The Effect of Consanguinity on Between-Individual Identity-by-Descent Sharing

Phase-type distributions in mathematical population genetics: An emerging framework

A phase-type distribution is the time to absorption in a continuous- or discrete-time Markov chain. Phase-type distributions can be used as a general framework to calculate key properties of the standard coalescent model and many of its extensions. Here, the 'phases' in the phase-type distribution correspond to states in the ancestral process. For example, the time to the most recent common ancestor and the total branch length are phase-type distributed. Furthermore, the site frequency spectrum follows a multivariate discrete phase-type distribution and the joint distribution of total branch lengths in the two-locus coalescent-with-recombination model is multivariate phase-type distributed. In general, phase-type distributions provide a powerful mathematical framework for coalescent theory because they are analytically tractable using matrix manipulations. The purpose of this review is to explain the phase-type theory and demonstrate how the theory can be applied to derive basic properties of coalescent models. These properties can then be used to obtain insight into the ancestral process, or they can be applied for statistical inference. In particular, we show the relation between classical first-step analysis of coalescent models and phase-type calculations. We also show how reward transformations in phase-type theory lead to easy calculation of covariances and correlation coefficients between e.g. tree height, tree length, external branch length, and internal branch length. Furthermore, we discuss how these quantities can be used for statistical inference based on estimating equations. Providing an alternative to previous work based on the Laplace transform, we derive likelihoods for small-size coalescent trees based on phase-type theory. Overall, our main aim is to demonstrate that phase-type distributions provide a convenient general set of tools to understand aspects of coalescent models that are otherwise difficult to derive. Throughout the review, we emphasize the versatility of the phase-type framework, which is also illustrated by our accompanying R-code. All our analyses and figures can be reproduced from code available on GitHub.

Analysis of disease characteristics of a large patient cohort with congenital generalized lipodystrophy from the Middle East and North Africa

BACKGROUND

Congenital generalized lipodystrophy (CGL) is a rare inherited disease characterized by a near-total absence of adipose tissue and is associated with organ system abnormalities and severe metabolic complications. Here, we have analyzed the disease characteristics of the largest CGL cohort from the Middle East and North Africa (MENA) who have not received lipodystrophy-specific treatment.

METHODS

CGL was diagnosed clinically by treating physicians through physical assessment and supported by genetic analysis, fat loss patterns, family history, and the presence of parental consanguinity. Data were obtained at the time of patient diagnosis and during leptin-replacement naïve follow-up visits as permitted by available medical records.

RESULTS

Data from 43 patients with CGL (37 females, 86%) were collected from centers located in eight countries. The mean (median, range) age at diagnosis was 5.1 (1.0, at birth-37) years. Genetic analysis of the overall cohort showed that CGL1 (n = 14, 33%) and CGL2 (n = 18, 42%) were the predominant CGL subtypes followed by CGL4 (n = 10, 23%); a genetic diagnosis was unavailable for one patient (2%). There was a high prevalence of parental consanguinity (93%) and family history (67%) of lipodystrophy, with 64% (n = 25/39) and 51% (n = 20/39) of patients presenting with acromegaloid features and acanthosis nigricans, respectively. Eighty-one percent (n = 35/43) of patients had at least one organ abnormality; the most frequently affected organs were the liver (70%, n = 30/43), the cardiovascular system (37%, n = 16/43) and the spleen (33%, n = 14/43). Thirteen out of 28 (46%) patients had HbA1c > 5.7% and 20/33 (61%) had triglyceride levels > 2.26 mmol/L (200 mg/dl). Generally, patients diagnosed in adolescence or later had a greater severity of metabolic disease versus those diagnosed during childhood; however, metabolic and organ system abnormalities were observed in a subset of patients diagnosed before or at 1 year of age.

CONCLUSIONS

This analysis suggests that in addition to the early onset of fat loss, family history and high consanguinity enable the identification of young patients with CGL in the MENA region. In patients with CGL who have not received lipodystrophy-specific treatment, severe metabolic disease and organ abnormalities can develop by late childhood and worsen with age.

