单交叉重组和祖先重组树
Single--crossover recombination and ancestral recombination trees
摘要：
我们认为赖特-费舍尔模型的人口$N$个人，每个确定了一个序列的有限数量的网站，和单交叉重组之间。我们从现在的种群中追溯单个个体的祖先。在没有参数或时间重新标度的$N \to \infty$极限中，这个祖先过程由随机树描述，其分支事件对应于由于重组而导致的序列分裂。借助分解的树到子树，我们计算的祖先树的拓扑的概率。同时，这些概率导致确定性单交叉方程的半显式解。后者是一个离散时间动力系统，通过大数定律从赖特-费舍尔模型中出现，并且已经等待了几十年的解决方案。
英文摘要：
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the $N \to \infty$ limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help of a decomposition of the trees into subtrees, we calculate the probabilities of the topologies of the ancestral trees. At the same time, these probabilities lead to a semi-explicit solution of the deterministic single-crossover equation. The latter is a discrete-time dynamical system that emerges from the Wright-Fisher model via a law of large numbers and has been waiting for a solution for many decades.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
