On the equality of origin and fixation times in genetics

For any sexually reproducing entity (e.g. asexual organism, mitochondrion or gene), the fixation time is the number of generations in the future before all entities are descended from a single one in the present. The origin time is the number of generations in the past when a single entity was ancestral to all entities in the present. It is proved that, over a sufficiently long time, the means and distributions of the fixation and origin times are identical. The proof holds even if population size varies, selection is acting, or conditions change with time.