Genome-Wide Detection for Runs of Homozygosity in Baoshan Pigs Using Whole Genome Resequencing

Baoshan pigs (BS) are a local breed in Yunnan Province that may face inbreeding owing to its limited population size. To accurately evaluate the inbreeding level of the BS pig population, we used whole-genome resequencing to identify runs of homozygosity (ROH) regions in BS pigs, calculated the inbreeding coefficient based on pedigree and ROH, and screened candidate genes with important economic traits from ROH islands. A total of 22,633,391 SNPS were obtained from the whole genome of BS pigs, and 201 ROHs were detected from 532,450 SNPS after quality control. The number of medium-length ROH (1-5 Mb) was the highest (98.43%), the number of long ROH (>5 Mb) was the lowest (1.57%), and the inbreeding of BS pigs mainly occurred in distant generations. The inbreeding coefficient FROH, calculated based on ROH, was 0.018 ± 0.016, and the FPED, calculated based on the pedigree, was 0.027 ± 0.028, which were positively correlated. Forty ROH islands were identified, containing 507 genes and 891 QTLs. Several genes were associated with growth and development (IGFALS, PTN, DLX5, DKK1, WNT2), meat quality traits (MC3R, ACSM3, ECI1, CD36, ROCK1, CACNA2D1), and reproductive traits (NPW, TSHR, BMP7). This study provides a reference for the protection and utilization of BS pigs.

Modeling the effects of consanguinity on autosomal and X-chromosomal runs of homozygosity and identity-by-descent sharing

Runs of homozygosity (ROH) and identity-by-descent (IBD) sharing can be studied in diploid coalescent models by noting that ROH and IBD-sharing at a genomic site are predicted to be inversely related to coalescence times-which in turn can be mathematically obtained in terms of parameters describing consanguinity rates. Comparing autosomal and X-chromosomal coalescent models, we consider ROH and IBD-sharing in relation to consanguinity that proceeds via multiple forms of first-cousin mating. We predict that across populations with different levels of consanguinity, (1) in a manner that is qualitatively parallel to the increase of autosomal IBD-sharing with autosomal ROH, X-chromosomal IBD-sharing increases with X-chromosomal ROH, owing to the dependence of both quantities on consanguinity levels; (2) even in the absence of consanguinity, X-chromosomal ROH and IBD-sharing levels exceed corresponding values for the autosomes, owing to the smaller population size and lower coalescence time for the X chromosome than for autosomes; (3) with matrilateral consanguinity, the relative increase in ROH and IBD-sharing on the X chromosome compared to the autosomes is greater than in the absence of consanguinity. Examining genome-wide SNPs in human populations for which consanguinity levels have been estimated, we find that autosomal and X-chromosomal ROH and IBD-sharing levels generally accord with the predictions. We find that each 1% increase in autosomal ROH is associated with an increase of 2.1% in X-chromosomal ROH, and each 1% increase in autosomal IBD-sharing is associated with an increase of 1.6% in X-chromosomal IBD-sharing. For each calculation, particularly for ROH, the estimate is reasonably close to the increase of 2% predicted by the population-size difference between autosomes and X chromosomes. The results support the utility of coalescent models for understanding patterns of genomic sharing and their dependence on sex-biased processes.

On the number of genealogical ancestors tracing to the source groups of an admixed population

