AI 中文总结
研究空间结构化种群中有害突变能否像中性突变那样借助确定性波动扩散。通过研究空间穆勒棘轮的确定性版本，分析有害突变分布、种群扩散速度，最终表明有害突变不能借助确定性波动扩散。
AI 中文摘要
在空间结构化种群中，罕见中性突变在范围扩张时能在大片区域扩散，即基因冲浪现象。有害突变能否如此尚不清楚。我们研究空间穆勒棘轮的确定性版本，由无限反应扩散方程组描述无性种群的突变、迁移及密度依赖的繁殖与死亡。确定方程组适定后，分析种群中有害突变分布。在单稳状态下，得出携带特定数量突变个体密度与无突变个体密度之比的定量界限。在费希尔 - KPP条件下，确定种群向空栖息地的扩散速度。最后表明有害突变不能借助确定性波动扩散，虽在扩张前沿存在，但只是野生型的近期后代。
英文摘要
In spatially structured populations, rare neutral mutations can spread through large regions during a range expansion, a phenomenon known as gene surfing. Whether deleterious mutations can also surf remains poorly understood. To address this question, we study a deterministic version of the spatial Muller's ratchet, given by an infinite system of reaction-diffusion equations describing an asexual population subject to mutation, migration, and density-dependent reproduction and death. After establishing that the system of PDEs is well-posed, we analyse the distribution of deleterious mutations within the population. In the monostable regime, we derive quantitative bounds on the ratio between the density of individuals carrying a given number of mutations and the density of mutation-free individuals. Under a Fisher-KPP condition, we further determine the spreading speed of the population into an empty habitat, confirming non-rigorous computations of Foutel-Rodier and Etheridge. Finally, using a tracer dynamics approach, we show that deleterious mutations cannot surf deterministic waves: although they are present at the expansion front, they only arise as recent descendants of the wild type.
Comments55 pages, 1 figure. This work was originally part of arXiv:2603.06478 and has been separated into a standalone manuscript
