater female survival throughout life gradually shifting the proportions toward females with increasing age (e.g., ref. 36). Sex-specific reproductive variances at adulthood measured in five extant hunter-gatherer groups, albeit using small sample sizes, were found to be 1.7- to 4.2-fold higher in males (25). Assuming equal sex proportions at adulthood, the corresponding reproductive variance ratios translate into a 6 to 20% increase in X:A diversity ratios. In turn, sex-specific generation times measured in seven hunter-gatherer groups were found to have mean generation times between 25 and 33 y and generation times ratios between 1.03 and 1.37 (31, 33), corresponding to a 0.5 to 5.2% decrease in X:A diversity ratios. Both of these life history ratios, however, may have taken values outside the aforementioned ranges during human evolution, as they do in other extant human populations (25, 33). The ratio of male-to-female mutation rates, $\alpha$, was estimated from pedigree studies (27) and found to increase approximately linearly with the generation times ratio in the two sexes, $G_M/G_F$, and depend negligibly on the sex-averaged generation time (ref. 37, and see Fig. 3). Based on these estimates, the male mutation bias would reduce X:A diversity ratios by ∼18% even without male-biased generation times and by ∼21% with $G_M/G_F=1.37$ (the largest estimate in extant hunter-gatherers). The effects of the ratios of reproductive variances and generation times (including both genealogical and mutational effects) on human X:A diversity ratios can also be considered jointly, assuming a constant population size (Fig. 1).

Fig. 3.

Substantial differences between estimates of male mutation bias ($\alpha )$ in humans based on X:A ratios of divergence to an outgroup (SI Appendix, section 2.3 and Table S3) and on pedigree studies in contemporary humans (SI Appendix, section 1 and ref. 27). Pedigree-based estimates strongly depend on (and are therefore shown as a function of) the generation time ratio, $G_M/G_F$ (SI Appendix, section 1 and ref. 37). They depend only weakly on the average generation time, $G_A$, as shown by the (cyan) range corresponding to $G_A$ between 25 and 35 y. The divergence-based estimates were calculated using Miyata’s formula $\left({\widehat{\alpha }}_D=f^{-1}\left(d_X/d_A\right)\right)$ and the divergence of humans from orangutans and rhesus macaques (SI Appendix, section 2.3).

Fig. 1.

Life history and mutational effects on the human X:A diversity ratio assuming a constant population size. Ratios of reproductive variances $\left(\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/\left({\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\right)\right)$ and generation times are varied within a range corresponding to estimates in extant hunter-gatherers (see text and refs. 25, 31, and 33). The male mutation bias dependence on the ratio of generation times is based on human pedigree studies (see text, Fig. 3, and ref. 37); this bias causes the diversity ratio to differ from 3/4 even when life history parameters are equal in both sexes. Note that these predictions are not directly comparable with most X:A diversity ratios reported in the literature, which are normalized by the X:A ratio of divergence to an outgroup.

Life History Effects in Populations of Changing Size.

Changes in population size affect X:A diversity ratios (24) in ways that are modulated by sex-specific life history (26). In Amster and Sella (26), we derive closed forms for these effects. Here we illustrate these effects by considering a simple bottleneck scenario roughly corresponding to that of the OoA bottleneck in humans (Fig. 2). In the absence of sex differences in life history, with an equilibrium X:A $N_e$ ratio of 3/4, diversity levels on the X experience more of a reduction during the bottleneck, and a faster recovery afterward, because the time scales of equilibration are 3/4 times shorter on the X (24). For OoA bottleneck parameters, these effects lead to a reduction in the X:A diversity ratios (Fig. 2, black curve).

Fig. 2.

The effect of a population bottleneck on the X:A diversity ratio is modulated by sex-specific life history. Bottleneck parameters were chosen to roughly correspond to autosomal estimates for the OoA bottleneck in humans (right y axis), with the population size dropping from $2\cdot {10}^4$ to $2\cdot {10}^3$ between 50 and 100 kya. We show the change in X:A diversity ratios, measured relative to their values at demographic equilibrium (left y axis), assuming an autosomal generation time of 30 y and four combinations of generation times and reproductive variances ratios. When both life history ratios have the same value, the ratio of $N_e$ at equilibrium is 3/4 (as is the case for black and dashed blue-red curves); when $G_M/G_F=1.25$, there are more generations on the X than on the autosomes per unit time $\left(G_X/G_A=0.72\right)$. See SI Appendix, Fig. S1 for the absolute rather than relative changes in diversity and $N_e$ ratios.

