MULLER%26apos;S RATCHET WITH COMPENSATORY MUTATIONS

作者：Pfaffelhuber P^*; Staab P R; Wakolbinger A

来源：Annals of Applied Probability, 2012, 22(5): 2108-2132.

DOI：10.1214/11-AAP836

• Muller%26apos
• s ratchet
• selection
• back mutation
• Fleming-Viot process
• Girsanov transform

We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the number of deleterious mutations it carries, where fitness of individuals carrying k mutations is decreased by alpha k for some alpha %26gt; 0. Along the individual lines of descent, new mutations accumulate at rate lambda per generation, and each of these mutations has a probability gamma per generation to disappear. While the case gamma = 0 is known as (the Fleming-Viot version of) Muller%26apos;s ratchet, the case gamma %26gt; 0 is associated with compensatory mutations in the biological literature. We show that the system has a unique weak solution. In the absence of random fluctuations in type frequencies (i.e., for the so-called infinite population limit) we obtain the solution in a closed form by analyzing a probabilistic particle system and show that for gamma %26gt; 0, the unique equilibrium state is the Poisson distribution with parameter lambda/(gamma + alpha).

• 出版日期2012-10