The coalescent tree of a Markov branching process with generalised logistic growth

Abstract

We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the population size moves towards a carrying capacity. A fixed number of individuals are sampled at a time while the population is still growing superlinearly. Taking the sampling time and carrying capacity simultaneously to infinity, we prove convergence of the coalescent tree. The limiting coalescent tree is in a sense universal over our class of models.