This post on the Genealogical World of Phylogenetic Networks dwelves into the rationale for using median networks to explore the signal behind the terminal subtrees, explains how to generate the shown collapsed median-joinging networks, and what information the inferred ancestor-descendant relationships of gene haplotypes provide when we interprete a tree's clades as phylogenetic groups in a classic-systematic, evolutionary sense, i.e. monophyly vs. paraphyly and likely evolutionary pathways: sorting (or not) of geno- and haplotypes during speciation processes.