Two P-values have been proposed for the corrected chi-square. The first one relies on the assumption that the corrected chi-square is proportional to a chi-square with one degree of freedom; the second one simply counts the proportion of in silico datasets for which the value of the corrected chi-square is above the observed value. Both P-values led to consistent results using a 5% rejection threshold, consistently with the fact that for all tested pairs the corrected chi-square fitted well with an under-dispersed chi-square with one degree of freedom (Fig. S1, Fig. S2 ). Which one should be used in practice actually depends on the simulation time. If simulations are fast enough and if running 1000 bootstrap is acceptable, P-value2 should be preferred. In the opposite case, a good option is to run much less bootstraps (typically 30) and to use P-value1.