Igelbrink J L, González Casanova A, Smadi C, Wakolbinger A
Goethe-Universität, Institut für Mathematik, Frankfurt am Main, 60629, Germany; Johannes Gutenberg-Universität, Institut für Mathematik, Staudingerweg 9, Mainz, 55128, Germany.
Universidad Nacional Autónoma de México (UNAM), Instituto de Matemáticas, Circuito exterior, Ciudad Universitaria, 04510, Mexico; Department of Statistics, 367 Evans Hall, University of California, Berkeley, CA 94720-386, United States of America.
Theor Popul Biol. 2024 Aug;158:121-138. doi: 10.1016/j.tpb.2024.06.001. Epub 2024 Jun 4.
Muller's ratchet, in its prototype version, models a haploid, asexual population whose size N is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers fitness proportional selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. (2009) we propose a parameter scaling which fits well to the "near-critical" regime that was in the focus of Etheridge et al. (2009) (and in which the mutation-selection ratio diverges logarithmically as N→∞). Using a Moran model, we investigate the"rule of thumb" given in Etheridge et al. (2009) for the click rate of the "classical ratchet" by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection. This variant of Muller's ratchet was introduced in González Casanova et al. (2023), and was analysed there in a subcritical parameter regime. Other than that of the classical ratchet, the size of the best class of the tournament ratchet follows an autonomous dynamics up to the time of its extinction. It turns out that, under a suitable correspondence of the model parameters, this dynamics coincides with the so called Poisson profile approximation of the dynamics of the best class of the classical ratchet.
缪勒棘轮在其原始版本中，模拟了一个单倍体无性种群，其种群大小(N)在各代中保持恒定。轻微有害的突变以恒定速率在谱系中积累，携带较少突变的个体具有选择优势。经典变体考虑适应度比例选择，但也可以设想其他适应度方案。受埃瑟里奇等人（2009年）工作的启发，我们提出了一种参数缩放，它非常适合埃瑟里奇等人（2009年）关注的“近临界”状态（在该状态下，突变选择比随着(N→∞)呈对数发散）。使用莫兰模型，我们将埃瑟里奇等人（2009年）给出的关于“经典棘轮”点击速率的“经验法则”置于棘轮最佳类大小在（二元）锦标赛选择下的长期演化新结果的背景中进行研究。缪勒棘轮的这种变体由冈萨雷斯·卡萨诺瓦等人（2023年）引入，并在那里的亚临界参数区域进行了分析。与经典棘轮不同，锦标赛棘轮最佳类的大小在灭绝之前遵循自主动态。结果表明，在模型参数的适当对应下，这种动态与经典棘轮最佳类动态的所谓泊松分布近似一致。
