A Comparison of Deep Learning Architectures for Inferring Parameters of Diversification Models from Extant Phylogenies Preprint
Abstract
To infer the processes that gave rise to past speciation and extinction rates across taxa, space and time, we often formulate hypotheses in the form of stochastic diversification models and estimate their parameters from extant phylogenies using Maximum Likelihood or Bayesian inference. Unfortunately, however, likelihoods can easily become intractable, limiting our ability to consider more complicated diversification processes. Recently, it has been proposed that deep learning (DL) could be used in this case as a likelihood-free inference technique. Here, we explore this idea in more detail, with a particular focus on understanding the ideal network architecture and data representation for using DL in phylogenetic inference. We evaluate the performance of different neural network architectures (DNN, CNN, RNN, GNN) and phylogeny representations (summary statistics, Lineage Through Time or LTT, phylogeny encoding and phylogeny graph) for inferring rates of the Constant Rate Birth-Death (CRBD) and the Binary State Speciation and Extinction (BISSE) models. We find that deep learning methods can reach similar or even higher accuracy than Maximum Likelihood Estimation, provided that network architectures and phylogeny representations are appropriately tuned to the respective model. For example, for the CRBD model we find that CNNs and RNNs fed with LTTs outperform other combinations of network architecture and phylogeny representation, presumably because the LTT is a sufficient and therefore less redundant statistic for homogenous BD models. For the more complex BiSSE model, however, it was necessary to feed the network with both topology and tip states information to reach acceptable performance. Overall, our results suggest that deep learning provides a promising alternative for phylogenetic inference, but that data representation and architecture have strong effects on the inferential performance.
What the paper shows and why it matters (AI-generated)
Diversification models describe how lineages split and go extinct; their rates are usually estimated from the family tree of living species by maximum likelihood or Bayesian inference, both of which need the likelihood, the probability of the tree given the parameters. For richer models this becomes intractable, and the usual fallback, approximate Bayesian computation, needs many simulations. Deep learning is a likelihood-free alternative, and Voznica et al. (2022) and Lambert et al. (2023) showed that convolutional networks on a full matrix encoding of the tree can match or beat likelihood-based methods without hand-picked summary statistics. But the many ways of encoding trees for networks had not been compared systematically. The paper asks whether one rich encoding with one type of network suits every model, or whether the best choice depends on the model.
The study shows that deep learning can infer the parameters of diversification models from phylogenetic trees about as accurately as maximum likelihood, provided that the representation of the tree and the type of network are matched to the model. It tests this on two models with computable likelihoods: a constant-rate birth–death model and a binary-state speciation and extinction (BiSSE) model (simplified here), in which a two-state trait affects the rates of speciation and extinction. For the birth–death model, networks given only the lineage-through-time curve (the number of lineages over time) did best, even beating maximum likelihood, presumably as the curve holds all the information the likelihood uses. For the BiSSE model that curve was not enough: only inputs with the tree’s shape and the tip trait states gave good accuracy, a convolutional network on the full encoding best. Networks on the tree as a graph did notably worse.
The results make deep learning look promising for models whose likelihoods are out of reach, but show that it is not one method: representation and network must suit the model. The paper speculates that where a compact summary holding all relevant information (a sufficient statistic) exists, it should be used, and that the full tree may be needed where none does. It calls the work a proof of concept on simple models. A follow-up preprint, Leroy et al. (2025), traces part of the poor performance of the graph-based networks in this paper to insufficient tuning.
References
- Voznica et al. (2022). Deep learning from phylogenies to uncover the epidemiological dynamics of outbreaks. Nature Communications 13, 3896. doi:10.1038/s41467-022-31511-0
- Lambert et al. (2023). Deep Learning from Phylogenies for Diversification Analyses. Systematic Biology 72, 1262–1279. doi:10.1093/sysbio/syad044
- Leroy et al. (2025). Graph Neural Networks for Likelihood-Free Inference in Diversification Models. bioRxiv. doi:10.1101/2025.08.14.670341