Evolutionary processes have been described not only in biology but also for a wide range of human cultural activities including languages and law. In contrast to the evolution of DNA or protein sequences, the detailed mechanisms giving rise to the observed evolution-like processes are not or only partially known. The absence of a mechanistic model of evolution implies that it remains unknown how the distances between different taxa have to be quantified. Considering distortions of metric distances, we first show that poor choices of the distance measure can lead to incorrect phylogenetic trees. Based on the well-known fact that phylogenetic inference requires additive metrics, we then show that the correct phylogeny can be computed from a distance matrix \({\mathbf {D}}\) if there is a monotonic, subadditive function \(\zeta\) such that \(\zeta ^{-1}({\mathbf {D}})\) is additive. The required metric-preserving transformation \(\zeta\) can be computed as the solution of an optimization problem. This result shows that the problem of phylogeny reconstruction is well defined even if a detailed mechanistic model of the evolutionary process remains elusive.

中文翻译：

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超越生物学的系统发育学。

进化过程不仅在生物学中得到了描述，而且在包括语言和法律在内的广泛的人类文化活动中也得到了描述。与 DNA 或蛋白质序列的进化相比，导致观察到的类似进化过程的详细机制尚不清楚或仅部分了解。缺乏进化的机械模型意味着如何量化不同分类群之间的距离仍然未知。考虑到度量距离的扭曲，我们首先表明距离度量的错误选择会导致不正确的系统发育树。基于系统发育推断需要附加度量这一众所周知的事实，然后我们表明可以从距离矩阵\({\mathbf {D}}\)计算正确的系统发育。如果存在一个单调的次加性函数\(\zeta\)使得\(\zeta ^{-1}({\mathbf {D}})\)是加性的。所需的度量保留变换\(\zeta\)可以计算为优化问题的解决方案。这一结果表明，即使进化过程的详细机械模型仍然难以捉摸，系统发育重建的问题也得到了很好的定义。