TKF91模型下祖先序列、系统发育和突变率的联合可识别性
Joint identifiability of ancestral sequence, phylogeny and mutation rates under the TKF91 model
AI总结：
研究在带有插入缺失的DNA序列演化模型中联合识别祖先序列、系统发育和参数的问题，基于经典TKF91模型导出了显式公式，并提出了假设更少且统计相合的新估计量。
摘要：
我们考虑在带有插入和缺失（indel）的DNA序列演化模型中，联合识别祖先序列、系统发育和参数的问题。在经典的TKF91序列演化模型下，我们获得了关于根序列、叶序列的成对距离，以及indel和替换的缩放率的显式公式，这些公式以任意系统发育的叶序列分布表示。这些显式公式不仅加强了现有的可逆性结果，适用于不一定是超度量的系统发育，而且与现有文献相比，还导出了假设更少的新估计量。我们的模拟研究表明，随着独立样本数趋于无穷大，这些估计量在统计上是相合的。
英文摘要：
We consider the problem of identifying jointly the ancestral sequence, the phylogeny and the parameters in models of DNA sequence evolution with insertion and deletion (indel). Under the classical TKF91 model of sequence evolution, we obtained explicit formulas for the root sequence, the pairwise distances of leaf sequences, as well as the scaled rates of indel and substitution in terms of the distribution of the leaf sequences of an arbitrary phylogeny. These explicit formulas not only strengthen existing invertibility results and work for phylogeny that are not necessarily ultrametric, but also lead to new estimators with less assumption compared with the existing literature. Our simulation study demonstrates that these estimators are statistically consistent as the number of independent samples tends to infinity.
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