邻区依赖的核苷酸取代过程的可解模型
Solvable models of neighbor-dependent nucleotide substitution processes
摘要：
我们证明了一类广泛的模型的马尔可夫邻相依替代过程的整数线是可解的。这门课包含了一些最近被分子生物学家引进并以经验研究的核苷酸取代模型。我们表明，多核苷酸的频率在平衡解决明确的有限大小的线性系。最后，动态的过程和平衡时的分布表现出一些严格的，而出乎意料的，独立的属性。例如，距离至少为3的核苷酸位点独立进化，并且如果编码为嘌呤和嘧啶，则这些位点独立进化。
英文摘要：
We prove that a wide class of models of Markov neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotide substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotide frequencies at equilibrium solve explicit finite-size linear systems. Finally, the dynamics of the process and the distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotide sites at distance at least three evolve independently, and the sites, if encoded as purines and pyrimidines, evolve independently.
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