Population-genetic influences on genomic estimates of the inbreeding coefficient: a global perspective

Abstract

Background/Aims

Culturally-driven marital practices provide a key instance of an interaction between social and genetic processes in shaping patterns of human genetic variation, producing, for example, increased identity by descent through consanguineous marriage. A commonly used measure to quantify identity by descent in an individual is the inbreeding coefficient, a quantity that reflects not only consanguinity, but also other aspects of kinship in the population to which the individual belongs. Here, in populations worldwide, we examine the relationship between genomic estimates of the inbreeding coefficient and population patterns in genetic variation.

Methods

Using genotypes at 645 microsatellites, we compare inbreeding coefficients from 5,043 individuals representing 237 worldwide populations to demographic consanguinity frequency estimates available for 26 populations, as well as to other quantities that can illuminate population-genetic influences on inbreeding coefficients.

Results

We observe higher inbreeding coefficient estimates in populations and geographic regions with known high levels of consanguinity or genetic isolation, and in populations with an increased effect of genetic drift and decreased genetic diversity with increasing distance from Africa. For the small number of populations with specific consanguinity estimates, we find a correlation between inbreeding coefficients and consanguinity frequency (r=0.349, P=0.040).

Conclusions

The results emphasize the importance of both consanguinity and population-genetic factors in influencing variation in inbreeding coefficients, and they provide insight into factors useful for assessing the effect of consanguinity on genomic patterns in different populations.

Introduction

Inbreeding refers to the production of offspring by the mating of related individuals, often via consanguinity—intra-familial unions of individuals related as second cousins or closer. A large body of ethnographic evidence supports the commonplace occurrence of consanguineous unions in many traditional human societies, with 353 of the 763 societies listed in the ethnographic tabulations of G.P. Murdock either permitting or favoring marriage between first or second cousins [1,2].

In addition to its occurrence through consanguinity, inbreeding often takes place in human populations “cryptically” as a consequence of background relatedness—recent but unknown kinship among mating pairs. It has been estimated that even in a large randomly mating population of 1 million individuals, at least one shared ancestor likely exists for any given pair of individuals within the last 11 generations [3]; this value decreases to six generations for a population of size 1,000. Compared with ostensibly outbred populations, groups that are more inbred can have a higher prevalence of rare recessive monogenic disorders [4,5]. Further, within-population comparisons have observed a higher prevalence of these disorders [6-8], and in many cases, common multifactorial disorders [9-14] and even infectious diseases [15-17], among inbred individuals compared with more outbred individuals. Thus, understanding worldwide patterns of inbreeding has important consequences for human genetic disease investigations, requiring knowledge both of sociocultural factors that promote overt inbreeding through consanguinity, and of population-genetic processes that underlie cryptic inbreeding through background relatedness.

A commonly used measure to quantify the level of inbreeding that exists in an individual’s lineage is the inbreeding coefficient. This measure seeks to estimate the proportion of a genome that is autozygous—homozygous for alleles inherited identically by descent from a common ancestor. Originally calculated theoretically from known pedigree structures and Mendel’s law of segregation [18], with the availability of genomic data, the inbreeding coefficient can now be estimated empirically from levels of genomic homozygosity [19-29] or inferred autozygosity [30]. In the absence of known pedigrees, genomic inbreeding coefficient estimates in an individual provide an empirical measure of the probability of identity by descent in the two parental copies at a randomly chosen locus. It has been found using simulations that genomic estimators estimate true empirical inbreeding coefficients more accurately than the pedigree-based estimator [3]. This observation can be explained as a consequence of stochasticity in Mendelian segregation ratios [31,32] and variation in cryptic relatedness [33] that pedigree-based inbreeding coefficient estimates ignore, but that are naturally taken into account by genomic estimates.