Sex differences in life history modulate these effects. For instance, a higher reproductive variance in males than in females increases the equilibrium X:A $N_e$ ratio (Eq. 1), moving it closer to 1, thereby leading to a smaller reduction in the diversity ratio in response to the bottleneck than expected in the vanilla model (Fig. 2, blue curve). In contrast, a longer generation time in males results in a larger reduction in the X:A diversity ratio (Fig. 2, red curve), for two reasons: 1) it reduces the equilibrium X:A $N_e$ ratio (Eq. 1), which accelerates the response to the bottleneck on the X relative to autosomes measured in generations, and 2) it shortens the generation time on the X relative to autosomes, which increases the relative number of generations on the X relative to on autosomes per unit time (in years). More generally, sex-specific life histories modulate the response of X:A diversity ratios to changes in population size by influencing the coalescence time scale of the response of X vs. autosomes in generations and by changing the generation times on X vs. autosomes and thus the relative number of generations per unit time (in years). These considerations imply that even if we knew the effective population size of autosomes, or even of X and autosomes, throughout history, we would still have to know past values of life history traits in order to predict the effects of demography on the X:A diversity ratio (Fig. 2 and SI Appendix, Fig. S1).

Normalizing Diversity Ratios by Divergence.

Most studies estimate X:A $N_e$ ratios by dividing diversity levels by estimates of the number of substitutions since the split from an outgroup (e.g., refs. 9, 11, 13, and 38). Primarily, this normalization step is meant to correct for the effect of male mutation bias on diversity ratios. From Eqs. 1 and 2 (and ignoring changes in population size), the relationship between diversity and $N_e$ ratios is

$$E\left({\pi }_X\right)/E\left({\pi }_A\right)=f\left(\alpha \right)\cdot N_e^X/N_e^A,$$ [3]

where $\alpha ={\mu }_M/{\mu }_F$ is the male mutation bias. The normalization relies on Miyata’s equation (28):

$$E\left(K_X\right)/E\left(K_A\right)=f\left(\alpha \right),$$ [4]

where $K_X$ and $K_A$ are the number of substitutions on X and autosomes, respectively. Assuming further that the male mutation bias remained constant on the time scales affecting diversity and divergence, then the X:A substitution ratio can be used to estimate $f\left(\alpha \right)$, and dividing the diversity ratio by this estimate should yield an accurate estimate of the X:A $N_e$ ratio. Both assumptions, however, are often violated.

Notably, when sex-specific life history is accounted for Miyata’s formula is replaced by

$$E\left(K_X\right)/E\left(K_A\right)=f\left({\alpha }^{\ast }\right)/f\left(G_M^{\ast }/G_F^{\ast }\right),$$ [5]

where the asterisk denotes parameters averaged over the lineage on which substitutions are measured, which is typically much longer than the lineage over which diversity levels are measured (31, 32). The normalized diversity ratio then takes the form

$$\frac{{\pi }_X/K_X}{{\pi }_A/K_A}=\left[\frac{f\left(\alpha \right)}{f\left({\alpha }^{\ast }\right)}\cdot f\left(G_M^{\ast }/G_F^{\ast }\right)\right]\cdot \frac{N_e^X}{N_e^A},$$ [6]

where we removed the expectations on the left-hand side, for legibility. This expression shows that for the normalization to cancel out the effect of male mutation bias and provide an accurate estimate of the X:A $N_e$ ratio, the bracketed term must equal 1. Previous work suggests that male mutation bias evolves substantially over phylogenetic time scales (29–31), and therefore the mutational term $f\left(\alpha \right)/f\left({\alpha }^{\ast }\right)$ is unlikely to cancel out. Even if it did, the dependence of the substitution ratio on the generation time ratio introduces an additional term, $f\left(G_M^{\ast }/G_F^{\ast }\right)$. Both terms lead to biased estimates of X:A $N_e$ ratios. Furthermore, as the degree of male mutation bias probably varies among populations [e.g., due to variation in generation times (33)], relative estimates of $N_e$ ratios in different populations will likely be biased as well.

