基因组进化中的随机与选择
Randomness versus selection in genome evolution
摘要：
我们提出了一个马尔可夫链的方法进化的系谱线的基因组。我们理想化的基因组具有$N$位点，并且每个位点可以处于状态$0$或$1$。在每一个时间步，我们随机选择一个地点。如果站点处于状态$0$，则以概率$p$将其翻转为状态1，或者以概率$1-p$将其保持在状态$0$。如果站点处于状态$1$，则以$1-p$的概率将其翻转为状态0，或者以$p$的概率将其保持在状态$1$。即使当状态1具有选择优势（即$p>1/2$）时，马尔可夫链也不太可能接近最适合的等位基因（即全1）。事实上，随机性（即哪个位点被挑出来进行可能的突变）和选择性（即$p$的值）相互平衡，因此基因组中$1$的数量收敛于以$Np$为中心的高斯分布。
英文摘要：
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we flip it to state 1 with probability $p$ or we keep it in state $0$ with probability $1-p$. If the site is in state $1$ we flip it to state 0 with probability $1-p$ or we keep it in state $1$ with probability $p$. Even when state 1 has a selective advantage (i.e. $p>1/2$) the Markov chain is quite unlikely to approach the most fit allele (i.e. all 1's). In fact, randomness (i.e. which site is picked for a possible mutation) and selection (i.e. the value of $p$) balance each other out so that the number of $1$'s in the genome converges to a Gaussian distribution centered around $Np$.
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。
