Genomic evidence for males of exceptional reproductive output (ERO) in apes and humans

ABSTRACT

It is widely suspected that a small percentage of males have exceptional reproductive output (ERO) but progeny numbers of males are rarely measurable, even in humans. If we define the variance ratio of reproductive-output in males and females as α′ = V_M/V_F, the ERO hypothesis would predict α′ ≫ 1. Since autosomal, X, and, Y chromosomes are found in males 1/2, 1/3, and 100% of the time, their DNA diversities can inform about α′. For example, autosomal and Y-linked diversities are governed, respectively, by (V_M + V_F)/2 and V_M. When comparing the chromosomal diversities, α′ appears to be near 20 for chimpanzees and orangutans, and 1–10 for gorillas. The exception is bonobos with α′ < 1. In humans, extensive genomic data are coupled to a theory, developed herein, that can filter out selection influences on Y-linked diversities. Hence, the estimation of α′ is rigorous, yielding values near or above 20, depending on the population. When α′ > 10, the presence of ERO males is very likely. These analyses can be applied more generally to species with XY sex determination.

INTRODUCTION

In sexually reproducing species, the two sexes may evolve divergent reproductive strategies toward breeding success [1–3], defined as each individual's progeny (K) reaching maturity. Obviously, the mean breeding success for males and females, E_M(K) and E_F(K), should be the same. In contrast, the variance of male breeding success, V_M(K), is likely larger than that of females, V_F(K).

An extreme form of male reproductive strategy may be the phenomenon of exceptional reproductive output (ERO) males. It has often been speculated that a small percentage of males in many species have an outsize contribution to the gene pool [4–6]. However, the difficulties in measuring male breeding success have hampered studies of social-sexual behaviors and, more generally, of sexual selection. Here, we are interested in great apes including humans. Despite extensive field studies on primates [7–12] as well as anthropology, sociology, and behavioral biology on humans [3,13], the breeding successes of individual males are usually uncertain.

If we define α′ = V_M(K)/V_F(K), field studies of monkeys have suggested α′ to be between 1.5 and 6.5 in Macaca or Mandrillus species [14,15]. Of greater challenges are ERO males whose reproductive successes (i.e. their K values) are outliers in the biological sense. (In statistical terms, outliers are males from the tail end of a highly kurtotic K distribution.) For example, if 1% of males are outliers with K = 40 while keeping E(K) ∼1 (per parent), V_M(K) and α′ would increase by >15-fold. In other words, K should be highly kurtotic if α′ is large, say >10 (see Discussion for further details). ERO males are therefore few and likely to be missed in field studies. They are occasionally known, or suspected, in human societies [5,16–18] but can be further investigated by estimating α′ more broadly across species with XY sex determination.

This ratio α′ can be obtained from the polymorphism data of the Y, X, and autosomes (A) as they respectively spend 100%, 1/3, and 1/2 of the evolutionary time in males. Note that the ratio of mutation rate between sexes, α (without the prime), has been estimated using the same logic [19]. The difference is that the mutation rate is estimated from the level of species divergence whereas α′ must be estimated from the within-species polymorphism.

The goal of this study is to obtain the levels of neutral polymorphisms among A, X, and Y to estimate α′. However, the relative levels of X/A and Y/A are simultaneously affected by selection and sex-dependent drift. While studies focus on either selection [20–22] or sex-dependent drift [4,23,24], it is clear that both are operative. In particular, selection is stronger on X- and Y-linked than on autosomal genes because recessive mutations are exposed to selection and X-Y recombination is absent. This exposure can reduce the X/A and Y/A polymorphism ratios [22,25,26].

Since our goal is to estimate α′ from DNA sequence data, it would be best to filter out cleanly the effect of selection on DNA diversities. As each Y chromosome is a non-recombining haplotype, Y's are amenable to estimation of the true neutral diversity whereas the task is more difficult for X. For this reason, the Y/A ratio, after correction for different selective pressures, should be more reliable for estimating α′ than X/A (see Results). When properly done, the estimation of α′ may provide new perspectives into the social-sexual behaviors of the great apes. Nevertheless, caution must be taken when applying the approach developed here to other taxa with chromosomal sex determination due to the many nuances that could make the estimation challenging. Such nuances include the different selective pressures on sex chromosomes vs autosomes [22,25,26] as well as the history of X vs. Y evolution [27,28]. Finally, because the dynamics of the XY and ZW systems mirror each other, one may wish to extend the analyses to the ZW systems. In the Discussion, we suggest the refinements that will be needed for such extensions.

RESULTS

In PART I, the theory for estimating α′ = V_M(K)/V_F(K) based on the data of neutral nucleotide diversity is provided. In the analyses of non-human apes in PART II, we use the measure of polymorphism that is relatively insensitive to selection, θ_w [29], when estimating the diversity ratios between X, Y, and autosomes. In contrast, another commonly used statistic, θ_π, is strongly influenced by selection [22,30] in this application. Nevertheless, there may still be residual influences of selection in the θ_w data. Because the X- vs. Y-linked reductions have opposite effects on α′, an MSE estimation is presented to balance the biases. In PART III, the extensive human data motivate the development of θ₀ estimation that is the theoretical limit of selection-free diversity. The caveat is that the procedure is applicable only to the non-recombining Y-linked mutations. Generally speaking, the estimations of α′ offer a clear picture of the evolution of the social-sexual behaviors in apes and humans.