We can assess the severity of these potential biases in estimates of human X:A $N_e$ ratios by comparing divergence- and pedigree-based estimates of the male mutation bias, $\alpha$ (Eq. 4 and Fig. 3). Assuming that differences in mutation rates between the X and autosomes arise predominantly from the male mutation bias (see Discussion), we would expect estimates of the mutational effects on X:A diversity ratios based on contemporary pedigree studies to be more reliable, for at least three reasons. First, mutation rates during the period affecting current neutral diversity—that is, roughly the past 1.5 My (39) (see Discussion)—are likely to be closer to rates in contemporary humans than to rates averaged over the time scales of divergence from orangutan and rhesus macaque [∼15 and ∼30 My, respectively (39)], the lineages commonly used to normalize human X:A diversity ratios (9, 11, 13, 15). Second, while both divergence- and pedigree-based estimates of $\alpha$ depend on the sex ratio of generation times, in pedigree studies this dependence is explicit and reflects only the effect of generation times on mutation rates (as opposed to the nonmutational term $f\left(G_M^{\ast }/G_F^{\ast }\right)$ for divergence). Third, pedigree-based estimates avoid the problem of ancestral diversity making distinct proportional contributions to X vs. autosome divergence and hence affecting their ratio. Again assuming a linear dependence on $G_M/G_F$ (ref. 37 and Fig. 3) and relying on estimates of $G_M/G_F$ in extant hunter-gatherers (31, 33), pedigree-based estimates of $\alpha$ range between 3.6 and 4.5, with estimates for most societies falling on the higher end of this range. These estimates are approximately twofold greater than those based on human–orangutan or human–macaque divergence (Fig. 3). This strongly suggests that current estimates of human X:A $N_e$ ratios are substantially biased.

Revised Estimates of Human X:A ${\mathit{N}}_{\mathit{e}}$ Ratios.

Given this finding, we revisit the estimation of X:A $N_e$ ratios in human populations and compare the old estimates based on normalizing by divergence with new ones based on pedigree studies.

We estimate neutral diversity ratios in the absence of selection at linked sites in two ways (SI Appendix, section 2.2). First, we apply the standard method (9), based on measuring diversity at putatively neutral sites far from exons. Second, rather than imposing a threshold distance from exons, we use putatively neutral sites throughout the genome and rely on the McVicker et al. B-maps to correct for the effects of selection at linked sites on diversity levels (19), an approach that allows us to use more data. Our estimates of diversity ratios based on the two approaches are consistent (SI Appendix, Fig. S5) and we henceforth rely on the more precise estimates from the second approach (Fig. 4). In particular, we apply this approach to estimate X:A diversity ratios both with and without the normalization by divergence (to rhesus macaque). For reasons that are unclear to us, our normalized estimates do not agree with those of Arbiza et al. (15), who rely on similar data but end up with values that are slightly higher in YRI (Yoruba) and much higher in other populations (using orangutan as an outgroup instead also yields a discrepancy and one that is slightly larger; SI Appendix, Table S3).

Fig. 4.

The X:A $N_e$ ratios in human populations are greater than previously appreciated. We rely on genome-wide polymorphism data from the 1000 Genomes Project (phase 3) to estimate neutral $N_e$ ratios in the absence of selection at linked sites, as described in the text and detailed in SI Appendix, section 2. Specifically, we estimate the ratios for the following six ancestry groups, as labeled by the 1000 Genomes (40): Yoruba (YRI), Mexican (MXL), Tuscan (TSI), Northern and Western European (CEU), Han Chinese (CHB), and Japanese (JPT). For the “old estimates” we rely on divergence from rhesus macaque to correct for male biased mutation, and for the “new estimates” we rely on a pedigree-based estimate of the male mutation bias ($\alpha =4.25$; see text for details). Confidence intervals are based on bootstrapping, in which we resample 1-Mb windows with replacement, excluding windows without any putatively neutral sites.

Using this approach, we obtain revised estimates of X:A $N_e$ ratios, assuming a male mutation bias of $\alpha =4.25$ from pedigree-based estimates and the average $G_M/G_F$ measured in extant hunter-gatherers (Fig. 3). Specifically, we divide our (unnormalized) estimates of diversity ratios by $f\left(4.25\right)\approx 0.79$. The new, pedigree-based estimates are ∼11% larger than the old ones, suggesting that X:A $N_e$ ratios in humans are substantially greater than previously appreciated (Fig. 4).