A number of sociogenetic and population-genetic processes can influence genomic estimates of the inbreeding coefficient, even in the absence of consanguinity. For example, cultural traditions that promote endogamy—the restriction of marriage to within a predefined preferred group of individuals—have the potential over many generations to inflate the inbreeding coefficient. Such traditions reduce the overall pool of mates, increasing relatedness with populations, and in turn, increasing the probability that cryptic inbreeding will arise through background relatedness. In other populations, historical bottlenecks, geographic isolation, or small population size can result in both high levels of relatedness among members of a population and reduced levels of genetic diversity; consequently, genomic inbreeding coefficients might be high in such populations due to high rates of cryptic inbreeding.

Here, to investigate population patterns in the inbreeding coefficient, we compute genomic inbreeding coefficient estimates in 5,043 individuals from 237 worldwide human populations, using genotypes at 645 microsatellite loci. We compare these patterns to demographic estimates of the frequency of consanguinity available for 26 of the populations, as well as to various population-genetic statistics that can assist in interpreting the potential for cryptic inbreeding. The results contribute to an understanding of the factors that influence variation in the inbreeding coefficient in populations worldwide.

Material and Methods

Genotype data

We used the MS5255 subset of the Pemberton et al. [34] human-only data set containing 645 autosomal microsatellite loci, restricting our analysis to 5,043 unrelated individuals (Table S1) from 237 worldwide human populations (Table S2) that had both a sample size of at least 10 individuals as well as available geographic coordinates. Geographic region assignments for populations follow Pemberton et al. [34], as do geographic distances of the 220 non-admixed populations from Addis Ababa, Ethiopia.

Population-genetic quantities

Heterozygosity

We evaluated the level of genetic variation in each population using observed and expected heterozygosity (H_obs and H_exp, respectively) averaged across the 645 microsatellite loci in the data set. For population p, we calculated H_exp,p with a sample size-corrected estimator [35], and H_obs,p as the mean across loci of the proportion of observed heterozygous genotypes, considering in the calculation at each locus only those individuals from population p with non-missing genotypes. Similarly, for individual i, we determined H_obs,i as the proportion of heterozygous genotypes in the genotype data of individual i, considering only those loci with non-missing genotypes. H_obs,i estimates appear for each individual in Table S1, and population H_obs,p and H_exp,p estimates appear in Table S2.

Population differentiation

We obtained genetic distances between all possible pairs among the 237 populations by computing F_st on the 645 microsatellites using Arlequin [36] (v.3.5.1.3). This approach employs the F_st estimator of Weir and Cockerham [37]. Separately for each population, we calculated mean pairwise F_st across the intra-geographic-region comparisons that included that population (Table S2).

Genomic inbreeding coefficient estimates

Individual-level genomic inbreeding coefficient estimates, F_hbd, were defined as the proportion of an individual genome inferred to be autozygous—or homozygous by descent (HBD)—by a maximum likelihood method that uses a hidden Markov model to infer HBD status along the genome. The method uses genotypes, allele frequencies, and a genomic map to probabilistically identify transitions along the genome between autozygous and non-autozygous regions and to estimate a parameter describing the probability that a genome is autozygous at a random location [30]. We calculated F_hbd using the program FEstim [38] with population-specific count estimates of allele frequencies, genetic map positions taken from Pemberton et al. [39], and a genotyping error rate of 0.008 based on the HGDP-CEPH component of the data set considered here [40]. Default parameter values were used for the number of Markov chain iterations (8,000) and for the initial values for the estimate of the inbreeding parameter (0.05) and the identity-by-descent rate of change (0.05). Individual F_hbd estimates appear in Table S1, and per-population means and standard deviations appear in Table S2.

Demographic estimates of consanguinity frequency

Demographic estimates of the frequency of consanguinity—intra-familial unions between couples related as second cousins or closer—in 26 populations were taken from the Global Consanguinity Database (www.consang.net; last updated June 13^th, 2012) (Table S2). This database contains consanguinity frequencies reported in the peer-reviewed literature. In instances in which a population spanned multiple countries, consanguinity frequency estimates were included only if they were obtained in the same country in which population-genetic sampling took place. In situations in which more than one estimate was available in the database for a population, the mean was used in our analyses.