PART I. General theory for estimating the V_M (K) /V_F (K) ratio

Let K be the progeny number of each individual. The mean values of K for males and females are generally the same, or E_M(K) = E_F(K). The variances of K are V_M(K) and V_F(K) and are generally believed to be V_M(K) > V_F(K) [11,31]. The ratio α′ is our main interest:

This ratio can be estimated from the polymorphisms of Y, X, and autosomal (A) sequences since they are present in males 100%, 1/3, and 1/2 of the time. The level of DNA polymorphism is governed by the parameter θ (=4N_eμ) where N_e is the effective population size and μ is the mutation rate. N_e and μ are both different for all three chromosomes. For convenience, we denote the mutation rate of X and Y chromosomes as xμ, and yμ, relative to the autosomal mutation rate μ. N_e is a function of the actual population size, N. The exact function would depend on the biology and evolution of the population. In the context of sexual reproduction, we use N_e = N/V(K), which was first obtained by [32,33] and further elaborated in [34,35]. For the three sets of chromosomes, under standard assumptions of diploidy and a 1:1 sex ratio, N_e(Y) = N(Y)/V_Y(K), N_e(X) = N(X)/V_X(K), and N_e(A) = N(A)/V_A(K) where N(A):N(X):N(Y) = 4:3:1 and V_{[Y,X or A]}(K)’s are as follows:

From the observed polymorphisms, θ (=4Nμ/V(K)) can be estimated. Supplementary Note 1 shows that α′ can be obtained three ways:

(1)

(2)

(3)

where R_YA, R_XA, and R_YX are, respectively, , and . The ratios can be estimated by the relative level of polymorphisms among the three chromosomes.

Two main challenges have to be met in applying Eqs (1–3) on genomic data to obtain α′. The first one is the extreme sensitivity of the α′ estimates to measurement errors in mutation rate and polymorphism. Figure 1a shows the dependence of α′ on R_YA and y. Note that the parameter spaces for α′ < 1 and α′ reaching infinity are much larger than the space for α′ in the feasible range (>1 but < infinity). The yellow band for the interval of [10, 20] is narrow, as shown, while the space for [20, infinity] is too small to show (see Fig. 1a legend). Hence, if the biology is such that α′ > 10, the data would likely show α′ < 10 or approaching infinity. Figure 1b shows the same sensitivity in the X vs. A comparison. The second challenge is natural selection (both positive and negative) which would reduce the level of polymorphism [36–38]. Interestingly, under-estimating polymorphism on X and Y would have opposite effects on the estimated α′ values (Fig. 1a vs. b).

Figure 1.

The dependence of α′ on the relative diversity (R) and mutation rate (x, y)—the α′ values are shown by different colors in the heatmap. (a) Estimation based on the Y-A comparison. The X axis is the y value, which is the relative mutation rate of Y and autosomes. The Y axis is R_YA (= θ_Y/θ_A). Note that the yellow band for α′ in the interval (10, 20) is much smaller than the green band for (1, 10). The band for α′ in the interval (20, infinity) is even thinner than the yellow band and is hence merged with the pink zone of infinity. The black rectangle represents the distribution of α′ at y = 1.68. Note that α′ increases as R_YA decreases. (b) Estimation based on the X-A comparison. The X axis is x value and the Y axis is R_XA. Contrary to (a), α′ decreases as R_XA decreases. In both (a) and (b), the yellow strip shows the narrow parameter space for α′ between 10 and infinity.

To meet these challenges, we use the statistics that mitigate the influence of selection and measurement errors in PART II. In PART III, an explicit model that incorporates selection and chromosome-dependent N_e is developed for human datasets.

PART II. Genomic polymorphisms in non-human apes

To estimate α′ by Eqs (1–3), we need to obtain the relative levels of polymorphism, R_YA, R_XA, and R_YX, as well as the relative levels of mutation rate, x and y. Since these quantities are based on neutral variants, noncoding region sequences are used. The values of x and y in humans and chimpanzees have been reported as x = 0.77–0.80 and y = 1.60–1.68 [39,40]. A salient property of population genetics is that the neutral rate of divergence between species can be formulated as 2Nμ(1/2 N) = μ [33,41]. The rate is hence a function of the mutation rate only (x and y here) and does not depend on N or N_e. We shall use the values most commonly used in long-term species divergence estimates [39] of x = 0.77, y = 1.68. It should be noted that most of the published numbers are within a tight range [40,42]. Furthermore, the paired (x, y) estimates of different studies vary in ways that minimally affect the estimation of α′ (see Fig. 1).

The extraction of θ’s from the sequence data demands close attention. As stated, the θ value of each chromosome has to represent its neutral level. However, the observed diversities on Y, X, and A may not reflect the neutral levels equally. In particular, both X- and Y-linked diversities are expected to be lower than autosomes due to the stronger influence of selection on two fronts: (1) the hemizygosity in XY males exposes recessive mutations; and (2) the hemizygosity also reduces recombination, thus facilitating hitchhiking with other mutations on the same X or Y chromosome. Between X and Y, genes on Y are fully linked but there are far fewer fitness-related mutations. This disparity arises from the Y chromosome's lower gene density and their preservation may enhance male fitness but with limited overall fitness impact [26,43,44].

