An impossibility result for phylogeny reconstruction from k-mer counts
An impossibility result for phylogeny reconstruction from k-mer counts
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DOI：
10.1214/22-aap1805
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发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
W. Fan;Brandon Legried;S. Roch
中科院分区：
文献类型：
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作者：
W. Fan;Brandon Legried;S. Roch
我们考虑通过树上的位点替换在序列进化的两种状态模型下进行系统发育估计。在序列长度趋于无穷大的渐近状态中，我们表明，对于任何固定的 $k$，仅从完整叶序列上的 $k$-mer 计数不可能得出统计上一致的系统发育估计。形式上，我们确定，当序列长度趋于无穷大时，两棵不同树上整个叶子序列上的 $k$-mer 计数的联合分布具有远离 $1$ 的总变异距离。我们的不可能结果意味着统计一致性需要更复杂地使用 $k$-mer 计数信息，例如先前理论工作中开发的块技术。
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent phylogeny estimation is possible from $k$-mer counts over the full leaf sequences alone. Formally, we establish that the joint distribution of $k$-mer counts over the entire leaf sequences on two distinct trees have total variation distance bounded away from $1$ as the sequence length tends to infinity. Our impossibility result implies that statistical consistency requires more sophisticated use of $k$-mer count information, such as block techniques developed in previous theoretical work.