重构谱系：重组突变模型的一些可识别性问题
Reconstructing pedigrees: some identifiability questions for a recombination-mutation model
摘要：
谱系是有向非循环图，表示种群中个体之间的祖先关系。基于一个示意性的重组过程，我们描述了两个简单的马尔可夫模型的序列演变的谱系-模型R（重组无突变）和模型RM（重组突变）。对于这些模型，我们问一个可识别性问题：是否有可能从现存序列的联合概率分布构建谱系？我们提出了一般谱系的部分可识别性结果：我们表明，当交叉概率足够小，某些生成子图序列可以从现存序列的联合分布计数。我们演示了如何谱系，较早似乎难以区分计数其生成子图序列。
英文摘要：
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R (recombinations without mutations) and Model RM (recombinations with mutations). For these models, we ask an identifiability question: is it possible to construct a pedigree from the joint probability distribution of extant sequences? We present partial identifiability results for general pedigrees: we show that when the crossover probabilities are sufficiently small, certain spanning subgraph sequences can be counted from the joint distribution of extant sequences. We demonstrate how pedigrees that earlier seemed difficult to distinguish are distinguished by counting their spanning subgraph sequences.
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