Fig. 1

a A species tree and a b gene tree with the leaf map indicated by solid, dashed, and dotted lines. c A species and locus map for these two trees where circular nodes correspond to gene nodes in the gene tree and the rectangular node \(g'\) is an implied speciation node. In this species map, \(\mathcal {M}(g_1) = \mathcal {M}(g_2) = \mathcal {M}(g') = s_1\), \(\mathcal {M}(g_3) = s_2\), \(\mathcal {M}(g_4) = \mathcal {M}(g_5) = s_3\), \(\mathcal {M}(g_6) = \mathcal {M}(g_7) = s_4\), and \(\mathcal {M}(g_8) = \mathcal {M}(g_9) = s_5\). The two loci are indicated in solid red and dashed blue. There is a single duplication on edge \((g', g_5)\) indicated by a star. This edge separates paralogs \(g_6\) and \(g_7\) as well as paralogs \(g_8\) and \(g_9\)