Birth-death Model Research Articles

The Fossilised Birth-Death Model is Identifiable.

Time-dependent birth-death sampling models have been used in numerous studies for inferring past evolutionary dynamics in different biological contexts, e.g. speciation and extinction rates in macroevolutionary studies, or effective reproductive number in epidemiological studies. These models are branching processes where lineages can bifurcate, die, or be sampled with time-dependent birth, death, and sampling rates, generating phylogenetic trees. It has been shown that in some subclasses of such models, different sets of rates can result in the same distributions of reconstructed phylogenetic trees, and therefore the rates become unidentifiable from the trees regardless of their size. Here we show that widely used time-dependent fossilised birth-death (FBD) models are identifiable. This subclass of models makes more realistic assumptions about the fossilisation process and certain infectious disease transmission processes than the unidentifiable birth-death sampling models. Namely, FBD models assume that sampled lineages stay in the process rather than being immediately removed upon sampling. Identifiability of the time-dependent FBD model justifies using statistical methods that implement this model to infer the underlying temporal diversification or epidemiological dynamics from phylogenetic trees or directly from molecular or other comparative data. We further show that the time-dependent fossilised-birth-death model with an extra parameter, the removal after sampling probability, is unidentifiable. This implies that in scenarios where we do not know how sampling affects lineages we are unable to infer this extra parameter together with birth, death, and sampling rates solely from trees.

Estimating pathogen spread using structured coalescent and birth–death models: A quantitative comparison

Elucidating disease spread between subpopulations is crucial in guiding effective disease control efforts. Genomic epidemiology and phylodynamics have emerged as key principles to estimate such spread from pathogen phylogenies derived from molecular data. Two well-established structured phylodynamic methodologies – based on the coalescent and the birth–death model – are frequently employed to estimate viral spread between populations. Nonetheless, these methodologies operate under distinct assumptions whose impact on the accuracy of migration rate inference is yet to be thoroughly investigated.In this manuscript, we present a simulation study, contrasting the inferential outcomes of the structured coalescent model with constant population size and the multitype birth–death model with a constant rate. We explore this comparison across a range of migration rates in endemic diseases and epidemic outbreaks. The results of the epidemic outbreak analysis revealed that the birth–death model exhibits a superior ability to retrieve accurate migration rates compared to the coalescent model, regardless of the actual migration rate. Thus, to estimate accurate migration rates, the population dynamics have to be accounted for. On the other hand, for the endemic disease scenario, our investigation demonstrates that both models produce comparable coverage and accuracy of the migration rates, with the coalescent model generating more precise estimates. Regardless of the specific scenario, both models similarly estimated the source location of the disease.This research offers tangible modelling advice for infectious disease analysts, suggesting the use of either model for endemic diseases. For epidemic outbreaks, or scenarios with varying population size, structured phylodynamic models relying on the Kingman coalescent with constant population size should be avoided as they can lead to inaccurate estimates of the migration rate. Instead, coalescent models accounting for varying population size or birth–death models should be favoured. Importantly, our study emphasises the value of directly capturing exponential growth dynamics which could be a useful enhancement for structured coalescent models.

Region‐specific diversification dynamics and biogeographic history of one of the most diverse families of insects

AbstractA long‐standing question in evolutionary biology is how historical biogeographic processes have shaped the current diversity of organisms, especially for highly diverse groups. We study the diversification dynamics and biogeographic processes of one of the most diverse families of Lepidoptera, Geometridae, with over 24,000 described species and a worldwide distribution. Despite the cosmopolitan distribution of the family, most species of Geometridae have limited distribution ranges. We present the largest historical biogeography and diversification study on the current diversity patterns and distribution ranges of Geometridae. We use a multi‐locus dataset of 1200 taxa to estimate the historical biogeography of Geometridae, implementing a Bayesian approach of the Dispersal‐Extinction‐Cladogenesis (DEC) model that incorporates palaeographic‐based dispersal graphs with uncertainty in geological ages in RevBayes. We also implement a Bayesian time‐variable, episodic birth–death model and a model that allows branch‐specific speciation rates to estimate the diversification dynamics in the family. Our results suggest that the most recent common ancestor of Geometridae was distributed in the New World, with the Neotropics being the most likely ancestral area. An increase in diversification rates occurred circa 30–40 million years ago (Mya), coinciding with a time of a major global climate cooling in the Eocene. Clade‐specific shifts in speciation rates also occurred around 10–15 Mya, coincident with another period of major climate change in the Oligocene. Our results point to different biogeographical and evolutionary histories per area to show the differences of the diversification rates in different biogeographical regions through time, showing the relative importance of each region in the diversification history of Geometridae.

