Fig. 3: Assessment of deep learning accuracy.

Comparison of inference accuracy by BEAST2 (in blue), deep neural network trained on SS (in orange) and convolutional neural network trained on the CBLV representation (in green) on 100 test trees. The size of training and testing trees was uniformly sampled between 200 and 500 tips. We show the relative error for each test tree. The error is measured as the normalized distance between the median a posteriori estimate by BEAST2 or point estimates by neural networks and the target value for each parameter. We highlight simulations for which BEAST2 did not converge and whose values were thus set to median of the parameter subspace used for simulations, by depicting them as red squares. We further highlight the analyses with a high relative error (>1.00) for one of the estimates, as black diamonds. We compare the relative errors for a BD-simulated, b BDEI-simulated and c BDSS-simulated trees. Average relative error is displayed for each parameter and method in corresponding colour below each figure. The average error of a FFNN trained on summary statistics but with randomly permuted target is displayed as black dashed line and its value is shown in bold black below the x-axis. The accuracy of each method is compared by two-sided paired z-test; P < 0.05 is shown as thick full line; non-significant is not shown.