The new estimates rely on two strong assumptions. The first, which seems plausible, is that mutation rates on the X can be reliably obtained from estimates (from pedigrees) of male and females mutation rates on autosomes, as we have done (see Discussion). The second, which is more problematic, is our assumed value of $G_M/G_F$—as already noted, pedigree-based estimates of $\alpha$ strongly depend on $G_M/G_F$. The ratio $G_M/G_F$ probably varied considerably over time and across populations, as it does among extant hunter-gatherers (31, 33), limiting our ability to estimate X:A $N_e$ ratios reliably. This limitation is not specific to our new estimates but instead highlights the difficulty of teasing apart the mutational and genealogical effects on X:A diversity ratios without making assumptions about the male mutation bias and its evolution, whether explicit or implicit.

Explaining Diversity Ratios in Human Populations.

Given this limitation, we turn the question on its head and ask whether effects of generation times, reproductive variances, and historical changes in population size could explain the estimates of X:A diversity ratios. To this end, we rely on pairwise multiple sequentially Markovian coalescent (MSMC)–based estimates of historical, autosomal effective population sizes for the six 1000 Genomes populations in which they were inferred (see Fig. 7A and ref. 41). In all cases considered, we assume that $G_A=30$, to match the assumptions of previous demographic inferences (41). We first consider the ratio in YRI, then the reduction in ratio in CEU relative to YRI, and, finally, the ratios in all six populations jointly.

Fig. 7.

Together, variation in sex-specific life history traits over time and across populations and changes in population sizes can explain the X:A diversity ratios observed in six human populations. (A) Changes in population sizes in six human populations inferred by pairwise MSMC (41). Split times among populations were determined visually and are marked by stars: blue for (YRI, non-African populations), black for ((CEU, TSI), (CHB, JPT), MXL), purple for (CEU, TSI), and red for (CHB, JPT). (B) Comparison of estimates of the X:A diversity ratios with those predicted under the historical changes in population size shown in A, assuming 1) no life history effects (black), 2) sex-specific life history parameters that vary within the ranges specified in the text and were chosen to best fit observations (red), and 3) the best fit further allowing sex-specific life history parameters to vary among populations after they split (blue). See text and SI Appendix, section 3 for details.

Diversity Ratio in YRI.

The X:A $N_e$ ratio in YRI is remarkably high (Fig. 4), indicative of high levels of polygyny (i.e., that a minority of males sired offspring with multiple females). Accounting for historical changes in population size and assuming, for example, the average generation time ratio estimate in extant hunter-gatherers $\left(G_M/G_F=1.26\right)$, this X:A $N_e$ ratio implies a reproductive variance ratio of $\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/{\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\cong 5.5$ (95% CI [3.9, 8.2]) and thus high reproductive variance in males ($V_M\ge 14.4$ assuming a sex ratio of 1). More generally, matching the estimated X:A diversity ratio in YRI defines a trade-off in which a higher generation time ratio implies a more male-biased reproductive variance ratio (Fig. 5). Given that the generation time ratio was likely greater than 1, our findings suggest substantial polygyny in the ancestors of YRI, and of other human populations (9).

Fig. 5.

The combinations of ratios of generation times and reproductive variances in the two sexes that are consistent with estimates of the X:A diversity ratio in YRI. Solid curves correspond to parameter values that would yield the point estimate of the diversity ratio, and shaded areas correspond to values that would yield ratios within the 95% CI of the diversity ratio estimate.

Reduced Diversity Ratio in CEU Relative to YRI.