Error-induced extinction in a multi-type critical birth–death process

Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth–death processes with n distinct types as a birth–death model of EEX in a growing population. Each type-i cell divides independently (i)→(i)+(i)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(i)\\rightarrow (i)+(i)$$\\end{document} or mutates (i)→(i+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(i)\\rightarrow (i+1)$$\\end{document} at the same rate. The total number of cells grows exponentially as a Yule process until a cell of type-n appears, which cell type can only divide or die at rate one. This makes the whole process critical and hence after the exponentially growing phase eventually all cells die with probability one. We present large-time asymptotic results for the general n-type critical birth–death process. We find that the mass function of the number of cells of type-k has algebraic and stationary tail (size)-1-χk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\ ext {size})^{-1-\\chi _k}$$\\end{document}, with χk=21-k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _k=2^{1-k}$$\\end{document}, for k=2,⋯,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=2,\\dots ,n$$\\end{document}, in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability (time)-ξk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\ ext {time})^{-\\xi _k}$$\\end{document}. We present applications of the results for studying extinction due to intolerable mutation rates in biological populations.

A birth–death model to understand bacterial antimicrobial heteroresistance from time-kill curves

Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test.

Practical guidelines for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC)

Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible solutions and possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Values for all model parameters need to be evaluated as well. Modern statistical methods involve not just the estimation of a tree, but also solutions to more complex models involving fossil record information and other data sources. Markov chain Monte Carlo (MCMC) is a leading method for approximating the posterior distribution of parameters in a mathematical model. It is deployed in all Bayesian phylogenetic tree estimation software. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. In this manuscript, we will offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them.

A macroevolutionary analysis of European Late Upper Palaeolithic stone tool shape using a Bayesian phylodynamic framework.

Phylogenetic models are commonly used in palaeobiology to study the patterns and processes of organismal evolution. In the human sciences, phylogenetic methods have been deployed for reconstructing ancestor-descendant relationships using linguistic and material culture data. Within evolutionary archaeology specifically, phylogenetic analyses based on maximum parsimony and discrete traits dominate, which sets limitations for the downstream role cultural phylogenies, once derived, can play in more elaborate analytical pipelines. Recent methodological advances in Bayesian phylogenetics, however, now allow us to infer evolutionary dynamics using continuous characters. Capitalizing on these developments, we here present an exploratory analysis of cultural macroevolution of projectile point shape evolution in the European Final Palaeolithic and earliest Mesolithic (approx. 15 000-11 000 BP) using a Bayesian phylodynamic approach and the fossilized birth-death process model. This model-based approach leaps far beyond the application of parsimony, in that it not only produces a tree, but also divergence times, and diversification rates while incorporating uncertainties. This allows us to compare rates to the pronounced climatic changes that occurred during our time frame. While common in cultural evolutionary analyses of language, the extension of Bayesian phylodynamic models to archaeology arguably represents a major methodological breakthrough.

Trait-mediated speciation and human-driven extinctions in proboscideans revealed by unsupervised Bayesian neural networks.

Species life-history traits, paleoenvironment, and biotic interactions likely influence speciation and extinction rates, affecting species richness over time. Birth-death models inferring the impact of these factors typically assume monotonic relationships between single predictors and rates, limiting our ability to assess more complex effects and their relative importance and interaction. We introduce a Bayesian birth-death model using unsupervised neural networks to explore multifactorial and nonlinear effects on speciation and extinction rates using fossil data. It infers lineage- and time-specific rates and disentangles predictor effects and importance through explainable artificial intelligence techniques. Analysis of the proboscidean fossil record revealed speciation rates shaped by dietary flexibility and biogeographic events. The emergence of modern humans escalated extinction rates, causing recent diversity decline, while regional climate had a lesser impact. Our model paves the way for an improved understanding of the intricate dynamics shaping clade diversification.

Mean-field interacting multi-type birth–death processes with a view to applications in phylodynamics

Multi-type birth–death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth–death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes – such as environmental carrying capacity or frequency-dependent selection – entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth–death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble’s stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth–death model.

Epidemic modelling by birth-death processes with spatial scaling

In epidemic modeling, interpretation of compartment quantities, such as s, i, and r in relevant equations, is not always straightforward. Ambiguities regarding whether these quantities represent numbers or fractions of individuals in each compartment rise questions about significance of the involved parameters. In this paper, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s’. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling.

Practical guidelines for Bayesian phylogenetic inference using Markov Chain Monte Carlo (MCMC)

Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible solutions and possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Modern statistical methods involve not just the estimation of a tree, but also solutions to more complex models involving fossil record information and other data sources. Markov Chain Monte Carlo (MCMC) is a leading method for approximating the posterior distribution of parameters in a mathematical model. It is deployed in all Bayesian phylogenetic tree estimation software. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. In this manuscript, we will offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them.