Statistical analyses

Pairwise comparisons were performed using R (v.3.0.0) [41]. Pearson’s product moment correlation coefficient r was calculated using cor.test, and Wilcoxon signed-rank and rank-sum tests using wilcox.test. To account for effects of population-genetic quantities on correlations of genomic inbreeding coefficients with geographic distance from East Africa, we performed partial-correlation analyses using pcor.test [42], calculating a Pearson’s partial correlation coefficient r_pc while including each population-genetic quantity as a covariate in separate computations.

Results and Discussion

Worldwide patterns in genomic inbreeding coefficients

Figure 1 plots F_hbd for each population, showing that individuals with non-zero F_hbd appear in all geographic regions. Values of F_hbd generally increase with geographic distance from East Africa (r=0.358, P=4.64×10^-8), with higher and more variable values occurring in most populations from the Middle East, Central/South Asia, Oceania, and the Americas than in most populations from Sub-Saharan Africa, Europe, and East Asia. Thus, a larger fraction of individuals from the Middle East, Central/South Asia, Oceania, and the Americas tend to have higher levels of parental relatedness, in accord with demographic estimates of high levels of consanguineous marriage [43,44] (Middle East, Central/South Asia) or the existence of large numbers of small or isolated populations (Oceania, Americas). The result is compatible with the expectation that homozygosity in these regions is more likely to reflect autozygosity than in Sub-Saharan Africa, Europe, and East Asia, where consanguinity is generally less frequent than in the Middle East and Central/South Asia and populations have not experienced the same bottleneck or isolation events as in Oceania and the Americas.

Figure 1.

Population-specific distributions of genomic inbreeding coefficients. Box-and-whisker plots represent distributions across individuals in each population for F_hbd Populations are ordered from left to right by geographic region and within regions by increasing geographic distance from Addis Ababa. Oceanian populations are separated into coastal, inland (light gray box), and Polynesian (dark gray box) groups, again ordering populations within groups by distance from Addis Ababa. Among the Central/South Asian populations, the eight Pakistani populations are indicated by a gray box, as are the two Taiwanese populations (Ami and Taruko) among East Asians.

Most Sub-Saharan African populations contain some individuals with non-zero F_bhd, with noticeably higher values occurring in such groups as the Hadza, Fulani (Mbororo), and Venda populations. The Hadza are a group of hunter-gatherers whose small population size and isolation [45-47] would be expected to create high levels of background relatedness, while their acceptance of consanguineous unions—only first-degree relatives are reportedly prohibited from marrying [48]—would be expected to produce non-trivial levels of overt inbreeding. The Fulani (Mbororo)—also known as Wodaabe—are a small nomadic subgroup of the Fulani ethnic group who actively practice consanguinity through arranged marriages between first cousins of the same lineage [49]. By contrast, the Venda are a large clan-based society within which arranged marriages occur frequently between members of the same clan, and as a consequence, are largely consanguineous [50,51]. The higher F_hbd values observed in these populations therefore reflect their traditional practices of kin marriage.

Considerable variation exists in values of F_hbd among Middle Eastern populations, with the highest values occurring in the Bedouin—consistent with the exceptionally high frequency of consanguineous unions reported in this traditionally nomadic tribal population [52,53]. Some of the lowest values are found in the Mozabite subgroup of the Berber ethnic group, in contrast to their reported preference for consanguineous marriage [54]. F_hbd values in European populations are almost exclusively below those observed in the Middle East. Curiously, the lowest values occur in the Ashkenazi Jewish group, well-known to have high-levels of identity by descent [55-59], and the highest occur in the French population, despite the low frequency of consanguinity reported among its Roman Catholic component [60].

Among Central/South Asians, several Pakistani non-tribal populations (Makrani, Balochi, Brahui, Pathan, and Sindhi) have noticeably higher and more variable values of F_hbd than those of the other populations—which are predominantly from India—with the highest values occurring in the Makrani and Balochi populations. These results are compatible with the higher rates of consanguinity reported among Pakistani populations than among Indian populations [43,44], and with documented preferences of the Makrani [61] and Balochi [62,63] populations for consanguineous marriage. Interestingly, whereas high levels of consanguinity have been reported among the Hazara in Afghanistan [64,65], F_hbd values in the Pakistani Hazara population in our data set are among the lowest observed in Central/South Asians.

