Inbreeding, pedigree size, and the most recent common ancestor of humanity

Bursts of coalescence within population pedigrees whenever big families occur

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

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.

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.

The effect of inbreeding constraints and offspring distribution on time to the most recent common ancestor

The expected time to the most recent common ancestor (MRCA) of two alleles in a diploid individual is 4N+2 under random mating with a Poisson progeny distribution, but 8N-2 under maximum avoidance of inbreeding, which entails two progeny per mating pair. (N is the number of mating pairs, hence 2N is the number of individuals, hence 4N is the number of alleles.) The interrelationship of inbreeding constraints and offspring distribution is investigated by varying the level of sib mating: prohibiting sib mating increases the time to MRCA by four generations and decreases the variance of the offspring distribution by 2/N. With two progeny per mating pair, the expected time to the MRCA is 8N-2 under both random mating and sib mating prohibited, as well as under maximum avoidance of inbreeding, but this result does not hold for all mating structures with two progeny per mating pair.

Ancestry Matters: Patrilineage Growth and Extinction

Patrilineality, the organization of kinship, inheritance, and other key social processes based on patrilineal male descent, has been a salient feature of social organization in China and many other societies for centuries. Because continuity or growth of the patrilineage was the central focus of reproductive strategies in such societies, we introduce the number of patrilineal male descendants generations later as a stratification outcome. By reconstructing and analyzing 20,000 patrilineages in two prospective, multi-generational population databases from 18th and 19th century China, we show that patrilineages founded by high status males had higher growth rates for the next 150 years. The elevated growth rate of these patrilineages was due more to their having a lower probability of extinction at each point in time than to surviving patrilineal male descendants having larger numbers of sons on average. As a result, patrilineal male descendants of high status males account for a disproportionately large share of the male population in later generations. In China and elsewhere, patrilineal kin network characteristics influence individuals' life chances; thus effects of a male founder's characteristics on patrilineage size many generations later represent an indirect channel of status transmission that has not been considered previously.

Ancestries of a recombining diploid population

We derive the exact one-step transition probabilities of the number of lineages that are ancestral to a random sample from the current generation of a bi-parental population that is evolving under the discrete Wright-Fisher model with n diploid individuals. Our model allows for a per-generation recombination probability of r . When r = 1, our model is equivalent to Chang's (Adv Appl Probab 31:1002-1038, 1999) model for the karyotic pedigree. When r = 0, our model is equivalent to Kingman's (Stoch Process Appl 13:235-248, 1982) discrete coalescent model for the cytoplasmic tree or sub-karyotic tree containing a DNA locus that is free of intra-locus recombination. When 0 < r < 1 our model can be thought to track a sub-karyotic ancestral graph containing a DNA sequence from an autosomal chromosome that has an intra-locus recombination probability r . Thus, our family of models indexed by r ∈ [0, 1] connects Kingman's discrete coalescent to Chang's pedigree in a continuous way as r goes from 0 to 1. For large populations, we also study three properties of the ancestral process corresponding to a given r ∈ (0, 1): the time Tn to a most recent common ancestor (MRCA) of the population, the time Un at which all individuals are either common ancestors of all present day individuals or ancestral to none of them, and the fraction of individuals that are common ancestors at time Un. These results generalize the three main results of Chang's (Adv Appl Probab 31:1002-1038, 1999). When we appropriately rescale time and recombination probability by the population size, our model leads to the continuous time Markov chain called the ancestral recombination graph of Hudson (Theor Popul Biol 23:183-201, 1983) and Griffiths (The two-locus ancestral graph, Institute of Mathematical Statistics 100-117, 1991).

Pedigree structure and kinship measurements of a mid-Michigan community: a new North American population isolate identified

Previous studies identified a cluster of individuals with an autosomal recessive form of deafness that reside in a small region of mid-Michigan. We hypothesized that affected members from this community descend from a defined founder population. Using public records and personal interviews, we constructed a genealogical database that includes the affected individuals and their extended families as descendants of 461 settlers who emigrated from the Eifel region of Germany between 1836 and 1875. The genealogical database represents a 13-generation pedigree that includes 27,747 descendants of these settlers. Among these descendants, 13,784 are presumed living. Many of the extant descendants reside in a 90-square-mile area, and 52% were born to parents who share at least one common ancestor. Among those born to related parents, the median kinship coefficient is 3.7 × 10(-3). While the pedigree contains 2,510 founders, 344 of the 461 settlers accounted for 67% of the genome in the extant population. These data suggest that we identified a new population isolate in North America and that, as demonstrated for congenital hearing loss, this rural mid-Michigan community is a new resource to discover heritable factors that contribute to common health-related conditions.

Evolutionary history and adaptation from high-coverage whole-genome sequences of diverse African hunter-gatherers

To reconstruct modern human evolutionary history and identify loci that have shaped hunter-gatherer adaptation, we sequenced the whole genomes of five individuals in each of three different hunter-gatherer populations at > 60× coverage: Pygmies from Cameroon and Khoesan-speaking Hadza and Sandawe from Tanzania. We identify 13.4 million variants, substantially increasing the set of known human variation. We found evidence of archaic introgression in all three populations, and the distribution of time to most recent common ancestors from these regions is similar to that observed for introgressed regions in Europeans. Additionally, we identify numerous loci that harbor signatures of local adaptation, including genes involved in immunity, metabolism, olfactory and taste perception, reproduction, and wound healing. Within the Pygmy population, we identify multiple highly differentiated loci that play a role in growth and anterior pituitary function and are associated with height.

Quantification of inbreeding due to distant ancestors and its detection using dense single nucleotide polymorphism data

Inbreeding depression, which refers to reduced fitness among offspring of related parents, has traditionally been studied using pedigrees. In practice, pedigree information is difficult to obtain, potentially unreliable, and rarely assessed for inbreeding arising from common ancestors who lived more than a few generations ago. Recently, there has been excitement about using SNP data to estimate inbreeding (F) arising from distant common ancestors in apparently “outbred” populations. Statistical power to detect inbreeding depression using SNP data depends on the actual variation in inbreeding in a population, the accuracy of detecting that with marker data, the effect size, and the sample size. No one has yet investigated what variation in F is expected in SNP data as a function of population size, and it is unclear which estimate of F is optimal for detecting inbreeding depression. In the present study, we use theory, simulated genetic data, and real genetic data to find the optimal estimate of F, to quantify the likely variation in F in populations of various sizes, and to estimate the power to detect inbreeding depression. We find that F estimated from runs of homozygosity (F_roh), which reflects shared ancestry of genetic haplotypes, retains variation in even large populations (e.g., SD = 0.5% when N_e = 10,000) and is likely to be the most powerful method of detecting inbreeding effects from among several alternative estimates of F. However, large samples (e.g., 12,000–65,000) will be required to detect inbreeding depression for likely effect sizes, and so studies using F_roh to date have probably been underpowered.