Parameter Estimation from Phylogenetic Trees Using Neural Networks and Ensemble Learning

Species diversification is characterized by speciation and extinction, the rates of which can, under some assumptions, be estimated from time-calibrated phylogenies. However, maximum likelihood estimation methods (MLE) for inferring rates are limited to simpler models and can show bias, particularly in small phylogenies. Likelihood-free methods to estimate parameters of diversification models using deep learning have started to emerge, but how robust neural network methods are at handling the intricate nature of phylogenetic data remains an open question. Here we present a new ensemble neural network approach to estimate diversification parameters from phylogenetic trees that leverages different classes of neural networks (dense neural network, graph neural network, and long short-term memory recurrent network) and simultaneously learns from graph representations of phylogenies, their branching times, and their summary statistics. Our best-performing ensemble neural network (which adjusts the graph neural network result using a recurrent neural network) delivers estimates faster than MLE and shows less sensitivity to tree size for constant-rate and diversity-dependent speciation scenarios. It performs well compared with an existing convolutional network approach. However, like MLE, our approach still fails to recover parameters precisely under a protracted birth-death process. Our analysis suggests that the primary limitation to accurate parameter estimation is the amount of information contained within a phylogeny, as indicated by its size and the strength of effects shaping it. In cases where MLE is unavailable, our neural network method provides a promising alternative for estimating phylogenetic tree parameters. If detectable phylogenetic signals are present, our approach delivers results that are comparable to MLE but without inherent biases.