关于具有长分支的大类属的推论：多长是太长？
On the inference of large phylogenies with long branches: How long is too long?
摘要：
最近的工作强调了高概率同源性重建的序列长度要求和祖先序列估计的相关问题之间的深刻联系。在[Daskalakis et al. '09]，建立在[Mossel'04]的工作基础上，获得了CFN模型的严格序列长度要求。特别地，高概率重建所需的序列长度被证明在祖先重建问题的“临界”分支长度$\critmlq$（如果存在）处经历急剧转变（从$O(\log n)$到$\hbox{poly}(n)$，其中$n$是叶的数量）。在这里，我们考虑GTR模型。对于该模型，[Roch'09]的最新结果表明，当分支长度低于$\critksq$（称为Kesten-Stigum（KS）界）时，可以用长度为$O(\log(n))$的序列准确地重建树。虽然对于CFN模型$\critmlq = \critksq$，但已知对于更一般的GTR模型，在许多情况下具有严格不等式的$\critmlq \geq \critksq$。在这里，我们表明，这种现象也适用于系统发育重建，表现出一个家庭的对称模型$Q$和系统发育重建算法，该算法恢复树从$O(\log n)$长度序列的范围内的一些分支长度$(\critksq,\critmlq)$。其次，我们证明了GTR模型下的系统发育重建需要一个多项式序列长度的分支长度以上$\critmlq$。
英文摘要：
Recent work has highlighted deep connections between sequence-length requirements for high-probability phylogeny reconstruction and the related problem of the estimation of ancestral sequences. In [Daskalakis et al.'09], building on the work of [Mossel'04], a tight sequence-length requirement was obtained for the CFN model. In particular the required sequence length for high-probability reconstruction was shown to undergo a sharp transition (from $O(\log n)$ to $\hbox{poly}(n)$, where $n$ is the number of leaves) at the "critical" branch length $\critmlq$ (if it exists) of the ancestral reconstruction problem. Here we consider the GTR model. For this model, recent results of [Roch'09] show that the tree can be accurately reconstructed with sequences of length $O(\log(n))$ when the branch lengths are below $\critksq$, known as the Kesten-Stigum (KS) bound. Although for the CFN model $\critmlq = \critksq$, it is known that for the more general GTR models one has $\critmlq \geq \critksq$ with a strict inequality in many cases. Here, we show that this phenomenon also holds for phylogenetic reconstruction by exhibiting a family of symmetric models $Q$ and a phylogenetic reconstruction algorithm which recovers the tree from $O(\log n)$-length sequences for some branch lengths in the range $(\critksq,\critmlq)$. Second we prove that phylogenetic reconstruction under GTR models requires a polynomial sequence-length for branch lengths above $\critmlq$.
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