Among the many statistics for θ [29,36,37,45,46], those giving more weight to low-frequency variants are less sensitive to selection (see Eq. (4) below), including θ_w [29] and θ₁. While θ_w is more commonly used, θ₁ (only singletons are considered) is much closer to the neutral state than other variants [37]. The most commonly used statistics, θ_π [22,30,47], would be dictated by the mid-range frequencies (near 0.5) where selection influence would predominate.

As noted in Fig. 1a and b, the estimated α′ values are very sensitive to even slight variations in the observed diversities (R_YA, R_XA, and R_YX). To alleviate the sensitivity, we combine the three estimates of Eqs (1–3) by identifying α′ that yields the minimum MSE (Mean Squared Error; see Eq. (5) in Methods). Note that a decrease in Y-linked polymorphism would lead to over-estimating α′ but the opposite trend is true for X-linked polymorphism. Therefore, the minimum MSE estimates of α′ should buffer against under-estimation of sex-linked (both X and Y) polymorphisms.

The data of non-human great apes were compiled by Hallast et al. [30] from various publications [25,48] on the 4 species—bonobo, chimpanzee, gorilla, and orangutan (Supplementary Materials and Table S1). We use θ_w to estimate the minimum MSE estimation of α′ in Table 1. The basic information is shown in the first five columns. In the three θ_w columns, X-linked diversity is usually lower than the autosomes and, crucially, Y-linked diversity is always lower than autosomes and by a larger margin.

Table 1.

α′ Estimates for non-human great apes (θ_w).

	n (Y, X, A)	θw(Y) (×10–3)	θw(X) (×10–3)	θw(A) (×10–3)	Z(YX)	Z(XA)	Z(YA)	MSE α′	Expanded n (Y, X, A)	MSE α′
Non-human great apes
Range for Z with α' >1*	–	–	–	–	<0.33	>0.75	<0.25	–	–	–
Bonobo	(4, 4, 26)	0.492	0.446	0.867	0.506†	0.669	0.338	0.570	(7‡,24§,26)	0.574
Chimpanzee
Western	(9, 7, 10)	0.034	0.533	1.624	0.029	0.426	0.012	4.98	(77‡,7,10)	4.140
Eastern	(3, 3, 12)	0.1442	1.044	1.446	0.063	0.938	0.059	25.9	(6‡,10§,12)	3.762
Nigeria-Cameroon	(4, 4, 20)	0.213	0.8181	0.703	0.119	1.511	0.180	Inf	–	–
Gorilla
W lowland	(7, 7, 54)	0.1376	0.7219	1.555	0.087	0.603	0.053	4.53	(7, 50§, 54)	5.366
E lowland	(3, 3, 18)	0.0653	0.0921	0.714	0.325	0.168	0.054	1.11	–	–
Mountain	(3, 3, 14)	0.0007	0.2211	0.652	0.001	0.440	0.001	6.07	–	–
Orangutan
Sumatran	(4, 4, 10)	0.0221	1.2282	2.0089	0.008	0.794	0.007	23.49	(4, 9§, 10)	22.356
Bornean	(2, 2, 10)	0.1354	0.5569	1.4369	0.111	0.503	0.056	3.35	(2, 9§, 10)	3.294

The X and Y data are from [30]; the autosomes data from [25], except the Gorilla autosome data which are from [48]. The sample sizes for each chromosome are denoted as n(Y, X, A). *This row gives the expected range of Z values for α′ >1. The expected value is based solely on the nominal numbers of A, X, and Y in the population, given that Z(YX), Z(XA), and Z(YA) are the ratios of the normalized nucleotide diversity with chromosome-specific mutation rate. ^†Red letters indicate cases of Z values yielding α′ <1. As explained in the main text, Z(YX), Z(XA), and Z(YA) are biased in different ways. If we examine each column separately, Z(YX) and Z(YA) columns are significantly different from the predicted values under α′ = 1. Whereas Z(XA) data by themselves do not reject the null hypothesis of α′ = 1. Expanded sample sizes are provided in the 10th column, with new data noted as follows: ^‡data from [85]; ^§data from [25].

These patterns are more intuitively readable in the next three Z columns. The Z ratios, Z(YA), Z(XA), and Z(YA), are represented by , , and , respectively. Hence, the Z values would reflect the chromosome polymorphism, normalized with chromosome-specific mutation rate, relative to copy number. For example, Z(YA) <0.25 would mean α′ > 1, since the copy number of Y is 1/4 of that of autosomes. Those entries that do not show α′ > 1 are shown in red letters. One can see that Z(XA) values are often shown in red. As stated, both X- and Y-linked polymorphisms are underestimated since natural selection is more effective on hemizygous chromosomes. The MSE estimates of α′ in the third column from the right would mitigate these biases as under-estimation of X- and Y-diversity affects α′ in the opposite direction.