Worldwide, East Asians have the lowest values of F_hbd, with only 8 of 16 populations containing individuals with nonzero values of F_hbd: Tundra Nentsi, Tujia, Miao, Yakut, Han, Ami, Taruko, and Japanese. Whereas the Han population, sampled in Southern China [66], contains individuals with nonzero F_hbd, the Han (Northern China) population does not, compatible with the higher reported frequency of consanguinity among Southern compared with Northern Han [67-69].

Populations from Oceania and the Americas contain individuals with the highest inbreeding coefficients observed worldwide. In Oceania, many of the individuals with exceptionally high F_hbd occur in coastal rather than inland Melanesian populations—in contrast with the increased isolation documented for inland compared with coastal populations [70-72]. Polynesian groups—Samoans and Maoris—have noticeably lower F_hbd than most other Oceanian populations. These observations are consistent with Samoan and Maori prohibition of incestuous unions—considered as first cousins or closer among Samoans [73] and second cousins or closer among Maori [74]—and the small size of many Melanesian populations [72,75].

In the Americas, which contain many small and isolated populations, several groups, including the Amazonian Ticuna (Arara) [75,76] and Andean Huilliche [75], have high values of F_hbd. However, many of the smallest groups do not have high F_hbd, including the Aché, a small population of hunter-gatherers who prohibit marriage at the level of first cousins or closer [75,77], the Waunana, a forest group that has increasingly intermarried with non-Waunana over the past 70 years [78], and the Pima, a relatively small and isolated population in which consanguinity is traditionally avoided [79].

Among Afro-European admixed populations, the Cape Mixed Ancestry population—in contrast to a low reported frequency of consanguinity [80]—has higher and more variable estimates than the three African-American populations, a result that we might hypothesize reflects greater historical isolation or fewer founders [81] compared to African Americans. Latino populations, descended primarily from European and Native American groups, share similar values of F_hbd that in most cases more closely resemble those found in Europeans than those of Native Americans.

Influence of consanguinity frequency on genomic inbreeding coefficients

We have observed higher and more variable inbreeding coefficients in geographic regions with known high levels of consanguineous marriage [43,44]—particularly the Middle East and Central/South Asia. These results are consistent with the expectation that genomic estimators of the inbreeding coefficient reflect consanguinity levels in a population. To further investigate the relationship between inbreeding coefficients and consanguinity, we examined the correlation of F_hbd with demographic estimates of the frequency of consanguinity, which was available for 26 of 237 populations (Table S2). In accord with the prior expectation, we observe a significant positive correlation of this variable with mean F_hbd across individuals in a population (Figure 2; r=0.349, P=0.040).

Figure 2.

Relationship between genomic inbreeding coefficients and the frequency of consanguinity. A scatter plot is shown of the relationship between demographic estimates of the frequency of consanguinity in 26 worldwide populations and mean F_hbd across individuals (r=0.349, P=0.040). The black dashed line depicts the regression line.

Population-genetic influences on genomic inbreeding coefficients

The high values of F_hbd in many of the populations might also partly reflect the influence of historical bottlenecks or genetic isolation on levels of genetic variability—processes that act separately from overt preferences for consanguineous marriage in inflating inbreeding coefficients. To investigate such influences, we examined relationships of genomic inbreeding coefficients with heterozygosity and F_st.

Heterozygosity

F_hbd measures excess homozygosity in individual genomes [30]; consequently, we might expect to observe negative correlations between this quantity and heterozygosity. Consistent with this expectation, F_bhd is negatively correlated with observed heterozygosity at both the population (H_obs,p; Figure 3A and Table 1) and individual (H_obs,i; Figure S1 and Table S3) levels. If we separately compare F_hbd with H_obs for each geographic region, we still observe negative correlations at both the population (Table 1) and individual (Table S3) levels, confirming the pattern seen at a worldwide scale. Some of the strongest negative correlations occur in regions with known high levels of consanguinity [43,44], particularly the Middle East and Central/South Asia (Tables 1 and S3).

