Phylodynamic Inference of Outbreak Transmission Trees

Phylodynamic inference of outbreak transmission trees is a computational framework that jointly models pathogen evolution, within-host dynamics, and between-host transmission to reconstruct the unobserved network of who infected whom [1, 33]. This approach integrates genomic sequence data, sampling times, and epidemiological information to estimate transmission events and key epidemiological parameters such as the effective reproduction number [2, 3]. The following sections systematically review the biological, statistical, and computational foundations of this field, with emphasis on applications in veterinary medicine.

Core Concepts and Definitions

A transmission tree is a directed graph in which nodes represent infected hosts (animals or humans) and edges represent documented transmission events from an infector to an infectee [1, 4]. In contrast, a pathogen phylogeny (or gene tree) describes the evolutionary relationships among sampled pathogen genomes and may diverge substantially from the transmission tree because of within-host pathogen diversity and incomplete transmission bottlenecks [5, 35]. The mapping between these two trees is obscured by four unobserved processes: transmission, case observation, within-host pathogen dynamics, and mutation [1, 33]. Phylodynamic inference methods aim to reverse these processes by probabilistically reconstructing the transmission tree from the observed sequence data, sampling times, and potentially other data types such as contact tracing records [6, 7, 4].

The fundamental unit of phylodynamic modeling is the birth-death process, in which "birth" corresponds to transmission (or speciation) and "death" corresponds to removal (recovery, death, or culling) [8, 9]. Birth-death-sampling (BDS) models extend this framework to account for non-random sampling of infected hosts through time [8, 10]. The coalescent model provides an alternative framework that describes the ancestral relationships among sequences backward in time and is commonly used for population-level inference [11, 10, 5]. The choice between these modeling families depends on the outbreak setting, sampling scheme, and evolutionary rate of the pathogen [10].

Methodological Families

Methods for transmission tree inference can be grouped into three families according to how genomic data are handled: non-phylogenetic (genetic distance based), sequential phylogenetic (phylogenetic inference first, then transmission reconstruction), and simultaneous phylogenetic (joint inference of phylogeny and transmission tree) [33]. The simultaneous phylogenetic family is considered the most statistically rigorous because it preserves the dependency among mutation, within-host dynamics, transmission, and observation [1, 33].

The R package phybreak implements a simultaneous Bayesian approach that combines elementary models for each of the four unobserved processes and uses Markov chain Monte Carlo (MCMC) to sample from the posterior distribution of transmission trees [1]. Phybreak has been extended to allow for multiple independent introductions of the pathogen into the study population, a critical feature for outbreaks in which spillover events occur repeatedly from an external reservoir, such as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) introductions into Dutch mink farms [12]. The method estimates the number of introductions and attributes each host to either an importation event or a local transmission chain [12, 13].

Another method, BadTrIP (Bayesian reconstruction of transmission histories from genomic polymorphisms), estimates transmission trees using whole-genome sequence data and uncertain infection times [14, 15]. It treats internal nodes of the transmission tree as transmission events and computes the likelihood under a phylogenetic model [14]. BadTrIP has been applied to outbreak investigations of multidrug-resistant Acinetobacter (MDRA) and SARS-CoV-2, demonstrating that inference accuracy depends on outbreak duration, genetic diversity, and the quality of infection time data [15].

ScITree and its predecessor ScTree are scalable spatio-temporal phylodynamic frameworks that adopt the infinite-sites assumption for modeling mutations, thereby avoiding explicit nucleotide-level modeling and achieving linear computational scaling with outbreak size [16, 17]. These methods have been validated on simulated data and applied to a foot-and-mouth disease (FMD) outbreak dataset, producing estimates consistent with earlier Bayesian approaches [16]. Their implementation in an R package facilitates real-time outbreak response.

EpiFusion integrates phylodynamic and epidemiological (case incidence) data using particle filtering to jointly estimate the effective reproduction number (Rt) through time [18, 3]. The framework weights simulated outbreak trajectories according to both a phylogenetic observation model (based on a time-scaled tree) and an epidemiological observation model (based on case counts) [3]. EpiFusion accommodates phylogenetic uncertainty by allowing a posterior distribution of trees as input [18].

Deep learning has emerged as a scalable alternative to traditional Bayesian MCMC for large outbreaks. PhyloDeep uses convolutional neural networks trained on simulated outbreak phylogenies to estimate epidemiological parameters such as the basic reproduction number (R0) and the superspreading parameter [7]. However, its predictive accuracy declines when phylogenies are poorly resolved (i.e., when genetic diversity is low) [7]. The integration of minimal contact tracing data substantially improves performance in such scenarios [7].

