论文标题
穆勒棘轮的点击之间的亚竞争力
Metastability between the clicks of Muller's ratchet
论文作者
论文摘要
我们证明了从穆勒棘轮模型得出的三个随机过程的准平台分布的存在和唯一性。该模型的发明旨在评估无性繁殖模式的局限性，以防止仅通过自然选择的有害突变积累。主要考虑的模型是非古典模型，因为它是在不规则的无限尺寸上演变的随机扩散，在超平面上进行了硬杀。尽管如此，即使在这种情况下，我们仍然能够证明总变化与准平台分布的指数收敛。最后一次收敛结果中的参数与穆勒棘轮的核心参数直接相关。对于无限尺寸模型，推导了与准平台分布的收敛速度，也是针对大量但有限数量的电位突变的近似值。同样，我们给出了准平台下种群中突变的经验分布的统一力矩估计。
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as it is a stochastic diffusion evolving on an irregular set of infinite dimension with hard killing on an hyperplane. We are nonetheless able to prove exponential convergence in total variation to the quasi-stationary distribution even in this case. The parameters in this last convergence result are directly related to the core parameters of Muller's ratchet. The speed of convergence to the quasi-stationary distribution is deduced both for the infinite dimensional model and for approximations with a large yet finite number of potential mutations. Likewise, we give uniform moment estimates of the empirical distribution of mutations in the population under quasi-stationarity.
