Elsevier

Journal of Theoretical Biology

Volume 261, Issue 2, 21 November 2009, Pages 238-247
Journal of Theoretical Biology

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

https://doi.org/10.1016/j.jtbi.2009.08.006Get rights and content

Abstract

How many generations ago did the common ancestor of all present-day individuals live, and how does inbreeding affect this estimate? The number of ancestors within family trees determines the timing of the most recent common ancestor of humanity. However, mating is often non-random and inbreeding is ubiquitous in natural populations. Rates of pedigree growth are found for multiple types of inbreeding. This data is then combined with models of global population structure to estimate biparental coalescence times. When pedigrees for regular systems of mating are constructed, the growth rates of inbred populations contain Fibonacci n-step constants. The timing of the most recent common ancestor depends on global population structure, the mean rate of pedigree growth, mean fitness, and current population size. Inbreeding reduces the number of ancestors in a pedigree, pushing back global common ancestry times. These results are consistent with the remarkable findings of previous studies: all humanity shares common ancestry in the recent past.

Introduction

All modern humans are ultimately related and the most recent common ancestor (MRCA) of humanity lived in the recent past. The exact timing of the MRCA depends on whether gene lineages or family trees are considered. Substantial numbers of individuals can trace their heredity to the likes of Niall of the Nine Hostages and Genghis Khan (Moore et al., 2006; Zerjal et al., 2003). On a grander scale, global coalescence times have been found for mtDNA and non-recombining Y chromosomal DNA lineages (Ayala, 1995; Cann et al., 1987; Thomson et al., 2000). However, the so-called “mitochondrial Eve” and “Y-chromosome Adam” need not be the most recent common ancestors of humanity. Relatedness does not require individuals to share an unbroken matrilineal or patrilineal lineage. Instead, two individuals are related if they share at least one direct ancestor (i.e. the same individual appears in the pedigrees of both individuals). The organismal MRCA is defined here as the most recent individual that is in the family tree of every present-day individual. This biparental definition captures the colloquial meaning of common ancestry. As family trees of present-day individuals are traced backwards in time, the likelihood of common ancestry increases. The number of ancestors in the pedigree of a single present-day individual can be used to calculate biparental coalescence times for an entire population (Chang, 1999). These methods yield estimates of global coalescence times as low as 33 generations for panmictic populations (Chang, 1999) and 76 generations for subdivided populations (Rohde et al., 2004).

Organismal lineages coalesce much faster than gene genealogies. Population size t generations ago is defined as Nt, with present-day population size equal to N0. Gene trees coalesce on the order of 2N0 generations, while organismal lineages in randomly mating populations coalesce on the order of log2N0 generations (Chang, 1999). This difference in time scales is because genes are inherited uniparentally and organismal ancestry is biparental (every individual has a mother and a father). However, the genetic contribution of the organismal MRCA to present-day individuals can be quite small and two individuals need not inherit the same genes from a shared ancestor (Hein, 2004; Matsen and Evans, 2008). Note that biparental coalescence times are much less variable than uniparental coalescence times (Chang, 1999). Additionally, the existence of a MRCA does not imply that only a single pair of individuals were alive: other individuals existed at the time of the MRCA (Ayala, 1995).

Population structure, such as inbreeding, influences the timing of the MRCA of humanity. Mating is rarely panmictic and inbreeding is ubiquitous in natural populations (Hedrick and Kalinowski, 2000; Keller and Waller, 2002). Regional estimates of consanguinity (second cousin or closer mating) range from <1% to >50% (Bittles, 2001). Inbreeding is defined here as positive assortative mating with respect to heredity, and does not refer to incidental matings between close relatives in small populations. Inbreeding causes the number of direct ancestors in a pedigree to differ from 2t (where t is the number of generations in the past). For example, the progeny of first cousin matings have six, rather than eight, great-grandparents. As inbreeding affects the number of ancestors in a pedigree, it results in modified organismal coalescence times. Previous studies of organismal coalescence times assumed random mating within demes and did not explicitly consider the effects of inbreeding.

In this paper, rates of pedigree growth are found for multiple types of inbreeding. This information is then combined with observed levels of inbreeding to estimate the timing of the most recent common ancestor of humanity. By incorporating inbreeding, estimates of TMRCA become more realistic. Inbreeding results in increased biparental coalescence times.

Section snippets

Model

A population of diploid individuals with discrete generations is modeled. Population sizes are finite, but large enough that sex ratios do not differ appreciably from 1:1. Inbreeding is the sole exception to random mating within demes. Thus, the Wright–Fisher model of population genetics is modified to include inbreeding and biparental inheritance. Within demes, individuals preferentially mate with relatives. A proportion of matings involve siblings, a proportion of matings involve first

Pedigree construction and recursion equations for the number of ancestors

Previous studies compute global coalescence times from the number of ancestors in a pedigree (Chang, 1999; Rohde et al., 2004). This approach can be extended to situations where the number of direct ancestors of each individual differs from two, such as species that reproduce both sexually and asexually (Donnelly et al., 1999; Hein et al., 2005). Similarly, inbreeding causes the rate of pedigree growth to differ from two. How fast do pedigrees grow for different types of inbreeding? This

Inbred pedigree growth rates are Fibonacci n-step constants

Inbred pedigrees for regular systems of mating are shown in Fig. 1. The number of ancestors at each level of a family tree and mating-specific rates of pedigree growth (rg) are listed in Table 1. Pedigrees in which every mating involves siblings contain two individuals each generation. Qualitative differences exist between first cousin and second cousin pedigrees. First cousin matings result in pedigrees that increase linearly as a function of time and second cousin matings result in pedigrees

Fibonacci constants and the decay of heterozygosity

The Fibonacci sequence also appears in equations for the decay of heterozygosity under regular systems of mating (Jennings, 1914; Wright, 1921). Heterozygosity decays geometrically in inbred populations (Crow and Kimura, 1970), with the parameter λg indicating the proportion of heterozygosity retained each generation (Fig. 3B). Note that the regular systems of mating in Fig. 3B involve multiple instances of inbreeding (e.g. double-first cousin and quadruple-second cousin matings), while regular

Conclusion

Ultimately, global coalescence times hinge upon within-deme population structure and between-deme patterns of migration. The number of ancestors in a family tree increases very quickly even when there is significant inbreeding. While inbreeding within local populations pushes the global TMRCA back a significant number of years, the qualitative conclusions of previous studies hold. Present-day individuals share common ancestors that lived in the relatively recent past. Exceptions involve

Acknowledgments

I thank members of Stony Brook University's Department of Ecology and Evolution, A. Bittles, J. Crow, J. Flowers, L. Jung, A. Onstine, P. Ralph, J. True, S. Yeh, and R. Yukilevich for stimulating discussions and constructive criticism during the preparation of this manuscript. Additional thanks are directed towards my own recent ancestors. This work was supported by an NIH Predodoctoral Training Grant (5 T32 GM007964-24).

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