Genealogies under logistic growth

Abstract

We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman, $\text{Beta}(2-\alpha, \alpha)$ and Bolthausen-Sznitman coalescents as a scaling parameter governing the population size is taken to infinity, the deduction going via the convergence in distribution of a modified lookdown construction. This resolves a question asked in arxiv:2501.16837 who studied the same population process forwards in time and showed convergence of the type frequency process to the corresponding $\Lambda$-Fleming-Viot process in each regime.