The Effect of Population History on the Lengths of Ancestral Chromosome Segments

An isolated population is a group of individuals who are descended from a founding population who lived some time ago. If the founding individuals are assumed to be noninbred and unrelated, a chromosome sampled from the population can be represented as a mosaic of segments of the original ancestral types. A population in which chromosomes are made up of a few long segments will exhibit linkage disequilibrium due to founder effect over longer distances than a population in which the chromosomes are made up of many short segments. We study the length of intact ancestral segments by obtaining the expected number of junctions (points where DNA of two distinct ancestral types meet) in a chromosome. Assuming random mating, we study analytically the effects of population age, growth patterns, and internal structure on the expected number of junctions in a chromosome. We demonstrate that the type of growth a population has experienced can influence the expected number of junctions, as can population subdivision. These effects are substantial only when population sizes are very small. We also develop an approximation to the variance of the number of junctions and show that the variance is large.