Figure 3.

Relationship between genomic inbreeding coefficients and population-genetic quantities. Scatter plots are shown of the relationships between per-population mean F_hbd across individuals and (A) H_obs,p, and (B) mean pairwise F_st across intra-geographic-region comparisons that include a population. African populations are assigned the same symbol if they had similar cluster memberships in the K=14 Structure analysis of Tishkoff et al. [110]. Pacific Islander populations from the same tribe [72] are assigned the same symbol. Pearson correlation coefficients for each comparison appear in Table 1.

Table 1.

Correlation between per-population means across individuals of F_hbd and population-genetic variables in each geographic region.

Geographic region	Number of populations	Hobs,p		Mean pairwise Fst
		R	P	r	P
World	237	-0.563	<10-16	0.331	5.16×10-7
Africa	102	-0.731	<10-16	0.465	8.46×10-7
Middle East	10	-0.820	0.004	0.017	0.960
Europe	8	-0.570	0.140	-0.506	0.201
Central/South Asia	24	-0.846	1.89×10-7	0.076	0.724
East Asia	16	-0.640	0.008	0.758	6.68×10-4
Oceania	38	-0.510	0.001	-0.137	0.411
Americas	22	-0.594	0.004	0.279	0.208
Afro-European	4	-0.999	0.001	0.968	0.032
Latino	13	-0.253	0.405	0.408	0.166

P-values less than 0.05 are shown in bold.

Consistent with previous investigations of H_exp,p [34,82-84], which is highly correlated with H_obs,p (Figure S2; r=0.975, P<10^-16), we observe H_obs,p to decrease with distance from Africa (Figure 4A; r=-0.905, P<10^-16). Taken together with the negative correlation observed between genomic inbreeding coefficients and H_obs, the observed decrease in H_obs with distance from Africa might at least in part explain the observed increase in F_hbd with distance from Africa (Figure 1). In this view, decreasing heterozygosity inflates identity by descent and in turn, the inbreeding coefficient. If we compute the partial correlation of F_hbd with geographic distance from Africa, accounting for the effect of H_obs, we observe a significant negative correlation (r_pc=-0.431, P=1.98×10^-12). This negative rather than positive correlation supports the view that much of the signal of higher F_hbd with increasing distance from Africa is attributable to the general patterns of decreasing genetic variability with distance from Africa.

Figure 4.

Population-specific distributions of population-genetic quantities. (A) Box-and-whisker plots representing the distribution across individuals of H_obs,i in each population. (B) Per-population means (dots) and standard deviations (vertical bars) of pairwise F_st across the intra-geographic-region comparisons that contain the population. The figure follows the same format as Figure 1.

Mean pairwise F_st

Pairwise F_st measures population differentiation, producing higher values when two populations have large between-population differences but small within-population differences. We expect larger values in comparisons involving genetically isolated populations, in whom we might also expect higher levels of cryptic inbreeding due to reduced mate choice. We can therefore predict mean pairwise F_st—calculated across intra-geographic-region pairwise comparisons that include a population—to be positively correlated with mean F_hbd across individuals. Consistent with this expectation, we observe a positive correlation between mean pairwise F_st and mean F_hbd (Figure 3B and Table 1). When we consider the relationship of mean pairwise F_st with mean F_hbd separately in each geographic region, we observe significant positive correlations in Africa and East Asia (Table 1); all other non-admixed regions had P>0.2. Similar results are obtained when mean pairwise F_st is instead calculated across all 236 worldwide pairwise comparisons that include a population (not shown). This result suggests that the positive correlation at the worldwide level is driven primarily by differences across regions in the regional levels of F_st and mean F_hbd, rather than by differences among populations within regions.

