Fig. 3.

Leave-one-out cross validation (LOOCV) tests. The models were validated under the context of divergence date (t) inference, by using LOOCV tests (see Methods for details). In (a), the recovered t values are shown against the reference t values, inferred under the co-speciation assumption. The colours of the data points correspond to the colours of the node bars in Fig. 1a. The node numbers refer to those in the trees in Fig. 1a. The grey lines show where the recovered t values are exactly equal to the references. The out-of-sample mean squared errors are shown in (b). A summary of the results can be found in Additional file 1: Table S4. VEX: vertically-translated exponential rate decay model; EX: simple exponential rate decay model; VPL: vertically-translated power-law rate decay model; and PL: simple power-law rate decay models