Department of Mathematics and Computer Science, University of the Balearic Islands, Palma, E-07122, Spain.
Balearic Islands Health Research Institute (IdISBa), Palma, E-07010, Spain.
J Math Biol. 2024 Oct 4;89(5):48. doi: 10.1007/s00285-024-02142-4.
Faith's Phylogenetic Diversity (PD) on rooted phylogenetic trees satisfies the so-called strong exchange property that guarantees that, for every two sets of leaves of different cardinalities, a leaf can always be moved from the larger set to the smaller set in such a way that the sum of the PD values does not decrease. This strong exchange property entails a simple polynomial-time greedy solution to the PD optimization problem on rooted phylogenetic trees. In this paper we obtain an exchange property for the rooted Phylogenetic Subnet Diversity (rPSD) on rooted phylogenetic networks, which involves a more complicated exchange of leaves. We derive from it a polynomial-time greedy solution to the rPSD optimization problem on rooted semibinary level-2 phylogenetic networks.
基于有根系统发生树的信仰系统进化多样性（PD）满足所谓的强交换属性，该属性保证对于任意两个不同基数的叶集，总是可以通过将一个叶从较大的集合移动到较小的集合的方式，使得 PD 值的总和不会减小。这种强交换属性为有根系统发生树的 PD 优化问题提供了一种简单的多项式时间贪婪解决方案。在本文中，我们为基于有根系统发生网络的有根系统发生子网多样性（rPSD）获得了一个交换属性，该属性涉及到更复杂的叶子交换。我们从中推导出基于半二元 2 级系统发生网络的 rPSD 优化问题的多项式时间贪婪解决方案。
