Ancestral lineages and uniform sampling in populations with density-dependent interactions

by Madeleine Kubasch (Sorbonne Université)

Tuesday Oct 21, 2025, 9:50 AM → 10:50 AM Europe/Paris

Amphi Scwhartz

We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the ancestral lineage of a uniformly sampled individual. We exhibit a time-inhomogeneous Markov process, which captures the average behavior of a sampled lineage in the population process, providing a many-to-one formula. This yields a direct interpretation of the underlying survivorship bias. We finally focus on uniform sampling in the large population limit. Under classical assumptions, the population type distribution can then be approached by a deterministic limit. Using coupling arguments, we quantify the approximation error which arises when sampling in the large population approximation instead of the finite-size population process.