TITLE:
Pairwise Shared Ancestry in Random-Mating Constant-Size Populations
AUTHORS:
Philip M. Service
KEYWORDS:
Pairwise Shared Ancestry, Genealogical Overlap, Quantitative Ancestry, Most Recent Common Ancestor, Number of Cousins
JOURNAL NAME:
Natural Science,
Vol.14 No.5,
May
24,
2022
ABSTRACT: 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.