We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where the expected sequence lengths tend to infinity, we show that no consistent distance estimation is possible from sequence lengths alone. More formally, we establish that the distributions of pairs of sequence lengths at different distances cannot be distinguished with probability going to one.

中文翻译：

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TKF91 模型下序列长度一致距离估计的不可能性

我们考虑在 TKF91 序列进化模型下通过系统发育的插入、删除和替换来估计距离的问题。在预期序列长度趋于无穷大的渐近机制中，我们表明仅从序列长度不可能进行一致的距离估计。更正式地，我们确定不同距离的序列长度对的分布不能在概率趋于一个的情况下区分。