A1182
Title: Ancestral reproductive bias in branching processes
Authors: Samuel Johnston - Kings College London (United Kingdom) [presenting]
Abstract: Consider a simple branching process modelling a growing population. A single particle at time zero is started with, and thereafter, each particle has a standard exponential lifetime. At the end of its lifetime, it dies and is instantaneously replaced by two particles. Allowing the process to run until a time $T > 0$ is considered, and a single particle is chosen uniformly at random from the population. The times at which the ancestors of this particle died are studied, and it is found that the reproduction law along this ancestral lineage is faster than that of the underlying population population. This is due to an "inspection paradox": cells with faster lifetimes are more likely to have one of their descendants sampled by virtue of their prolificity. This inspection paradox is explored (as well as other inspection paradoxes in the broader probability literature), and the resulting bias is linked to recent observations in genetic data.
