Probability of Mitochondrial Lineage Extinction in Female Offspring, Modern and Paleolithic: Branching Process Analysis

Abstract

We evaluate the probability of extinction of the female offspring of two populations of women: the one Paleolithic, the other that of Italy today. In both cases it is assumed that possible extinction arises exclusively on account of limitations in the degree of fertility and/or an imbalance in the sex-ratio of the population. The value is obtained as the probability that a Branching Process describing the evolution of the offspring by a progenitor degenerates to a “Blank Generation,” that is, a generation without women. Mathematically, it derives from a solution between 0 and 1 of a linear equation whose coefficients are the probabilities that a single progenitor breeds various integer numbers of daughters. We evaluated such probabilities by consulting literature. The probability of branch extinction is also the probability of extinction of progenitor’s mitochondrial lineage.