Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its ‘ancestral profile’ (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying phylogenetic network. A recent paper considered a new class of phylogenetic networks called ‘orchard networks’ where this uniqueness was claimed to hold. Here we show that an additional restriction on the network, that of being ‘stack-free’, is required in order for the original uniqueness claim to hold. On the other hand, if the additional stack-free restriction is lifted, we establish an alternative result; namely, there is uniqueness within the class of orchard networks up to the resolution of vertices of high in-degree.

当网状进化过程在起作用时，有根系统发育网络比系统发育树更完整地表示物种之间的祖先关系。重建系统发育网络的一种方法是考虑其“祖先轮廓”（从每个祖先顶点到每片叶子的路径数）。通常，此信息并不能唯一确定潜在的系统发育网络。最近的一篇论文考虑了一类新的系统发育网络，称为“果园网络”，据称这种独特性是存在的。在这里，我们表明需要对网络进行额外的限制，即“无堆栈”，以便保持原始唯一性声明。另一方面，如果取消额外的无堆栈限制，我们建立一个替代结果；即，