共识方法与超树方法的单调性与非矛盾性综述
A survey of the monotonicity and non-contradiction of consensus methods and supertree methods
AI总结：
本文分析了系统发育学中共识方法在发现新演化支时的单调性，探讨了新见解不与先前共识树矛盾而仅细化的性质，并研究了MRP和MRC等超树方法，得出多数规则和严格共识方法的积极结果。
摘要：
在最近的一项研究中，Bryant, Francis 和 Steel 探讨了系统发育学中共识方法的“前瞻性验证”概念。也就是说，他们研究了此类方法是否能够对引入额外数据（如添加的树或新物种）保持鲁棒性。在本文稿中，我们从引入新数据的不同角度分析共识方法，即关于新演化支的发现。在进化生物学中，以前未解决的演化支通常通过改进的重建方法或新的遗传数据分析得到解决。在我们的稿件中，我们研究了共识方法的哪些性质可以保证此类新见解不与先前发现的共识树相矛盾，而只是对其进行细化，这一性质被称为单调性。在分析单调性的同时，我们还研究了两种已确立的超树方法，即 Matrix Representation with Parsimony (MRP) 和 Matrix Representation with Compatibility (MRC)，文献中也建议将它们作为共识方法。虽然我们（就像 Bryant, Francis 和 Steel 在其最近的研究中一样）遗憾地不得不对一般共识方法得出一些否定答案，但我们也陈述了关于多数规则（$\mathtt{MR}$）和严格共识方法的一些相关且积极的结果，这些是最常用的共识方法之一。此外，我们证明了存在无穷多个具有单调性及其他一些理想性质的共识方法。关键词：consensus tree, phylogenetics, majority rule, tree refinement, matrix representation with parsimony。MSC：C92B05, 05C05。
英文摘要：
In a recent study, Bryant, Francis and Steel investigated the concept of \enquote{future-proofing} consensus methods in phylogenetics. That is, they investigated if such methods can be robust against the introduction of additional data like added trees or new species. In the present manuscript, we analyze consensus methods under a different aspect of introducing new data, namely concerning the discovery of new clades. In evolutionary biology, often formerly unresolved clades get resolved by refined reconstruction methods or new genetic data analyses. In our manuscript we investigate which properties of consensus methods can guarantee that such new insights do not disagree with previously found consensus trees, but merely refine them, a property termed \emph{monotonicity}. Along the lines of analyzing monotonicity, we also study two {established} supertree methods, namely Matrix Representation with Parsimony (MRP) and Matrix Representation with Compatibility (MRC), which have also been suggested as consensus methods in the literature. While we (just like Bryant, Francis and Steel in their recent study) unfortunately have to conclude some negative answers concerning general consensus methods, we also state some relevant and positive results concerning the majority rule ($\mathtt{MR}$) and strict consensus methods, which are amongst the most frequently used consensus methods. Moreover, we show that there exist infinitely many consensus methods which are monotonic and have some other desirable properties. \textbf{Keywords:} consensus tree, phylogenetics, majority rule, tree refinement, matrix representation with parsimony \textbf{MSC:} C92B05, 05C05
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