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Pairwise Shared Ancestry in Random-Mating Constant-Size Populations

Natural Science 2022年第5期14卷 193-202页

作者： Philip M. Service Department of Biological Sciences Northern Arizona University Flagstaff USA

In a panmictic population of constant size N, random pairs of individuals will have a most recent shared ancestor who lived slightly more than 0.5 log2N generations previously, on average. The probability that a random pair of individuals will share at least one ancestor who lived 0.5 log2N generations ago, or more recently, is about 50%. Those individuals, if they do share an ancestor from that generation, would be cousins of degree (0.5 log2N) - 1. Shared ancestry from progressively earlier generations increases rapidly until there is universal pairwise shared ancestry. At that point, every individual has one or more ancestors in common with every other individual in the population, although different pairs may share different ancestors. Those ancestors lived approximately 0.7 log2N generations in the past, or more recently. Qualitatively, the ancestries of random pairs have about 50% similarity for ancestors who lived about 0.9 log2N generations before the present. That is, about half of the ancestors from that generation belonging to one member of the pair are present also in the genealogy of the other member. Qualitative pairwise similarity increases to more than 99% for ancestors who lived about 1.4 log2N generations in the past. Similar results apply to a metric of quantitative pairwise genealogical overlap.

关键词： Pairwise Shared Ancestry Genealogical Overlap Quantitative Ancestry most recent common ancestor Number of Cousins

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Pairwise Shared Genealogical Ancestry in Structured Populations

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Natural Science 2022年第8期14卷 305-321页

作者： Philip M. Service Department of Biological Sciences Northern Arizona University Flagstaff AZ USA

Simulation was used to investigate the effects of population structure and migration on metrics of pairwise shared ancestry. Random and hierarchical structures, or migration geometries, were examined. Compared to panmictic populations, progress to all qualitative metrics of pairwise ancestry is delayed in structured populations. However, unless migration is very low, the time required is generally less than triple and often less than twice that required in a panmictic population of the same total size. Population structure also increases, to a similar degree, the time required for a population-wide most recent common ancestor (MRCA). As a result, the relationships between various qualitative metrics of pairwise shared ancestry and MRCA time are relatively unaffected by population structure. For example, the mean time to most recent shared ancestor (MRSA) with global sampling of pairs is 40% - 50% of the MRCA time for almost all simulated structures and migration levels. Quantitative pairwise genealogical overlap is strongly affected by population structure. With global sampling, pairwise quantitative overlap never approaches 1.0, as it does in panmictic populations;and instead eventually becomes stationary at much lower values. Possible implications of the present results for human pairwise shared ancestry are discussed. For globally sampled pairs, the longest time to most recent shared ancestor (MRSA) for humans is suggested to be approximately 2100 years before the present. If generation time is 30 years, then all humans are 69th, or closer, cousins. For people with recent European ancestry, the MRSA time may be only half as long, about 1000 years.

关键词： Population Structure Pairwise Shared Ancestry Genealogy Migration most recent common ancestor Humans

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