Graph Neural Networks for Likelihood-Free Inference in Diversification Models

A common approach to infer the processes that gave rise to past speciation and extinction rates across taxa, space and time is to formulate hypotheses in the form of probabilistic diversification models and estimate their parameters from extant phylogenies using Maximum Likelihood or Bayesian inference. A drawback of this approach is that likelihoods can easily become computationally intractable, limiting our ability to extend current diversification models with new hypothesized mechanisms. Neural networks have been proposed as a likelihood-free alternative for parameter inference of stochastic models, but so far there is little experience in using this method for diversification models, and the quality of the results is likely to depend on finding the right network architecture and data representation. As phylogenies are essentially graphs, graph neural networks (GNNs) appear to be the most natural architecture but previous results on their performance are conflicting, with some studies reporting poor accuracy of GNNs in practice. Here, we show that this underperformance was likely caused by optimization issues and inappropriate pooling operations that flatten the information along the phylogeny and make it harder to extract relevant information about the diversification parameters. When equipped with PhyloPool, a new time-informed pooling procedure, GNNs show similar or better performance compared to all other architectures and data representations (including Maximum Likelihood Estimation) that we tested for two common diversification models, the Constant Rate Birth-Death and the Binary State Speciation and Extinction. We conclude that GNNs could serve as a generic tool for estimating diversification parameters of complex diversification models with intractable likelihoods.