In accord with the observed positive correlations with mean F_hbd, mean pairwise F_st generally increases with a population’s distance from East Africa (Figure 4B, r=0.768, P<10^-16). Taken together with the positive correlation between genomic inbreeding coefficients and mean pairwise F_st, the increase in mean pairwise F_st with distance from Africa might partly explain the parallel increases in F_hbd (Figure 1). The hypothesis is that genetic isolation, as measured by F_st, inflates identity by descent and the inbreeding coefficient. If we compute the partial correlation of F_hbd with geographic distance from Africa, accounting for the effect of mean pairwise F_st, we observe a weaker positive correlation (r_pc=0.172, P=0.010) than in the unadjusted comparison. These results support the view that increasing F_st with increasing distance from Africa contributes to the signal of higher F_hbd with distance from Africa, though to a lesser extent than is observed in the corresponding computation with heterozygosity.

Conclusions

Genomic estimates of the inbreeding coefficient are used frequently in measuring parental relatedness, owing to their relative ease of estimation from genetic data. Many estimators rely on the relationship between autozygosity and parental relatedness [28-30]. However, when predicting the proportion of the genome that is autozygous, these estimators can fluctuate with levels of homozygosity that vary as a consequence of population processes unconnected to consanguinity [85,86]. We have examined the relationship with different population-genetic quantities of a genomic inbreeding coefficient estimator based on inferred autozygosity [30] in genome-wide data from a large number of populations [34].

Inbreeding coefficients increased with the geographic distance of a population from a proxy for the origin of the out-of-Africa migration of anatomically modern humans, and decreased with increasing heterozygosity. These results are compatible with a migration model outward from East Africa that predicts increases in genetic drift and identity by descent and decreases in heterozygosity with distance from Africa [83,84,87]. The positive correlation between inbreeding coefficients and distance from Africa was eliminated if heterozygosity was controlled, indicating that the increase in inbreeding coefficient is a manifestation of the same reduction of ancestral population size outward from Africa that contributes to decreasing heterozygosity. We detected a positive correlation between inbreeding coefficients and mean pairwise F_st, a proxy for genetic isolation; in a partial correlation computation, this variable was also seen to explain part of the signal of increasing inbreeding coefficients with distance from Africa. These results suggest that the increase in inbreeding coefficients with distance from Africa reflects the reduction in genetic variability and increase in genetic isolation outward from Africa during the history of human migrations, rather than increases in cultural practices of consanguinity.

In agreement with a recent study that produced related results on genomic inbreeding coefficients in a smaller set of populations [88], superimposed on the signal of the out-of-Africa migration, we observed high inbreeding coefficients in populations from geographic regions with known high levels of consanguinity [43,44]—particularly the Middle East and Central/South Asia. This result reflects the importance of consanguinity in addition to the cryptic inbreeding generated by the out-of-Africa migration in giving rise to high inbreeding coefficients, and we found a significant positive correlation between demographic estimates of the frequency of consanguinity and inbreeding coefficients in populations for which consanguinity frequency estimates were available. It is noteworthy that variability in the criteria used in determining the frequency of consanguinity for the various populations [52,67-69,80,89-109] likely introduced stochastic variation among these estimates. Given the suggestive nature of the result and the small number of populations examined, it will be worthwhile to revisit this analysis as standardized data on the frequency of consanguinity become available for additional populations.

We note that although the population samples examined have not been sampled by inbreeding status, they generally are not entirely random, and some may lie at one or another extreme in levels of consanguinity. For example, if a population has many communities and only one was sampled, heterozygosity might be underestimated and inbreeding overestimated. Consequently, the observed inbreeding coefficient patterns might not accurately reflect true patterns in such populations, providing a possible explanation for instances in which genomic inbreeding coefficient estimates disagreed with consanguinity estimates. Nevertheless, because F_hbd had sensible patterns of geographic structure and correlations with consanguinity frequencies and population-genetic statistics, and because we have no reason to suspect systematic differences by geography in the oversampling or undersampling of inbreeding, it is likely that any non-random sampling of inbreeding levels within populations is insufficient to obscure underlying geographic and population-genetic influences that we have detected on inbreeding coefficients.