The ancestry of a genome or The amazing ubiquity of exponential distributions

Abstract

AbstractMotivated originally by the increasing number of examples where a lone member of a once thriving population or even species now survives, we investigate what genomes of that population the survivor may represent. More generally it is of interest to consider what genomes of our ancestry each of us may represent. We consider only diploid dioecious organisms, and consider primarily the ancestry of a haploid genome, for example the maternal autosomes of the focal individual. Our ancestors are many and, in an unbounded population, increase exponentially in number. Our genetic ancestors are few, bounded by the number of ancestral genome segments which increases linearly over past generations. First we show that the major loss of potential ancestral lineages is at 8-11 generations, and that thereafter the number of genetic ancestors increases approximately linearly, but does not approach the upper bound. Over many generations, there remain tightly linked but not contiguous segments that result from the same ancestral lineage. Second we analyze the process of these ”repeated” ancestral segments that continue to be formed in distant ancestry, even as others are lost by recombination. Thirdly, we consider the effect of a finite population, with one model of a geographically structured population. Ancestors are many, and soon fill the entire species range even with low migration rates. Genetic ancestors are not only few, but remain geographically local.