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Genetic composition of supercritical branching populations under power law mutation rates
Mardi, 16 Janvier, 2024 - 14:00 à 15:00
Résumé :
Understanding the evolution of the genetic composition of cancer cell populations is of key interest for clinicians. In this talk we will study a toy model of carcinogenesis by considering a branching individual based model representing a cell population where cells divide, die and mutate along the edges of a finite directed graph (V,E). Following typical parameter values in cancer cell populations we study the model under large population and power law mutation rates limit, in the sense that the mutation probabilities are parameterized by negative powers of n and the typical sizes of the population of our interest are positive powers of n.
Under non-increasing growth rate condition, namely the growth rate of any subpopulation is smaller than the growth rate of trait 0, we describe the time evolution of the first-order asymptotics of each subpopulation on the log(n) time scale, as well as in the random time scale at which the initial population, resp. the total population, reaches the size n^{t}. Such results allow to characterize whose mutational paths along the edges of the graph are actually contributing to the size order of each subpopulation.
Without any condition on the growth rates, the analysis to get the first-order asymptotics of the mutant subpopulations is far more complex. We will explain this increasing difficulty and give some recent results for a mono-directional graph whose last mutation is the first selective one.
Institution de l'orateur :
ENS Lyon
Thème de recherche :
Probabilités
Salle :
4
