Mutational pattern of a sample from a critical branching population.

Abstract excerpt

We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises as the law of the genealogy of a sample in a large class of nearly critical branching populations with rare mutations at birth, namely populations converging, in a large...

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