一种用于半定向果园系统发育网络的μ-距离
A $μ$-distance for semidirected orchard phylogenetic networks
AI总结：
本文提出一种新的μ-表示方法，用于区分不同的二元半定向果园系统发育网络，并提供可计算的真距离。
摘要：
在进化生物学中，系统发育网络现在广泛用于表示物种和种群之间的历史关系，当这个历史包含如杂交、基因流动和种群间杂交等网状事件时。当某些边的方向和根的位置无法从数据中确定时，半定向系统发育网络是适当的模型。比较半定向网络在许多应用中很重要。对于有根和定向网络，最初引入了μ-表示法以区分树儿童网络，此后在两个不同方向上进行了扩展：通过添加一个额外的组件来计数到网状结构的路径，扩展到更大的果园定向网络类别；并通过边变体扩展到半定向网络。然而，后者不提供半定向和果园网络之间的距离。本文介绍了一种新的基于边的μ-表示法，能够区分不同的二元半定向果园网络。对于此类网络，我们提供了一种重建算法，因此获得了一个可计算的真距离，该距离可以在多项式时间内计算。
英文摘要：
In evolutionary biology, phylogenetic networks are now widely used to represent the historical relationships between species and population, when this history includes reticulation events such as hybridization, gene flow and admixture between populations. Semidirected phylogenetic networks are appropriate models when the direction of some edges and the root position are not identifiable from data. Comparing semidirected networks is important in many applications. For rooted and directed networks, a $μ$-representation was originally introduced to distinguish tree-child networks, and has since been extended in two different directions: to the larger class of orchard directed networks by adding an extra component that counts paths to reticulations; and to semidirected networks, through an edge-based variant. However, the latter does not provide a distance between semidirected and orchard networks. We introduce here a new edge-based $μ$-representation capable of distinguishing distinct orchard binary semidirected networks. For this class, we provide a reconstruction algorithm and therefore obtain a true distance that is computable in polynomial time.
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