European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities

MS93-05

16 Jul 2026, 10:40

20m

05.12 - HS (University of Graz)

Minisymposium Talk Numerical, Computational, and Data-Driven Methods Stochastic agent- and particle-based models in biology: methods and analytical insights

Speaker

Marta Dai Pra (Humboldt University Berlin)

Description

Abstract
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage. We first study the frequency of the disadvantageous type, once the population approaches the carrying capacity. Adapting techniques from [Kat91], we show that this process converges to a Gillespie-Wright-Fisher diffusion process. We then study the dynamics backward in time: we fix a time horizon at which the population is at carrying capacity and we study the ancestral relations of a sample of individuals. We prove that, provided that the advantageous and disadvantageous branching measures are stochastically ordered, this ancestral line process converges to the moment dual of the limiting diffusion. This talk is based on [DPK25].

References
[DPK25] M. Dai Pra and J. Kern. Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities. 2025.
[Kat91] G. Katzenberger. Solutions of a stochastic differential equation forced onto a manifold by a large drift. The Annals of Probability, 19(4):1587 – 1628, 1991.