Because the data come from multiple sources, we choose a subset that is most consistent in quality (such as read length, coverage and clarity in annotation). As a result, the sample size is sometimes on the lower side. In the last two columns, the stringency of data filtering is relaxed to allow for a larger sample size (Table 1). The alternative α′ estimates are largely concordant with those of the stringent set; however, one glaring discrepancy exists. The augmented α′ for Eastern chimpanzee is reduced from 25.9 to 3.76. There are both biological and technical reasons for such a large difference. Nevertheless, both estimates still show α′ >1.

Overall, the bonobo is exceptional as all α′ estimates are <1. The species has a matriarch social-sexual society [8,10,49]. It would seem plausible that V_F(K) would be unusually large and V_M(K) would be relatively small. All other α′ estimates are >1. In gorillas, α′ estimates are smaller than those in chimpanzees. Perhaps, with the harem system [9,50–52], gorillas may not have as many outlier males of high reproductive output as chimpanzees may have. Nevertheless, we should caution again that α′ estimates are very sensitive to measurement errors.

Figure 1a and b shows that the parameter space for α′ in [1, 10] or > 20 is large. In contrast, the parameter space for [10–20] is only a tiny strip shown by the yellow band in Fig. 1. Indeed, among chimpanzees, gorillas, and orangutans, 5 α′ values fall in the range of [1–10] and 3 fall above α′ >20. If we interpret α′ as the degree of highly biased reproductive success, the result may suggest a bimodal distribution of male reproductive behavior among these species, or even among populations. However, this would not be the correct biological interpretation. If there are no measurement errors, α′ values could be quite common in the interval of [10, 20]. In fact, α′ ≫20 would seem biologically implausible for many species.

PART III. Analyses of human polymorphisms incorporating selection and drift

To reduce any potential batch effects in analyzing multiple data sets from different resources, we obtained whole-genome deep sequencing data of Africans, Europeans, and East Asians from the Human Genetic Diversity Panel (HGDP) [53]. For the A, X, and Y diversities, we randomly selected 84 males of each population to obtain the polymorphism data. Only one haploid of the autosomes is used from each male, thus guaranteeing an identical sample size of n = 84 for each chromosome. The same procedure is then applied to the data analysis of the 1000 Genomes Project [54] data with n = 46. Details can be found in Supplementary Materials.

We will show mathematically that the low-frequency portion of the mutation spectrum is closest to the expected pattern under no selection. Therefore, both θ_w [29] and θ₁ [37] are used. While both positive selection and negative selection can influence θ estimation, PART III will focus on negative selection. Positive selection is of lesser concern and can be more easily interpreted after all results have been presented (see Supplementary Note 5).

Estimation of α′ based on θ_w and θ₁

In Table 2, we present the analysis of human polymorphisms based on the HGDP sample of n = 84. (Results from a second dataset of KGP with n = 46, shown in the last column, will be discussed later.) The upper part of Table 2 is based on θ_w as in Table 1. Here, the α′ values in the three populations are close to those of gorillas but lower than those of chimpanzees. The lower part of Table 2 presents the analysis of θ₁. In comparison, θ₁ exhibits higher values, indicating a higher degree of correction for the selection effect. Consequently, Z(XA) is larger by θ₁than by θ_w, leading to a larger α′. With θ₁, the lower part of Table 2 indeed reveals α′ >1 by all three measures, Z(XA), Z(YA), and Z(YX) and the MSE estimates of α′ in humans fall in the range of 10–20.

Table 2.

α′ Estimate in humans based on θ_w and θ₁.

	θ(Y)	θ(X)	θ(A)	Z(YX)	Z(XA)	Z(YA)	MSE α′ (n = 84) [Dev1 vs. Dev2]	MSE α′ (KGP n = 46)
θw (×10–3)
Range for Z with a′ > 1				<0.333	>0.75	<0.250
African	0.0535	0.8505	1.4301	0.029	0.772	0.022	13.850 [0.031 vs. 0.274]	12.164
Asian	0.0520	0.3835	0.7194	0.062	0.692*	0.043	6.822 [0.019 vs. 0.117]	4.586
European	0.0359	0.3842	0.7382	0.043	0.676	0.029	7.842 [0.015 vs. 0.0983]	6.202
θ1(×10–3)
Range for Z with a′ > 1				<0.333	>0.75	<0.250
African	0.1714	1.6314	2.4691	0.048	0.850	0.041	17.412 [0.051 vs. 0.224]	Inf
Asian	0.1886	0.8804	1.2137	0.098	0.942	0.093	11.690 [0.037 vs. 0.260]	Inf
European	0.1374	0.7948	1.1410	0.079	0.905	0.072	13.216 [0.036 vs. 0.168]	Inf

Data from HGDP, n = 84 for each population, except the last column for KGP, n = 46. *Red letters indicate cases of Z values yielding α < 1. See also legends of Table 1. Dev1 is the deviation covering the 95% confidence interval obtained by the resampling of DNA segments and Dev2 is the deviation based on the resampling of individuals (see main text for details).

