MULLER'S RATCHET WITH COMPENSATORY MUTATIONS

• 成果类型: Article
• 署名作者: Pfaffelhuber, P.; Staab, P. R.; Wakolbinger, A.
• 署名单位: University of Freiburg; Goethe University Frankfurt
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP836
• 发表日期: 2012
• 页码: 2108-2132
• 关键词: asexual populations; EVOLUTION; selection; accumulation; adaptation; fitness; dna

摘要

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 > 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's ratchet, the case gamma > 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 > 0, the unique equilibrium state is the Poisson distribution with parameter lambda/(gamma + alpha).