On the connections between the spatial Lambda–Fleming–Viot model and other processes for analysing geo-referenced genetic data

The introduction of the spatial Lambda-Fleming–Viot model (ΛV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (Barton et al., 2010; Barton et al., 2013). The ΛV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the “pain in the torus” issue with Wright and Malécot’s isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the ΛV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the ΛV whereby lineages move rapidly over small distances. Using simulations, we show that the induced ΛV tree-generating process is well approximated by a birth–death model. Our results also indicate that Brownian motions modelling the movements of lines of descent along birth–death trees do not generally provide a good approximation of the ΛV due to habitat boundaries effects that play an increasingly important role in the long run. Accounting for habitat boundaries through reflected Brownian motions considerably increases the similarity to the ΛV model however. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the ΛV model.

NestedBD: Bayesian inference of phylogenetic trees from single-cell copy number profiles under a birth-death model.

Copy number aberrations (CNAs) are ubiquitous in many types of cancer. Inferring CNAs from cancer genomic data could help shed light on the initiation, progression, and potential treatment of cancer. While such data have traditionally been available via "bulk sequencing," the more recently introduced techniques for single-cell DNA sequencing (scDNAseq) provide the type of data that makes CNA inference possible at the single-cell resolution. We introduce a new birth-death evolutionary model of CNAs and a Bayesian method, NestedBD, for the inference of evolutionary trees (topologies and branch lengths with relative mutation rates) from single-cell data. We evaluated NestedBD's performance using simulated data sets, benchmarking its accuracy against traditional phylogenetic tools as well as state-of-the-art methods. The results show that NestedBD infers more accurate topologies and branch lengths, and that the birth-death model can improve the accuracy of copy number estimation. And when applied to biological data sets, NestedBD infers plausible evolutionary histories of two colorectal cancer samples. NestedBD is available at https://github.com/Androstane/NestedBD .

Testing extinction events and temporal shifts in diversification and fossilization rates through the skyline Fossilized Birth-Death (FBD) model: The example of some mid-Permian synapsid extinctions.

In the last decade, the Fossilized Birth-Death (FBD) process has yielded interesting clues about the evolution of biodiversity through time. To facilitate such studies, we extend our method to compute the probability density of phylogenetic trees of extant and extinct taxa in which the only temporal information is provided by the fossil ages (i.e. without the divergence times) in order to deal with the piecewise constant FBD process, known as the "skyline FBD", which allows rates to change between pre-defined time intervals, as well as modelling extinction events at the bounds of these intervals. We develop approaches based on this method to assess hypotheses about the diversification process and to answer questions such as "Does a mass extinction occur at this time?" or "Is there a change in the fossilization rate between two given periods?". Our software can also yield Bayesian and maximum-likelihood estimates of the parameters of the skyline FBD model under various constraints. These approaches are applied to a simulated dataset in order to test their ability to answer the questions above. Finally, we study an updated dataset of Permo-Carboniferous synapsids to get additional insights into the dynamics of biodiversity change in three clades (Ophiacodontidae, Edaphosauridae and Sphenacodontidae) in the Pennsylvanian (Late Carboniferous) and Cisuralian (Early Permian), and to assess support for end-Sakmarian (or Artinskian) and end-Cisuralian mass extinction events discussed in previous studies.

A macroevolutionary role for chromosomal fusion and fission in Erebia butterflies.

The impact of large-scale chromosomal rearrangements, such as fusions and fissions, on speciation is a long-standing conundrum. We assessed whether bursts of change in chromosome numbers resulting from chromosomal fusion or fission are related to increased speciation rates in Erebia, one of the most species-rich and karyotypically variable butterfly groups. We established a genome-based phylogeny and used state-dependent birth-death models to infer trajectories of karyotype evolution. We demonstrated that rates of anagenetic chromosomal changes (i.e., along phylogenetic branches) exceed cladogenetic changes (i.e., at speciation events), but, when cladogenetic changes occur, they are mostly associated with chromosomal fissions rather than fusions. We found that the relative importance of fusion and fission differs among Erebia clades of different ages and that especially in younger, more karyotypically diverse clades, speciation is more frequently associated with cladogenetic chromosomal changes. Overall, our results imply that chromosomal fusions and fissions have contrasting macroevolutionary roles and that large-scale chromosomal rearrangements are associated with bursts of species diversification.

Scalable gradients enable Hamiltonian Monte Carlo sampling for phylodynamic inference under episodic birth-death-sampling models.

