Description of two statistics used in this study. In the first step (1), one gene tree is sampled for each locus; for observed data, these would be estimated gene trees or trees sampled from a posterior distribution; for simulated data, trees for each locus would be simulated under identical models of population structure. These trees, one from each locus, are then fit into each of the hypotheses being tested (2). The measure of fit for the sampled gene trees is calculated for each species tree hypothesis (3); in this case, the minimum number of deep coalescences is used to measure the absolute fit of gene trees to each species trees. Finally, the difference in the two measures of absolute fit is used as the relative measure of fit to the two hypotheses being tested (4).