For the confidence intervals, we perform two different bootstrapping procedures on the larger dataset of n = 84. For this purpose, we may resample either the DNA segments or the individuals, yielding deviations as Dev1 and Dev2, respectively. While the commonly used procedure is to resample the same number of times from the original sample with replacement [55,56], the two procedures are very different in scale. There are more than 3 million 1Kb segments to be resampled while there are only 84 individuals for bootstrapping. Details of the bootstrapping procedure are given in Methods.

As shown in the second to last column of Table 2, Dev1 (from resampling DNA segments) is very small, most likely due to the sheer number of DNA segments. Dev2 (from resampling individuals) is substantially larger with 84 individuals to be resampled. Nevertheless, the confidence intervals are small by either scheme. Importantly, resampling individuals introduces substantial bias due to the nature of the θ statistics. In particular, θ₁ relies on variants that occur in only one individual. In resampling, such singleton variants can be easily missed or appear more than once, and thus not counted. For that reason, we report Dev2 values as confidence intervals surrounding the estimates of the original estimates.

Regardless of how bootstrapping is carried out, it is still based on the information embedded in the original sample. For that reason, we use a separate but smaller dataset (KGP) to calculate independent estimates for α′. As shown in the last column of Table 2, these independent estimates are fairly close to the HGDP-based estimations. Considering that these two datasets are both based on samples from multiple populations within Africa, Asia, and Europe, we can be confident that the results of Table 2 are robust.

The extrapolation of variant frequency to 0

It would be desirable to cleanly filter out the influence of negative selection on Y-linked polymorphisms. If the variant frequency approaches 0, then Y/A should ideally represent the neutral ratio. In PART III, we let x be the variant frequency of both Y- and A-variants. This subsection presents only Eq. (4) of the theory for θ₀ where x approaches 0. This would be a check of how closely θ₁ represents the neutral value. Details are shown in Methods.

Let be the site frequency spectrum of Y-linked variants that are under selection of intensity s and be that of the autosomal variants without selection. The selective coefficient, s of SFS represents the joint effect of selection on all mutants on the Y (could be as low as one single mutant), averaged over time. The ratio, F(x) = , is obtainable from the polymorphism data. We assume N = 7500 for human autosomes [57,58]. For the Y chromosome, N′ = ηN where η = 0.5 in the ideal population. Hence, η < 0.5 is a measure of V_M(K). Also, we use the relative mutation rate ratio of Y-to-A = 1.68 [39]. When x is in the low frequency range (<0.1), the derivation in Methods show:

(4)

Importantly, Eq. (4) is a linear function of x with a slope of 15 000ηs. It can be seen from Eq. (4) that the low-frequency portion of the spectrum (x ∼ 0) is minimally affected by selection when the 15 000ηx approaches 0.

The goal is to obtain F(x ∼ 0) from Eq. (4), which will be equated with R_YA in the calculation of α′ by Eq. (1). Since ln [F(x)] is linear with x, we should be able to obtain F(x ∼ 0) from the observed data [i.e. F(i/n)] if we know the slope. (In practice, we only do the extrapolation from F(1/n) as its level of polymorphism is highest and sufficiently reliable.) To obtain the slope, we calculate one slope for each pair of ln [F(i/n)] and ln [F(j/n)] for , . We also use a dummy F*(x ∼ 0) = ηy = 0.5 y, which is the theoretical maximum for F(x ∼ 0). For each dataset, there should be 10 slopes for five data points [= ]. Each slope is used to calculate a different F(x ∼ 0) estimate, thus yielding 10 different α′ estimates from one dataset (see Methods).

Estimation of α′ based on θ (x ∼ 0)

For each human population, there are 18 estimates of α′, 9 from each dataset. Because the estimation is sensitive to measurement errors, we present each α′ estimate that represents one set of parameter measurements (i.e. the slope of Eq. (4)). The spread of these α′ estimates should more faithfully show where the actual α′ falls. The details are presented in Table S4.

The overall results are summarized in Fig. 2 which includes those of Tables 1 and 2. In Fig. 2, great apes in general show α′ > 1 based on θ_w. The parameter space for α′ falling in (1–10), (10–20), and (>20) are displayed according to the size of the segment. (Note that the expanded dataset, collected from various sources, yield concordant results but with one exception; see legends of Fig. 2.) The bonobo is a singular exception with both α′ < 1. Gorillas have all four estimates in the interval of (1–10). For chimpanzees and orangutans, the α′ estimates fall on the two sides of the (10–20) interval, suggesting that the true values may indeed be within, or slightly to the right of (10–20).

Figure 2.

Summary of the estimation of α′ = (V_M (K) / V_F (K)). The estimation of α′ has been done by procedures based on various θ statistics, each of which is accompanied by bootstrapped confidence intervals. Here, we further present all α′ estimates obtained from different datasets and procedures in one single figure to portray the broader range of α′ estimation. The estimates of α′ fall into 4 intervals (<1, 1–10, 10–20, and >20). The estimates based on θ_w are shown by red letters: Bonobo (B), Chimpanzee: Western (C_W), Eastern (C_E), Nigeria-Cameroon (C_NC); Gorilla: Western lowland (G_W), Eastern lowland (G_E), Mountain (G_M); Orangutan: Sumatran (O_S), Bornean (O_B), and Human. For non-human great apes, the α′ estimates by expanded sample size corresponding to the last column of Table 1, are shown as the expanded data set. Two α′ estimates for the same species are connected by grey lines. For humans, the green &’s are based on θ₁. The bootstrapping values of H's and &’s are provided in Table 2 and Table S3, respectively, along with estimates from another dataset (see text for further detials). The black 0’s are θ₀ estimates based on Eq. (4). Each 0 represents an estimate based on a different subset of the observed diversity values. The estimates are placed, roughly in order, only in intervals up to 20. When an α′ estimate falls above 20, there is little resolution. Hence, 0’s in that interval should all be read simply as α′ > 20.

