论文标题
遗传元件拷贝数变化的二倍体种群模型
A diploid population model for copy number variation of genetic elements
论文作者
论文摘要
我们研究了以下模型，用于恒定大小$ n $的二倍体种群：每个人都携带随机数量的（遗传）元素。复制事件发生后，两个父母中的每一个都独立传递了每个元素，概率$ \ tfrac 12 $ in to the oferspring。我们研究该过程$ x^n =（x^n（1），x^n（2），...）$，其中$ x_t^n（k）$是携带$ k $元素的个人的频率，并证明了$ x^n $的融合（在某些弱感中），其经验性的首次$ z^n $ to $ z^n $ $ z^n $ $ s $ s $ s $ n $ n $（k） \ text {poi}（z_t）$和$ z $根据关键的候选者分支过程进化。我们讨论了解释这一发现以及一些扩展和局限性的启发式方法。
We study the following model for a diploid population of constant size $N$: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability $\tfrac 12$ on to the offspring. We study the process $X^N = (X^N(1), X^N(2),...)$, where $X_t^N(k)$ is the frequency of individuals at time $t$ that carry $k$ elements, and prove convergence (in some weak sense) of $X^N$ jointly with its empirical first moment $Z^N$ to the ``slow-fast'' system $(Z,X)$, where $X_t = \text{Poi}(Z_t)$ and $Z$ evolves according to a critical Feller branching process. We discuss heuristics explaining this finding and some extensions and limitations.