Without life history effects (model i in Fig. 6 and ref. 15), historical changes in population size and in particular the OoA bottleneck lead only to about half of the observed reduction of 18.4% in X:A diversity ratios in the CEU relative to YRI. Yet, ratios of generation times and reproductive variances in males and females almost certainly differed from 1 in the past and varied over time and across populations (e.g., ref. 33). To explore what the potential effects of such changes could be, we consider several models in which values of $G_M/G_F$ are constrained to be between 0.9 and 1.4 and values of $\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/\left({\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\right)$ are constrained to be between 1 and 2.5; these ranges are somewhat arbitrary but they are clearly possible, given estimates for extant hunter-gatherers (33) and other extant human populations (25). Requiring these ratios to have been the same in both populations and constant over time (model ii in Fig. 6), we find that the maximal reduction in the X:A diversity ratio in CEU relative to YRI is 12.3% (see SI Appendix, section 3 for details on the maximization). Allowing the ratios to have different values before and after the split between YRI and CEU but requiring them to be the same in both populations (model iii in Fig. 6) results in only a slightly greater maximal reduction of 12.7% in the X:A diversity ratio. Further allowing for population-specific parameter values after the split (model iv in Fig. 6), the maximal reduction in the diversity ratio in CEU relative to YRI rises to 20%, which is greater than the observed reduction. Although beyond the scope of this analysis, we note that this combination of life history parameters would also have the effect of increasing $F_{ST}$ between CEU and YRI on the X relative to autosomes, as has been observed (12, 42). In summary, our results illustrate that fairly recent changes to life history traits (relative to the average age of neutral polymorphism in either population) can dramatically affect X:A diversity ratios. In particular, we show that the reduction in diversity ratio in CEU relative to YRI can be explained by assuming that life history parameters varied within plausible ranges over time and across populations.

Fig. 6.

The expected reduction in X:A diversity ratios in CEU vs. YRI given previously inferred historical changes in population size (Fig. 7A) and different models of life history (see text for details). (i) Without life history effects: $G_M/G_F=\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/\left({\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\right)=1$. (ii–iv) The ratios $G_M/G_F$ and $\left({\gamma }_M{V}_M+{\gamma }_F/{\gamma }_M\right)/\left({\gamma }_F{V}_F+{\gamma }_M/{\gamma }_F\right)$ are allowed to vary within the ranges detailed in the text and are chosen to maximize the current reduction in diversity ratios in CEU relative to YRI given: (ii) life history ratios that are constant over time and populations; (iii) life history ratios that can differ before and after the populations split but are the same in both populations; and (iv) life history ratios that are the same before the populations split but different after. The observed reduction in the X:A diversity ratio in CEU relative to YRI is shown for comparison.

Diversity Ratios in Six Populations.

Next, we examine whether variation in life history can explain the diversity ratios observed in all six populations jointly. For comparison, we first consider the model without sex-specific life history parameters, which expectedly yields a poor fit (Fig. 7B). Next, we allow for sex-specific life history parameters (within the ranges detailed above) and let them vary among the intervals defined by the approximate split times among populations (Fig. 7A). In particular, we seek the parameter values that minimize a weighted squared distance between predicted and estimated diversity ratios (SI Appendix, section 3). Allowing sex-specific life history parameters to vary over time but not among populations substantially improved the fit but fails to account for some features, for example the high ratio in YRI (Fig. 7B). Further allowing sex-specific life history parameters to differ after populations split from one another, we are able to closely match the point estimates for all six populations (with mean distance <0.11 SEM averaged over the observed estimates; Fig. 7B).

Life History Traits during Human Evolution.

Our results illustrate that historical changes in sex-specific life history traits and in population size can explain the X:A diversity ratios in extant human populations. Our analysis relied on somewhat arbitrary decisions to fit a few current diversity ratios using many “historical” life history parameters, which included assumptions about possible parameter ranges, the time intervals in which they could vary, and the distance between predictions and estimates that was minimized. Alternative decisions would doubtless result in other sets of parameters that match the estimates of diversity ratios to a similar degree (accounting for uncertainty). The specific set of values we found (SI Appendix, Fig. S7) should therefore be treated as one of many possibilities; narrowing these sets down will require bringing to bear richer summaries of the data (see Discussion). Nonetheless, our results suggest a few conclusions. The first is that ancestral human populations were highly polygynous, as explaining the diversity ratios in YRI would be difficult otherwise. Second, they indicate that non-African populations experienced a substantial reduction in polygyny and/or increase in male-biased generation times around the OoA bottleneck, helping to explain the large reduction in diversity ratios in non-African populations. Third, we find that, quite surprisingly, fairly recent changes in sex-specific life history have had a substantial impact on current diversity levels and in particular can help to account for the reduced ratios in European populations relative to African ones, and Asian populations relative to European ones.