PhyloRt is a deep-learning framework that decomposes large phylogenies into overlapping subtrees and applies hierarchical inference to classify subtrees as having constant or time-varying reproductive numbers [2]. It has been applied to SARS-CoV-2 and influenza outbreaks, recovering transmission dynamics consistent with classical Bayesian phylodynamic analyses [2].

BELLA uses unsupervised Bayesian neural networks to flexibly model non-linear relationships between phylodynamic parameters (speciation, extinction, transmission, migration) and external covariates such as traits or environmental variables [19]. The method does not require training data and provides interpretable estimates of predictor importance through explainable artificial intelligence [19].

Key Parameters and Models

The effective reproduction number (Rt) is the most commonly estimated epidemiological parameter in phylodynamic analyses [2, 3, 8]. Birth-death skyline models allow Rt to vary piecewise-constantly over time, reflecting changes in transmission due to interventions, seasonality, or depletion of susceptible hosts [8]. The identifiability of time-varying birth-death parameters from phylogenetic trees alone has been formally studied: parameter identifiability is restored when additional information on hidden birth events (unsampled transmissions) is available from mutation accumulation at birth events [9].

The transmission bottleneck size (the number of pathogen genomes transmitted from donor to recipient) is another crucial parameter that influences the relationship between phylogeny and transmission tree [20, 21]. Methods that account for a relaxed bottleneck and use multiple genomes per host dramatically improve inference accuracy and allow estimation of within-host growth rates and bottleneck size [20, 21].

Superspreading (the phenomenon where a small proportion of hosts is responsible for a large proportion of transmissions) can be quantified by the dispersion parameter k of a negative-binomial offspring distribution [7]. Deep learning approaches can estimate k from phylogenies, but accuracy is limited in poorly resolved trees unless contact tracing data are incorporated [7].

Data Integration

The combination of genomic data with epidemiological data such as sampling times, infection times, and contact records consistently improves transmission tree inference [4, 6, 22]. A systematic review found that 17 of 22 identified methods model the transmission process, but only 8 account for imperfect case detection (unsampled hosts) [33]. Contact data are particularly informative when genetic diversity is low, as is the case in fast-spreading outbreaks of RNA viruses with high evolutionary rates but short timescales [6, 7].

The method developed by Roest et al. (2025) extends phybreak to incorporate data on different types of contact between cases (e.g., shared personnel, shared equipment, geographic proximity) and estimates the fraction of transmissions attributable to each contact type [6]. Applied to the SARS-CoV-2 outbreak in Dutch mink farms, the model estimated that 76% of between-farm transmissions occurred through shared personnel links [6]. This approach can guide targeted interventions in veterinary settings, such as movement restrictions or disinfection protocols.

For outbreaks with multiple introductions, the method by van der Roest et al. (2023) does not a priori partition the outbreak into phylogenetic clusters but instead infers the number and timing of introductions jointly with the transmission tree [12]. This is essential for settings such as influenza A virus in swine, where repeated incursions from wild birds or humans occur.

Computational Scalability

The computational cost of Bayesian MCMC methods has historically limited their application to outbreaks of moderate size (few hundred sequences) [16, 17]. ScITree achieves linear scaling by adopting the infinite-sites assumption and developing efficient data-augmentation MCMC, making it tractable for large outbreaks [16]. Gradient-based Hamiltonian Monte Carlo (HMC) sampling, as implemented for episodic birth-death-sampling models, provides a 10- to 200-fold increase in effective sample size per unit time compared to Metropolis-Hastings, enabling inference with high-dimensional parameter vectors [8].

Online Bayesian inference allows the posterior distribution to be updated sequentially as new sequences become available, without recomputing the entire phylogeny from scratch [23]. This framework, implemented in BEAST, uses a distance-based measure to insert new taxa into the current tree and reuses tuned transition kernels, substantially reducing the time to converge [23].

Simulation-based inference (SBI) methods, particularly neural posterior estimation (NPE), avoid explicit likelihood calculations and are well suited for models with intractable likelihoods [24]. NPE uses neural density estimators to learn the posterior directly from simulated data and has been applied to both compartmental transmission models and birth-death phylodynamic models for Ebola virus [24].

Applications in Veterinary Medicine

Phylodynamic inference has been applied to several veterinary outbreaks, including FMD in the United Kingdom [16, 17, 25], SARS-CoV-2 in farmed mink [6, 12], and bacterial infections such as methicillin-resistant Staphylococcus aureus (MRSA) in remote communities in Australia and Papua New Guinea [26]. In the FMD outbreak, transmission tree inference using a relaxed bottleneck model with multiple genomes per host (if available) provides more precise estimates than single-genome approaches [20, 21].

For livestock diseases, the ability to identify the contribution of different contact types (e.g., shared transport, feed suppliers, veterinary services) to transmission is valuable for designing biosecurity measures [6]. In the Dutch mink farm outbreak, veterinary service providers and feed suppliers were less strongly associated with transmission than shared personnel, suggesting a prioritization of biosecurity resources [6].

