论文标题
基因组进化中的随机性与选择
Randomness versus selection in genome evolution
论文作者
论文摘要
我们提出了马尔可夫链方法，以进化基因组的谱系线。我们理想化的基因组具有$ n $站点，每个站点都可以在州$ 0 $或$ 1 $。在每个时间步骤，我们随机选择一个站点。如果该网站处于状态$ 0 $，我们将其用概率$ p $将其翻转为状态1，或者我们将其保留在状态$ 0 $的情况下，概率$ 1-p $。如果该网站处于状态$ 1 $，我们将其翻转为概率$ 1-p $的状态0，或者我们将其保留在状态$ 1 $的情况下，并带有概率$ p $。即使状态1具有选择性优势（即$ p> 1/2 $），马尔可夫链也不太可能接近最合适的等位基因（即所有1）。实际上，随机性（即选择哪个站点以进行突变）和选择（即$ p $的值）相互平衡，以使基因组中的$ 1 $的数量收敛于左右$ NP $的高斯分配。
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 $Np$.
