On the utility of Deep Learning for model classification and parameter estimation on complex diversification scenarios

Birth-Death models applied to dated phylogenies are useful tools to study past diversification dynamics. Parameters in these stochastic models are typically inferred using likelihood-based methods; however, these approaches can exhibit computational tractability issues for models of moderate to high complexity. One approach to increase model complexity while remaining computationally tractable is Deep Learning. These techniques have recently been explored in the context of serially-sampled phylogenies (phylodynamics) and trait-dependent birth-death models (macroevolution). Here, we explore the power of Convolutional Neural Networks (CNNs) to solve classification (model selection) and regression (parameter estimation) tasks for extant-only phylogenies under six constant-rate and time-varying, lineage-homogeneous diversification scenarios: Constant Birth-Death, High Extinction, Mass Extinction, Diversity-Dependent Diversification, and the piecewise-constant scenarios Stasis-and-Radiate and Waxing-and-Waning. We simulated 10,000 phylogenetic trees under each diversification scenario, which were encoded using the CDV vectorization procedure to capture branch length information. The encoded trees were used to train a set of CNNs models designed to match three empirical phylogenies of eucalypts, conifers, and cetaceans, which have previously been used for benchmarking diversification models and differ in the number of extant tips. Additionally, we compared CNN performance with Maximum Likelihood Estimation (MLE) for the same set of scenarios. We found that CNNs exhibited classification accuracy levels of 80-93%, whereas MLE achieved levels of 70-74%. The most difficult scenarios for CNN classification were High Extinction and Mass-Extinction. For regression tasks, mean average errors were slightly higher for MLE compared with DL. Both approaches had difficulty estimating ratio parameters such as mass-extinction survival and relative extinction. Finally, we applied our CNN models for parameter estimation on the three empirical phylogenies under the best-fit diversification scenario. This allows us to discuss shortcomings and future avenues for improvement, such as the inclusion of rate-variable, lineage-heterogeneous models.