For humans, α′ estimates are shown by θ_w (red letter H in Fig. 2), θ₁ (green &), and θ₀ (0’s in Fig. 2; based on Eq. (4)). First, the red-lettered α′ estimates based on θ_w are lower than the green letters based on θ₁. Since the other apes are analyzed by θ_w, their α′ values could be underestimated as well. Second, α′ estimates by θ₀ (with the arrowhead showing the median of 0’s) are moderately higher than by θ₁. Third, α′ estimates for Africans are consistently higher than for Asians and Europeans. The conservative conclusion is that, with the exception of the bonobos, great apes including humans have α′ near, or larger than, 10. Given the small parameter space shown in Fig. 1a, the resolution is reliable up to α′ ∼ 10, whereas there is little resolution between α′ ∼ 20 and infinity (see Fig. 1 legend).

Despite the difficulties in obtaining reliable confidence intervals for α′, the statistical patterns of Fig. 2 are robust. The H and & symbols are supported by bootstrapping on the larger data set (second to last column, Table 2). Furthermore, a smaller independent dataset yields concordant estimates (last column, Table 2). Finally, these conservative estimates, as expected, fall in the tail end of a cloud of estimates based on θ₀ (the 0’s). In Discussion, we will connect the high α′ estimates to the ‘ERO males’ hypothesis.

DISCUSSION

The conclusion of ERO males, based on the genomic data, can now be treated as a hypothesis. Importantly, the basis of comparison should be the ‘adjusted’ level of polymorphism after the different strengths of selection among X, Y, and autosomes have been accounted for. Among the measures, θ_π, θ_w, θ₁, and θ₀, the last one (i.e. θ₀ estimate of Y-linked polymorphism) is most appropriate. Its feasibility is due to the complete linkage that enables the estimation of selection on the entire Y. (In contrast, comparisons involving X are less accurate because its θ₀ estimate cannot be obtained due to recombination.)

Given that the equations for the XY and ZW systems are mirror images, the approach seems easily transferrable to the ZW system whereby females are heterogametic, as in birds and butterflies. However, in such systems, the confounding effects of selection would pose far more difficulties. In particular, most published diversities in ZW species are based on θ_π’s [59,60], the least desirable measures. It seems obvious that further developments of theories as done in PART III for Y will be necessary for the Z and W chromosomes. We shall now discuss three types of tests: (i) field observations, (ii) social-sexual conditions, and (iii) other possible tests.

(i) Field observations—The overall conclusions are broadly consistent with the general understanding of the social-sexual behaviors of great apes [3,9]. Bonobo is the only species with α′ < 1 as calculated by θ_w. Since the estimation based on θ_w would yield a lower α′ than θ₁ (Table 2), its α′ value may be closer to 1 than estimated. Bonobos are not expected to have ERO males given their strongly matriarchal society [8,10,49]. It is possible that their V_M(K) is unusually small whereas V_F(K) is unusually large, thus giving rise to α′ ≤ 1.

Gorillas have the second smallest α′ that falls between 1 and 10. They usually have a harem structure [9,50–52] whereby α′ is expected to be >1. However, α′ may not be very high since males do not have access to a large number of females to become ERO males. For chimpanzees, humans, and Sumatran orangutans, α′ values are likely ≥20, reflecting a very large V_M(K). While both orangutan species share a semi-solitary lifestyle, Sumatran orangutans live in higher-density populations with more frequent social interactions, increased male competition, and greater access to females than Bornean orangutans [61–63]. This heightened competition may lead to greater reproductive skew, which explains the higher α′ values observed in Sumatran orangutans.

While this study focuses on humans and great apes, the reported patterns may be general. Table 3 compiles field observations of three species of old-world monkeys and one rodent species. Although the reported K*’s are observed progeny numbers rather than the formulated K (reproductive success), the trend is as expected. The ratio of progeny variance between males and females is indeed much larger in species of polygeny than in species of polyandry or monogamy. However, field observations do not yield α′ estimates, which are obtainable only from the genomic data as explained below.

Table 3.

Field observations of progeny numbers (K*) in non-ape mammals under three different socio-sexual structures.

