Pairwise Shared Genealogical Ancestry in Structured Populations

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.