Méthodes et Algorithmes pour la Bioinformatique, LIRMM, CNRS-Université de Montpellier, 161 rue Ada, 34392 Montpellier, France.
Bull Math Biol. 2010 Oct;72(7):1820-39. doi: 10.1007/s11538-010-9510-y. Epub 2010 May 7.
Minimum evolution is the guiding principle of an important class of distance-based phylogeny reconstruction methods, including neighbor-joining (NJ), which is the most cited tree inference algorithm to date. The minimum evolution principle involves searching for the tree with minimum length, where the length is estimated using various least-squares criteria. Since evolutionary distances cannot be known precisely but only estimated, it is important to investigate the robustness of phylogenetic reconstruction to imprecise estimates for these distances. The safety radius is a measure of this robustness: it consists of the maximum relative deviation that the input distances can have from the correct distances, without compromising the reconstruction of the correct tree structure. Answering some open questions, we here derive the safety radius of two popular minimum evolution criteria: balanced minimum evolution (BME) and minimum evolution based on ordinary least squares (OLS + ME). Whereas BME has a radius of 1/2, which is the best achievable, OLS + ME has a radius tending to 0 as the number of taxa increases. This difference may explain the gap in reconstruction accuracy observed in practice between OLS + ME and BME (which forms the basis of popular programs such as NJ and FastME).
最小进化是一类基于距离的系统发育重建方法的指导原则，包括邻接法（NJ），它是迄今为止引用最多的树推断算法。最小进化原则涉及搜索具有最小长度的树，其中长度使用各种最小二乘标准进行估计。由于进化距离不能精确地知道，只能估计，因此研究系统发育重建对这些距离的不精确估计的稳健性非常重要。安全半径是这种稳健性的一种度量：它由输入距离相对于正确距离的最大相对偏差组成，如果不影响正确树结构的重建，则该偏差可以存在。回答一些悬而未决的问题，我们在这里推导出两种流行的最小进化标准的安全半径：平衡最小进化（BME）和基于普通最小二乘的最小进化（OLS + ME）。BME 的半径为 1/2，是可实现的最佳半径，而 OLS + ME 的半径随着分类单元数量的增加趋于 0。这种差异可能解释了在实践中观察到的 OLS + ME 和 BME 之间重建准确性的差距（BME 是 NJ 和 FastME 等流行程序的基础）。