The use of portable nanopore sequencing combined with random forest SNP polishing and birth-death skyline models enables real-time outbreak reconstruction in settings with limited infrastructure [26]. This approach was used to estimate effective reproduction numbers for two MRSA outbreaks in remote communities, demonstrating epidemic growth (Re > 1) and providing actionable information for infection control [26].

Future Directions

Several challenges remain. Low sequence diversity during the early stages of an outbreak hinders phylodynamic inference, but the birth-death model outperforms the coalescent under such conditions because it explicitly uses sampling times [10]. Contact data and multiple genomes per host further mitigate this limitation [6, 20]. Parameter identifiability for time-varying rates can be ensured by exploiting mutation accumulation at transmission events [9].

Deep learning methods continue to improve scalability, but they require pathogen-specific training datasets that match the expected phylogenetic resolution [2]. The development of amortized posterior estimators, such as those used in NPE, may eventually enable real-time phylodynamic inference without the need for model-specific training [24].

Finally, the integration of phylodynamic inference with spatial and ecological models is a growing area, as demonstrated by phylogeographic analyses of SARS-CoV-2 Delta variant spread using novel transmission count statistics [27] and the use of kernel-based ABC for discriminating contact network structures in HIV epidemics [34, 35]. In veterinary medicine, such approaches could be used to infer transmission networks for pathogens such as avian influenza virus, which spread across wild bird and poultry populations, or Pasteurella multocida in waterfowl (see Avian Cholera in Waterfowl and Avian Cholera (Pasteurella multocida) in Poultry).

Workflow for Transmission Tree Inference

graph TD
    A[Pathogen genomes from host samples], > B[Multiple sequence alignment]
    B, > C[Phylogenetic inference (time-scaled tree)]
    C, > D[Phylodynamic model specification]
    E[Sampling times & infection windows], > D
    F[Contact tracing data (optional)], > D
    D, > G{Inference engine}
    G, > H[Outline: Bayesian MCMC | Deep learning | Particle filter]
    H, > I[Posterior distribution of transmission trees]
    I, > J[Consensus transmission tree & parameter estimates]
    J, > K[Epidemiological interpretation (Rt, bottleneck, introductions)]
    K, > L[Targeted control measures]

Frequently Asked Questions

What is the difference between a phylogenetic tree and a transmission tree?

A phylogenetic tree (or gene tree) represents the evolutionary relationships among sampled pathogen genomes, while a transmission tree represents the epidemiological relationships among infected hosts [1, 5]. The two trees can differ substantially because of within-host pathogen diversity, incomplete transmission bottlenecks, and unsampled hosts [5, 35].

What types of data are required for transmission tree inference?

The minimal data required are pathogen genome sequences (or alignments) and sampling times for each infected host [1, 33]. Additional data such as infection windows, contact tracing records, and spatial locations improve inference accuracy, particularly when genetic diversity is low [6, 7, 4].

How do phylodynamic models account for multiple introductions?

Methods such as the extended phybreak package estimate the number and timing of introductions jointly with the transmission tree, without requiring a priori clustering of sequences [12, 13]. This is essential for outbreaks where spillover from an external reservoir occurs repeatedly, such as SARS-CoV-2 in mink farms [12].

Can transmission tree inference be performed in real time?

Online Bayesian inference allows posterior updating as new sequences are collected, reducing computational time compared to full rerunning of MCMC [23]. Deep learning methods such as PhyloRt provide near-instantaneous estimation of time-varying Rt from large tree files [2]. Portable sequencing combined with rapid phylodynamic pipelines enables real-time outbreak response in remote settings [26].

Why is contact data important for poorly resolved phylogenies?

When genetic diversity is low (e.g., fast-spreading outbreaks of RNA viruses), phylogenies contain little information about transmission links. Contact tracing data, even if sparse or imperfect, can dramatically improve the posterior probability of the correct transmission tree [7, 4]. The method by Roest et al. (2025) uses structured contact data to estimate the contribution of different contact types to transmission [6].

How is the transmission bottleneck size inferred?

Methods that use multiple genomes per host can estimate the bottleneck size by examining the distribution of genetic variants shared between donor and recipient [20, 21]. A relaxed bottleneck model, where a small number of genomes are transmitted, improves the accuracy of transmission tree reconstruction compared to a strict bottleneck assumption [20].

What are the main computational challenges in phylodynamic inference?

Traditional Bayesian MCMC methods scale poorly with outbreak size, often exhibiting exponential increases in runtime [16, 17]. Scalable approaches include the use of the infinite-sites assumption (ScITree), gradient-based HMC sampling, deep learning surrogates, and simulation-based inference with neural posterior estimation [16, 8, 2, 24].

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