We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, "consensus" tree (say, a species tree). Various stability criteria have been explored in this context, seeking to model desirable consistency properties of consensus methods as the experimental data is updated (e.g., more taxa, or more trees, are mapped). However, such stability conditions can be incompatible with some basic regularity properties that are widely accepted to be essential in any meaningful consensus method. Here, we prove that such an incompatibility does arise in the case of extension stability on binary trees and in the case of associative stability. Our methods combine general theoretical considerations with the use of computer programs tailored to the given stability requirements.

中文翻译：

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系统发育共识方法稳定性的不可能结果

我们回答了 Bryant、Francis 和 Steel 在他们关于系统发育学共识方法的工作中提出的两个问题。共识方法适用于需要将一组给定的系统发育树（例如，基因进化树）聚合为结果的“共识”树（例如，物种树）的每个实际实例。在这方面已经探索了各种稳定性标准，寻求随着实验数据的更新（例如，映射更多分类群或更多树）对共识方法的理想一致性属性进行建模。然而，这样的稳定​​性条件可能与一些被广泛接受为任何有意义的共识方法必不可少的基本规律性属性不兼容。这里，我们证明了在二叉树的扩展稳定性和结合稳定性的情况下确实会出现这种不兼容性。我们的方法将一般的理论考虑与针对给定稳定性要求定制的计算机程序的使用相结合。