Evaluating different quartet scanning statistics and significance assessments. The percentages of correctly top-ranked recombinants for three different statistics and three different approaches to evaluate significance are summarized for simulated data in the absence (b and d) and presence (a and c) of rate variation among partitions. The upper graphs (a and b) and the lower graphs (c and d) summarize the results for the symmetric and asymmetric trees respectively. Dashed lines represent the frequency by which a recombinant is correctly ranked on top, independent of whether significant evidence for recombination can be detected in the replicate set. The full lines represent the same frequency, but now supported with significant evidence for recombination in the replicate set. The different statistics, dmax, dtot and dav, are represented by blue, red and black lines/symbols respectively. Simulation, permutation and redistribution to generate null distributions for these test statistics are represented by open circles, open squares and filled triangles respectively. The results are shown for simulations using three different tree depths (0.5, 1.0 and 1.5 substitutions per site).