Members of genetically admixed populations possess ancestry from multiple source groups, and studies of human genetic admixture frequently estimate ancestry components corresponding to fractions of individual genomes that trace to specific ancestral populations. However, the same numerical ancestry fraction can represent a wide array of admixture scenarios within an individual's genealogy. Using a mechanistic model of admixture, we consider admixture genealogically: how many ancestors from the source populations does the admixture represent? We consider African-Americans, for whom continent-level estimates produce a 75-85% value for African ancestry on average and 15-25% for European ancestry. Genetic studies together with key features of African-American demographic history suggest ranges for parameters of a simple three-epoch model. Considering parameter sets compatible with estimates of current ancestry levels, we infer that if all genealogical lines of a random African-American born during 1960-1965 are traced back until they reach members of source populations, the mean over parameter sets of the expected number of genealogical lines terminating with African individuals is 314 (interquartile range 240-376), and the mean of the expected number terminating in Europeans is 51 (interquartile range 32-69). Across discrete generations, the peak number of African genealogical ancestors occurs in birth cohorts from the early 1700s, and the probability exceeds 50% that at least one European ancestor was born more recently than 1835. Our genealogical perspective can contribute to further understanding the admixture processes that underlie admixed populations. For African-Americans, the results provide insight both on how many of the ancestors of a typical African-American might have been forcibly displaced in the Transatlantic Slave Trade and on how many separate European admixture events might exist in a typical African-American genealogy.

Genome-wide data from medieval German Jews show that the Ashkenazi founder event pre-dated the 14th century

We report genome-wide data from 33 Ashkenazi Jews (AJ), dated to the 14^th century, obtained following a salvage excavation at the medieval Jewish cemetery of Erfurt, Germany. The Erfurt individuals are genetically similar to modern AJ, but they show more variability in Eastern European-related ancestry than modern AJ. A third of the Erfurt individuals carried a mitochondrial lineage common in modern AJ and eight carried pathogenic variants known to affect AJ today. These observations, together with high levels of runs of homozygosity, suggest that the Erfurt community had already experienced the major reduction in size that affected modern AJ. The Erfurt bottleneck was more severe, implying substructure in medieval AJ. Overall, our results suggest that the AJ founder event and the acquisition of the main sources of ancestry pre-dated the 14^th century and highlight late medieval genetic heterogeneity no longer present in modern AJ.

Limiting distribution of X-chromosomal coalescence times under first-cousin consanguineous mating

By providing additional opportunities for coalescence within families, the presence of consanguineous unions in a population reduces coalescence times relative to non-consanguineous populations. First-cousin consanguinity can take one of six forms differing in the configuration of sexes in the pedigree of the male and female cousins who join in a consanguineous union: patrilateral parallel, patrilateral cross, matrilateral parallel, matrilateral cross, bilateral parallel, and bilateral cross. Considering populations with each of the six types of first-cousin consanguinity individually and a population with a mixture of the four unilateral types, we examine coalescent models of consanguinity. We previously computed, for first-cousin consanguinity models, the mean coalescence time for X-chromosomal loci and the limiting distribution of coalescence times for autosomal loci. Here, we use the separation-of-time-scales approach to obtain the limiting distribution of coalescence times for X-chromosomal loci. This limiting distribution has an instantaneous coalescence probability that depends on the probability that a union is consanguineous; lineages that do not coalesce instantaneously coalesce according to an exponential distribution. We study the effects on the coalescence time distribution of the type of first-cousin consanguinity, showing that patrilateral-parallel and patrilateral-cross consanguinity have no effect on X-chromosomal coalescence time distributions and that matrilateral-parallel consanguinity decreases coalescence times to a greater extent than does matrilateral-cross consanguinity.

Fine-scale population structure and demographic history of British Pakistanis

Previous genetic and public health research in the Pakistani population has focused on the role of consanguinity in increasing recessive disease risk, but little is known about its recent population history or the effects of endogamy. Here, we investigate fine-scale population structure, history and consanguinity patterns using genotype chip data from 2,200 British Pakistanis. We reveal strong recent population structure driven by the biraderi social stratification system. We find that all subgroups have had low recent effective population sizes (N_e), with some showing a decrease 15‒20 generations ago that has resulted in extensive identity-by-descent sharing and homozygosity, increasing the risk of recessive disorders. Our results from two orthogonal methods (one using machine learning and the other coalescent-based) suggest that the detailed reporting of parental relatedness for mothers in the cohort under-represents the true levels of consanguinity. These results demonstrate the impact of cultural practices on population structure and genomic diversity in Pakistanis, and have important implications for medical genetic studies.

