The Total Branch Length of Sample Genealogies in Populations of Variable Size

We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we study the distribution of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression-Equation 20-for the moments of this distribution with a given arbitrary dependence of the population size on time. We investigate how the frequency of population-size variations alters the total branch length.