Species	Order	Sex	E(K*)	V(K*)	V(K*)M/V(K*)F	[V/E]M/[V/E]F	Mating system	Literature
Macaca mulatta	Primates	Female	7.7	15.4	6.41	5.67	polygyny	Dubuc, Ruiz-Lambides [14]
		Male	8.7	98.7
Mandrillus sphinx	Primates	Female	4.7	19.8	3.44	4.63	polygyny	Setchell, Charpentier [11]
		Male	3.5	68.2
Macaca sylvanus	Primates	Female	1.2	2.9	1.34	1.08	polygynandry	Kuester, Paul [15]
		Male	1.5	3.9
Peromyscus californicus	Rodentia	Female	4.7	7.7	1.78	1.90	monogamy	Ribble [86]
		Male	4.4	13.7

Note that K* is the observed number of births whereas K formulated in this study is the long-term reproductive success. While E(K) should be close to 1, E(K*) reported here is substantially larger.

The high α′ values so obtained for humans and great apes are interpreted to mean a small percentage of ERO males. Note that a high α′ is equivalent to a high V_M(K) which can be due to either a few outlier males with very large breeding successes or many males with moderate successes. The former is favored because of the constraint of E_M(K) = E_F(K) ∼ 1 [= E(K)] as E(K) should be close to 1 over the evolutionary time scale. Thus, if many males have high reproductive successes, females should be equally productive, thus raising E(K) to an unsustainable level. For example, if 10% of males produce K = 5 progeny (while other males and all females having E(K) = V(K) = 1), α′ would be <2, but E(K) would be nearly 1.5. On the other hand, if there are only 1% outlier males with K = 40, then α′ would be >15 with a similar E(K), while allowing some males to have no offspring can maintain E(K) close to 1. In other words, only large K’s can lead to large α′ without substantially increasing E(K). In Supplementary Note 4 and Fig. S2, we provide a more formal analysis using the Gamma distribution.

It is noteworthy that the long-term stochastic effect is determined by the generation with the largest variation. (Thus, the long-term N_e is the harmonic mean of N’s across generations.) Therefore, ERO males only need to emerge once in a while to have a large impact on evolution.

(ii) Social-sexual conditions—Many factors of the social-sexual structure may contribute to the emergence of ERO males and large α′ values. We shall discuss only two such factors. First, the absence of paternal care may permit males to pursue ever higher K’s. That may be part of the differences between chimpanzees and gorillas, as gorilla fathers are known to provide protection [12], while paternal care in chimpanzees is rare or negligible [64]. Neither do orangutans show paternal care [12,65]. For example, ERO males have been observed in Macaca mulatta and Mandrillus sphinx. Both males provide little paternal care and can sire a maximum of 47 and 41 offspring [11,14], respectively, much higher than the reproductive output of females.

Second, and most interesting, the reproductive advantage of males can be amplified non-genetically. Powerful parents, either maternal or paternal, can help their sons gain social-sexual advantages [66,67]. So do successful brothers who form coalitions [8]. Consequently, the advantages in one generation may be amplified in several subsequent generations, as speculated [68]. Humans and chimpanzees share some of these behavioral traits. They include male philopatry with female-biased dispersal [69,70], allowing males to remain in their natal groups and form male–male cooperation within strong alliances [8,71,72]. Furthermore, maternal support for sons in their pursuit of social dominance and mating opportunities are also well known [8,71,72]. Genomic studies have indeed suggested that humans are closer to chimpanzees than to gorillas in their male reproductive strategies [2]. A new direction taken by neuro-scientists who use non-human primates as a research model may be promising in resolving some of these issues [73–76]. Field studies such as those on colobine monkeys [77] should be able to discover additional social conditions for the emergence of ERO males.

(iii) Other tests—It should be noted that the ERO phenomenon reflects the average over the evolutionary time span, close to the coalescence time of Y-linked genes, roughly 50–250 000 years in humans [4]. In contrast, observations in field studies reflect social-sexual patterns in specific ethnic groups during a specific period. The two lines of evidence are not always compatible. For example, in Brown et al.’s survey [31] of modern human society, α′ is between 1 and 5. A possible explanation can be found in the studies of Yanomama and other South American ethnic groups. J. V. Neel [5] observed that the unacculturated ethnic groups tend to have a few ERO males (or headmen) that sire large numbers of children and grandchildren. Such strong reproductive biases may also account for the unusually large genetic differentiations among local tribes. In this context, there would be particular interest in humans’ recent past [13,78,79], whereby ‘field observations’ in the form of historical documents and sociological records are extensive. Hence, if we can infer the recently accumulated variations on the A, X, and Y chromosomes [80,81], field observations and genomic data would be directly comparable.

In conclusion, while previous studies have invoked either selection or sex differences in breeding success (but not both [4,21,22,38]), this study takes into account both forces (see Supplementary Note 5 for discussions on positive vs. negative selection). Consequently, the estimation of α′ reveals an extreme form of sexual selection that could only be speculated before.

MATERIALS AND METHODS

Non-human data collection, θ_w estimation, and human data processing

Details are presented in Supplementary Materials.