The effect of consanguinity on coalescence times on the X chromosome

Consanguineous unions increase the frequency at which identical genomic segments are inherited along separate paths of descent, decreasing coalescence times for pairs of alleles drawn from an individual who is the offspring of a consanguineous pair. For an autosomal locus, it has recently been shown that the mean time to the most recent common ancestor (T_MRCA) for two alleles in the same individual and the mean T_MRCA for two alleles in two separate individuals both decrease with increasing consanguinity in a population. Here, we extend this analysis to the X chromosome, considering X-chromosomal coalescence times under a coalescent model with diploid, male-female mating pairs. We examine four possible first-cousin mating schemes that are equivalent in their effects on autosomes, but that have differing effects on the X chromosome: patrilateral-parallel, patrilateral-cross, matrilateral-parallel, and matrilateral-cross. In each mating model, we calculate mean T_MRCA for X-chromosomal alleles sampled either within or between individuals. We describe a consanguinity effect on X-chromosomal T_MRCA that differs from the autosomal pattern under matrilateral but not under patrilateral first-cousin mating. For matrilateral first cousins, the effect of consanguinity in reducing T_MRCA is stronger on the X chromosome than on the autosomes, with an increased effect of parallel-cousin mating compared to cross-cousin mating. The theoretical computations support the utility of the model in understanding patterns of genomic sharing on the X chromosome.

Extensive Ethnolinguistic Diversity in Vietnam Reflects Multiple Sources of Genetic Diversity

Vietnam features extensive ethnolinguistic diversity and occupies a key position in Mainland Southeast Asia. Yet, the genetic diversity of Vietnam remains relatively unexplored, especially with genome-wide data, because previous studies have focused mainly on the majority Kinh group. Here, we analyze newly generated genome-wide single-nucleotide polymorphism data for the Kinh and 21 additional ethnic groups in Vietnam, encompassing all five major language families in Mainland Southeast Asia. In addition to analyzing the allele and haplotype sharing within the Vietnamese groups, we incorporate published data from both nearby modern populations and ancient samples for comparison. In contrast to previous studies that suggested a largely indigenous origin for Vietnamese genetic diversity, we find that Vietnamese ethnolinguistic groups harbor multiple sources of genetic diversity that likely reflect different sources for the ancestry associated with each language family. However, linguistic diversity does not completely match genetic diversity: There have been extensive interactions between the Hmong-Mien and Tai-Kadai groups; different Austro-Asiatic groups show different affinities with other ethnolinguistic groups; and we identified a likely case of cultural diffusion in which some Austro-Asiatic groups shifted to Austronesian languages during the past 2,500 years. Overall, our results highlight the importance of genome-wide data from dense sampling of ethnolinguistic groups in providing new insights into the genetic diversity and history of an ethnolinguistically diverse region, such as Vietnam.

Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population

Recent modeling studies interested in runs of homozygosity (ROH) and identity by descent (IBD) have sought to connect these properties of genomic sharing to pairwise coalescence times. Here, we examine a variety of features of pairwise coalescence times in models that consider consanguinity. In particular, we extend a recent diploid analysis of mean coalescence times for lineage pairs within and between individuals in a consanguineous population to derive the variance of coalescence times, studying its dependence on the frequency of consanguinity and the kinship coefficient of consanguineous relationships. We also introduce a separation-of-time-scales approach that treats consanguinity models analogously to mathematically similar phenomena such as partial selfing, using this approach to obtain coalescence-time distributions. This approach shows that the consanguinity model behaves similarly to a standard coalescent, scaling population size by a factor 1-3c, where c represents the kinship coefficient of a randomly chosen mating pair. It provides the explanation for an earlier result describing mean coalescence time in the consanguinity model in terms of c. The results extend the potential to make predictions about ROH and IBD in relation to demographic parameters of diploid populations.

