Hobolth Asger, Jensen Jens Ledet
Bioinformatics Research Center, Aarhus University, Denmark.
Department of Mathematics, Aarhus University, Denmark.
Theor Popul Biol. 2014 Dec;98:48-58. doi: 10.1016/j.tpb.2014.01.002. Epub 2014 Jan 28.
The coalescent with recombination process has initially been formulated backwards in time, but simulation algorithms and inference procedures often apply along sequences. Therefore it is of major interest to approximate the coalescent with recombination process by a Markov chain along sequences. We consider the finite loci case and two or more sequences. We formulate a natural Markovian approximation for the tree building process along the sequences, and derive simple and analytically tractable formulae for the distribution of the tree at the next locus conditioned on the tree at the present locus. We compare our Markov approximation to other sequential Markov chains and discuss various applications.
具有重组过程的溯祖过程最初是按时间逆向构建的，但模拟算法和推断程序通常是沿着序列应用的。因此，通过沿着序列的马尔可夫链来近似具有重组过程的溯祖过程是非常有意义的。我们考虑有限基因座情况以及两条或更多条序列。我们为沿着序列的树构建过程制定了一种自然的马尔可夫近似，并推导了基于当前位点的树的条件下，下一个位点处树的分布的简单且易于分析处理的公式。我们将我们的马尔可夫近似与其他序列马尔可夫链进行比较，并讨论各种应用。
