skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, June 13 until 2:00 AM ET on Friday, June 14 due to maintenance. We apologize for the inconvenience.

Title: Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong

Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.

more » « less
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Systematic Biology
Medium: X Size: p. 183-206
["p. 183-206"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters, such as divergence times and population sizes, they form a generative process of molecular sequence evolution. Early work on computational methods for phylogenetic network inference focused exclusively on reticulations and sought networks with the fewest number of reticulations to fit the data. As processes such as incomplete lineage sorting (ILS) could be at play concurrently with hybridization, work in the last decade has shifted to computational approaches for phylogenetic network inference in the presence of ILS. In such a short period, significant advances have been made on developing and implementing such computational approaches. In particular, parsimony, likelihood, and Bayesian methods have been devised for estimating phylogenetic networks and associated parameters using estimated gene trees as data. Use of those inference methods has been augmented with statistical tests for specific hypotheses of hybridization, like the D-statistic. Most recently, Bayesian approaches for inferring phylogenetic networks directly from sequence data were developed and implemented. In this chapter, we survey such advances and discuss model assumptions as well as methods’ strengths and limitations. We also discuss parallel efforts in the population genetics community aimed at inferring similar structures. Finally, we highlight major directions for future research in this area. 
    more » « less
  2. Abstract Motivation

    Phylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the method’s applicability.


    In this article, we first demonstrate why likelihood computations of networks take orders of magnitude more time when compared to trees. We then propose an approach for inference of phylogenetic networks based on pseudo-likelihood using bi-allelic markers. We demonstrate the scalability and accuracy of phylogenetic network inference via pseudo-likelihood computations on simulated data. Furthermore, we demonstrate aspects of robustness of the method to violations in the underlying assumptions of the employed statistical model. Finally, we demonstrate the application of the method to biological data. The proposed method allows for analyzing larger datasets in terms of the numbers of taxa and reticulation events. While pseudo-likelihood had been proposed before for data consisting of gene trees, the work here uses sequence data directly, offering several advantages as we discuss.

    Availability and implementation

    The methods have been implemented in PhyloNet (

    more » « less
  3. Abstract

    We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at

    more » « less
  4. Abstract

    Placing new sequences onto reference phylogenies is increasingly used for analyzing environmental samples, especially microbiomes. Existing placement methods assume that query sequences have evolved under specific models directly on the reference phylogeny. For example, they assume single-gene data (e.g., 16S rRNA amplicons) have evolved under the GTR model on a gene tree. Placement, however, often has a more ambitious goal: extending a (genome-wide) species tree given data from individual genes without knowing the evolutionary model. Addressing this challenging problem requires new directions. Here, we introduce Deep-learning Enabled Phylogenetic Placement (DEPP), an algorithm that learns to extend species trees using single genes without prespecified models. In simulations and on real data, we show that DEPP can match the accuracy of model-based methods without any prior knowledge of the model. We also show that DEPP can update the multilocus microbial tree-of-life with single genes with high accuracy. We further demonstrate that DEPP can combine 16S and metagenomic data onto a single tree, enabling community structure analyses that take advantage of both sources of data. [Deep learning; gene tree discordance; metagenomics; microbiome analyses; neural networks; phylogenetic placement.]

    more » « less
  5. Abstract Background

    The expanding usage of complex machine learning methods such as deep learning has led to an explosion in human activity recognition, particularly applied to health. However, complex models which handle private and sometimes protected data, raise concerns about the potential leak of identifiable data. In this work, we focus on the case of a deep network model trained on images of individual faces.

    Materials and methods

    A previously published deep learning model, trained to estimate the gaze from full-face image sequences was stress tested for personal information leakage by a white box inference attack. Full-face video recordings taken from 493 individuals undergoing an eye-tracking- based evaluation of neurological function were used. Outputs, gradients, intermediate layer outputs, loss, and labels were used as inputs for a deep network with an added support vector machine emission layer to recognize membership in the training data.


    The inference attack method and associated mathematical analysis indicate that there is a low likelihood of unintended memorization of facial features in the deep learning model.


    In this study, it is showed that the named model preserves the integrity of training data with reasonable confidence. The same process can be implemented in similar conditions for different models.

    more » « less