Long Runs of Homozygosity Are Correlated with Marriage Preferences across Global Population Samples

Children of consanguineous unions carry long runs of homozygosity (ROH) in their genomes, due to their parents' recent shared ancestry. This increases the burden of recessive disease in populations with high levels of consanguinity and has been heavily studied in some groups. However, there has been little investigation of the broader effect of consanguinity on patterns of genetic variation on a global scale. This study, which collected published genetic data and information about marriage practice from 395 worldwide populations, shows that reported preference for cousin marriage has a detectable association with the distribution of long ROH in this sample, increasing the expected number of ROH longer than 10 cM by a factor of 2.2. Variation in marriage practice and consequent rates of consanguinity are therefore an important aspect of demographic history for the purposes of modeling human genetic variation. However, reported marriage practices explain a relatively small proportion of the variation in ROH distribution, and consequently, population genetic data are only partially informative about cultural preferences.

Recent Common Origin, Reduced Population Size, and Marked Admixture Have Shaped European Roma Genomes

The Roma Diaspora-traditionally known as Gypsies-remains among the least explored population migratory events in historical times. It involved the migration of Roma ancestors out-of-India through the plateaus of Western Asia ultimately reaching Europe. The demographic effects of the Diaspora-bottlenecks, endogamy, and gene flow-might have left marked molecular traces in the Roma genomes. Here, we analyze the whole-genome sequence of 46 Roma individuals pertaining to four migrant groups in six European countries. Our analyses revealed a strong, early founder effect followed by a drastic reduction of ∼44% in effective population size. The Roma common ancestors split from the Punjabi population, from Northwest India, some generations before the Diaspora started, <2,000 years ago. The initial bottleneck and subsequent endogamy are revealed by the occurrence of extensive runs of homozygosity and identity-by-descent segments in all Roma populations. Furthermore, we provide evidence of gene flow from Armenian and Anatolian groups in present-day Roma, although the primary contribution to Roma gene pool comes from non-Roma Europeans, which accounts for >50% of their genomes. The linguistic and historical differentiation of Roma in migrant groups is confirmed by the differential proportion, but not a differential source, of European admixture in the Roma groups, which shows a westward cline. In the present study, we found that despite the strong admixture Roma had in their diaspora, the signature of the initial bottleneck and the subsequent endogamy is still present in Roma genomes.

The Iberian legacy into a young genetic xeroderma pigmentosum cluster in central Brazil

In central Brazil, in the municipality of Faina (state of Goiás), the small and isolated village of Araras comprises a genetic cluster of xeroderma pigmentosum (XP) patients. The high level of consanguinity and the geographical isolation gave rise to a high frequency of XP patients. Recently, two founder events were identified affecting that community, with two independent mutations at the POLH gene, c.764 + 1 G > A (intron 6) and c.907 C > T; p.Arg303* (exon 8). These deleterious mutations lead to the xeroderma pigmentosum variant syndrome (XP-V). Previous reports identified both mutations in other countries: the intron 6 mutation in six patients (four families) from Northern Spain (Basque Country and Cantabria) and the exon 8 mutation in two patients from different families in Europe, one of them from Kosovo. In order to investigate the ancestry of the XP patients and the age for these mutations at Araras, we generated genotyping information for 22 XP-V patients from Brazil (16), Spain (6) and Kosovo (1). The local genomic ancestry and the shared haplotype segments among the patients showed that the intron 6 mutation at Araras is associated with an Iberian genetic legacy. All patients from Goiás, homozygotes for intron 6 mutation, share with the Spanish patients identical-by-descent (IBD) genomic segments comprising the mutation. The entrance date for the Iberian haplotype at the village was calculated to be approximately 200 years old. This result is in agreement with the historical arrival of Iberian individuals at the Goiás state (BR). Patients from Goiás and the three families from Spain share 1.8 cM (family 14), 1.7 cM (family 15), and a more significant segment of 4.7 cM within family 13. On the other hand, the patients carrying the exon 8 mutation do not share any specific genetic segment, indicating an old genetic distance between them or even no common ancestry.