The α′ estimate with minimum MSE (Mean Squared Error)

To mitigate the issue of the α′ estimation's extreme sensitivity to measurement errors in chromosome diversity and mutation rate, we employed a combination of Eqs (1–3) and minimum MSE to determine the optimal α′. We generated a range of potential values ranging from 0 to 200, with increments of 0.001. For each α′, we computed the expected three diversity ratios Exp[R_YA], Exp[R_XA], and Exp[R_YX], using Equations in Supplementary Note 1. Subsequently, based on the observed diversity ratios, Obs[R_YA], Obs[R_XA], and Obs[R_YX], and the calculated Exp[R], we estimated the MSE for each α′ as follows:

(5)

The α′ value corresponding to the minimum MSE was used in Tables 1 and 2. Values exceeding 200 are designated as ‘Inf’. We applied this method to investigate the α′ estimate with the minimum MSE, incorporating three observed diversity ratios for each pair of chromosomes.

Bootstrapping procedure

Resampling DNA segments—The noncoding portion of chromosome sequences from 84 individuals in the HGDP dataset were grouped by chromosome type (n = 84 for X, Y, and autosomes) and aligned within each group. The pooled alignments were then divided into non-overlapping 1Kb segments, yielding 2 875 310 segments for the haploid autosomes, 156 060 for the X, and 57 240 for the Y. Bootstrapping was re-iterated 10 000 times. Each time, 120 000 segments were sampled with replacement from autosomes, X, and Y for the calculation of α′, based on the resampled θ_w and θ₁, respectively (see Supporting Materials for details). Note that α′ ± Dev1 in Table 2 covers ≥95% of the bootstrapping values.

Resampling individuals—In each of the 100 iterations, 84 individuals were sampled with replacement from the HGDP dataset (n = 84). For each bootstrap iteration, α′ was estimated based on θ_w and θ₁, following the same procedure as applied to the original dataset. The reported α′ ± Dev2 in Table 2 represents the interval covering ≥95% of the bootstrapping values.

Linear extrapolation for F(x ∼ 0)

Here, Eq. (6) is an extension of [82], and in a somewhat different form from [83], for the effect of selection on the site frequency spectrum (SFS) (detailed derivations are given in Supplementary Note 2),

(6)

When s = 0, Eq. (6) is reduced to

(7)

as is generally known. Φ(x) is the probability density of mutations of frequency x in the population. Here, we use Eq. (6) to portray the mutation spectrum of Y-linked mutations under selection, denoting the variant frequency, population size, and mutation rate as x′, N′, and v′, respectively. The simpler Eq. (7) is for autosomal mutations. What we need is the SFS ratio of Y to autosome, hence,

(8)

While s can be positive or negative selection, the numerical results presented will only be about cases of s <0; i.e. the so-called background selection on Y [22,38,84]. N is for the autosomes. For the Y chromosome, N′ = ηN where η = 0.5 in the standard WF population as only half of the population has Y. Importantly, η < 0.5 is a measure of V_M(K). Furthermore, because N is at least 1000 and . F(x) in the logarithmic form when x ≪ 1 would be Eq. (4), with further details provided in Supplementary Note 3.

To estimate the F(x ∼ 0) through linear extrapolation, we utilized ξ_i in the human population (Table S3), where i = 1, 2, 3, 4. Based on Eq. (4), we defined the ratio of F(0) to F(1/n) as ,

Considering the N is large and s is a negative value of deleterious mutations, both and . Therefore, with transformed,

(9)

We set N = 7500, with sample sizes of n = 84 for HGDP and n = 46 for KGP. was simplified as and accordingly.

For each dataset, we generated pairs of ln [F(i/n)] and ln [F(j/n)], where 0 ≤ i < j and j ≤ 4, resulting in 10 slopes for five data points. Notably, the slope between F*(x ∼ 0) and F(1/n) was treated as a dummy number and was not used in the analysis. Next, we employed the nine slopes generated from Eq. (4) along with Eq. (9) to produce a set of . Each slope was used to calculate a distinct F(x ∼ 0) estimate, thus yielding nine different α′ estimates from one dataset.

Finally, we extrapolated F(x ∼ 0) from F(1/n)

(10)

Hence, we obtained R_YA = F(x ∼ 0). By applying R_YA to Eq. (1), we derived nine α′(YA) values for each population from one dataset (Table S4).

FUNDING

This work was supported by the National Natural Science Foundation of China (32293193/32293190, 32150006 to C.I.W., 82341092 to H.J.W., 32370659 to G.L., and 32288101, 32030020 to S.X.), the Guangzhou Science and Technology Planning Project (2025A04J3499 to Y.R), the Guangdong Basic and Applied Basic Research Foundation (2023A1515010016), the Shanghai Science and Technology Commission Program (25JS2810100 to S.X.). The CFFF Computing Platform of Fudan University supported the computational work in this study.

AUTHOR CONTRIBUTIONS

C.-I.W. and X.W. conceptualized the study. X.W. and Y.R. designed the analytical framework for estimating α″. H.C. performed the main analyses of human genomic data. X.W., L.Z., M.H. and Y.G. curated and organized datasets of non-human species and contributed to data visualization. X.L. and P.F. provided expertise in animal behavioral ecology, while S.X. offered guidance and data references from human genomics projects. H.W., M.T. and L.H. contributed resources and technical support. C.-I.W., H.W., Y.R., and S.X. supervised the research and secured funding. X.W. and C.-I.W. wrote the initial draft. All authors contributed to data interpretation and revised the manuscript.

Conflict of interest statement. None declared.