Discussion

Life history traits, and generation times in particular, affect X:A diversity ratios in multiple ways, and these effects can be surprisingly strong (2, 26). In humans in particular, we have shown that the longer generation times in males than in females substantially reduce the mutation rate and increase coalescence rates on the X relative to autosomes. They also substantially enhance the reduction in the X:A diversity ratio due to bottlenecks, both by accelerating the response time in generations and by increasing the number of generations per unit time on the X relative to autosomes. These generation time effects compound those of higher variance in male offspring numbers than females (i.e., polygyny) that were explored by previous studies (2, 5, 9, 12, 15, 24). Higher male variances reduce coalescence rates on X relative to autosomes and dampen the effects of changes in population size on X:A diversity ratios. We have shown that, considered jointly, these effects can explain observed X:A diversity ratios across human populations.

While our results have clear implications about life history traits in recent human evolution, our ability to draw quantitative conclusions is limited by remaining gaps in our knowledge of demographic history. Current demographic inferences assume that the autosomal generation time and mutation rate were constant, whereas both have doubtless changed over time. Ignoring such changes introduces errors in estimates of effective population sizes and in their assignment to past dates (i.e., in years). Correcting these errors is unlikely to change our qualitative conclusions but would likely affect the life history parameter estimates. The same is true of demographic complications that we did not consider, including historical migration/admixture among populations (43) and ancient introgression (44, 45), and possible sex biases in these processes (9, 10, 46).

Our analysis also relied on pedigree-based estimates of mutation rates in contemporary humans in order to model mutational effects on X:A diversity ratios. We used these estimates to infer X:A $N_e$ ratios and to relate models of historical life history trait values to current X:A diversity ratios. Because pedigree-based estimates to date report only autosomal mutations, we assumed that mutation rates on the X are well predicted by the average rates in males and females, i.e., that ${\mu }_X=\frac{1}{3}{\mu }_F+\frac{2}{3}{\mu }_M$. Although this assumption is inexact, given evidence that other factors influence mutation rates on the X, the observed effects are fairly subtle (47). In the future, larger pedigree studies in humans, with a sufficient number of mutations on the X, should allow direct estimation of mutation rates on the X. Our approach also assumes that the male mutation bias and the dependence on generation times observed today hold for the entire period over which neutral diversity in extant humans arose, i.e., over the past ∼1.5 My (39). The evidence regarding evolutionary change in male mutation bias is contradictory. Divergence-based estimates of $\alpha$ in great apes are extremely variable across lineages, with estimates of 2.81 for humans, 5.13 for chimpanzees, 1.15 for gorillas, and 1.96 for orangutans (29). In contrast, pedigree-based estimates of $\alpha$ in extant species spanning a much greater phylogenetic range, that is, mammals, appear to be stable (albeit with large confidence intervals) and consistent with the estimates in humans (37, 48–53). Larger pedigree-based studies in other catarrhine species will likely resolve this apparent conflict and inform the plausibility of our assumption. More generally, we note that pedigree-based estimates of the autosomal mutation rate have triggered a wholesale revision of the chronology of human evolution obtained from genetic data (39). Similarly, our results call for a revision of our thinking about human X:A diversity ratios in light of pedigree-based estimates of the male mutation bias.

Novel insights about mutation may also facilitate direct inferences about historical changes in life history traits. Such inferences could rely on the fact that different kinds of mutations have distinct dependencies on male and female generation times (27) but share the same genealogies. It may therefore be possible to infer male and female generation times from the ratios of different kinds of mutations of similar age on X and autosomal genealogies. It might also be possible to extend methods like MSMC to utilize data about different kinds of mutations on the X and autosomes jointly, in order to infer historical changes in both generation times and effective population sizes, and possibly even sex-dependent migration between populations. It is, however, hard to predict whether such approaches would be well powered, especially given more limited data on the X.

While we focused our analysis on humans, for which there are more data, there is every reason to think that life history substantially affected X:A diversity ratios in other species as well. Notably, sex differences in life history traits and changes in population size, as well as extensive variation in these factors among populations and closely related species, are pervasive [e.g., among vertebrates (54)]. It almost necessarily follows that the life history and particularly the generation-time effects that we describe would have affected their X:A diversity ratios.

Data Availability.

The data we used are publicly available as detailed in SI Appendix. Documented versions of all of the software we used are available at https://github.com/sellalab/XA_poly.