Data from: 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 to 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.