Fig. 4

Minimal examples in which ancient duplications lead to false positives (FP) or false negatives (FN) when choosing outgroups as described in the text. (A) The species tree S displaying the triple (\(\sigma (X)\sigma (Y)|\sigma (Z)\)). (B-D) Gene trees T with two ancient duplications. We assume that \(y'\) and \(y''\) are the only extant genes of color \(\sigma (Y)\), i.e. color \(\sigma (Y)\) is extinct in the subtree of x in each of the shown cases. The asterisk marks the discriminating edge for the quartet inference. (B) A quartet \((xy'|y''z)\) is inferred so that only \(y'\) but not \(y''\) is a best match, \((x, y'')\) is a FN. (C) A quartet \((xz|y'y'')\) is inferred so that \(y'\) is a false best match, \((x, y')\) is a FP. (D) A quartet \((xy'|y''z)\) is inferred so that \((x, y')\) is a FP and \((x, y'')\) is a FN