Muller's ratchet clicks in finite time

International audienceWe consider the accumulation of deleterious mutations in an asexual population, a phenomenon known as Muller's ratchet, using the continuous time model proposed by A. Etheridge, P. Pfa ffelhuber and A. Wakolbinger. We show that for any rate and toxicity of mutations the ratchet clicks a.s. in fi nite time. That is to say the minimum number of deleterious mutations in the population goes to infi nity a.s