Birth-death models play a key role in phylodynamic analysis for their interpretation in terms of key epidemiological parameters. In particular, models with piecewise-constant rates varying at different epochs in time, to which we refer as episodic birth-death-sampling (EBDS) models, are valuable for their reflection of changing transmission dynamics over time. A challenge, however, that persists with current time-varying model inference procedures is their lack of computational efficiency. This limitation hinders the full utilization of these models in large-scale phylodynamic analyses, especially when dealing with high-dimensional parameter vectors that exhibit strong correlations. We present here a linear-time algorithm to compute the gradient of the birth-death model sampling density with respect to all time-varying parameters, and we implement this algorithm within a gradient-based Hamiltonian Monte Carlo (HMC) sampler to alleviate the computational burden of conducting inference under a wide variety of structures of, as well as priors for, EBDS processes. We assess this approach using three different real world data examples, including the HIV epidemic in Odesa, Ukraine, seasonal influenza A/H3N2 virus dynamics in New York state, America, and Ebola outbreak in West Africa. HMC sampling exhibits a substantial efficiency boost, delivering a 10- to 200-fold increase in minimum effective sample size per unit-time, in comparison to a Metropolis-Hastings-based approach. Additionally, we show the robustness of our implementation in both allowing for flexible prior choices and in modeling the transmission dynamics of various pathogens by accurately capturing the changing trend of viral effective reproductive number.

A new amphibamiform from the Early Permian of Texas elucidates patterns of cranial diversity among terrestrial amphibamiforms

Abstract Amphibamiform temnospondyls are at the forefront of discourse surrounding modern amphibian evolutionary origins. Here we present a new amphibamiform, Kermitops gratus gen. et sp. nov., from the Lower Clear Fork Formation of the Early Permian of Texas. Kermitops reveals a mosaic of features shared with other amphibamiforms and possesses unique characteristics, including an internarial fontanelle formed by the premaxillae without contribution of the nasals. It possibly possesses a basioccipital that contributes to the occipital condyle, which has significant implications for recent hypotheses of the evolution of the modern amphibian neurocranium. Parsimony analyses recover non-traditional amphibamiform relationships but place Kermitops within Amphibamiformes. Bayesian inference analysis captures a more traditional hypothesis of amphibamiform relationships; however, the time-calibrated analysis under the fossilized birth–death model recovers a topology that mirrors the parsimony topologies. The low robusticity of topologies across different permutations employing traditional and modern methods suggest a need for improvement of current morphological datasets of lissamphibian origins. A morphometric analysis of the crania of terrestrial amphibamiforms reveals the evolution of disparate cranial morphologies among coeval taxa from the Early Permian of Texas.

Exploring the Distribution of Phylogenetic Networks Generated Under a Birth-Death-Hybridization Process

Gene-flow processes such as hybridization and introgression play important roles in shaping diversity across the tree of life. Recent studies extending birth-death models have made it possible to investigate patterns of reticulation in a macroevolutionary context. These models allow for different macroevolutionary patterns of gene flow events that can either add, maintain, or remove lineages—with the gene flow itself possibly being dependent on the relatedness between species—thus creating complex diversification scenarios. Further, many reticulate phylogenetic inference methods assume specific reticulation structures or phylogenies belonging to certain network classes. However, the distributions of phylogenetic networks under reticulate birth-death processes are poorly characterized, and it is unknown whether they violate common methodological assumptions. We use simulation techniques to explore phylogenetic network space under a birth-death-hybridization process where the hybridization rate can have a linear dependence on genetic distance. Specifically, we measured the number of lineages through time and role of hybridization in diversification along with the proportion of phylogenetic networks that belong to commonly used network classes (e.g., tree-child, tree-based, or level-1 networks). We find that the growth of phylogenetic networks and class membership are largely affected by assumptions about macroevolutionary patterns of gene flow. In accordance with previous studies, a lower proportion of networks belonged to these classes based on type and density of reticulate events. However, under a birth-death-hybridization process, these factors form an antagonistic relationship; the type of reticulation events that cause high membership proportions also lead to the highest reticulation density, consequently lowering the overall proportion of phylogenies in some classes. Further, we observed that genetic distance–dependent gene flow and incomplete sampling increase the proportion of class membership, primarily due to having fewer reticulate events. Our results can inform studies if their biological expectations of gene flow are associated with evolutionary histories that satisfy the assumptions of current methodology and aid in finding phylogenetic classes that are relevant for methods development.

Abstract IA016: Bayesian phylodynamics to quantify cancer growth across space and time

Abstract Phylogenetics has traditionally inferred shared genetic histories of species over macroevolutionary time. With the expansion of cancer multi-region and single-cell sequencing, phylogenetic approaches have found new uses mapping the evolutionary histories of tumors as well. Recently developed “phylodynamic” methods that integrate phylogenetic and population dynamic modeling offer further promise - uncovering cancer growth dynamics from the topologies and branch lengths of tumor trees. Here, I discuss two recent efforts in this area: 1) Heterogeneous growth rates across a tumor become encoded in the branching patterns of phylogenetic trees built from multi-region sequencing. We introduce a cancer-specific extension to a class of multi-state birth-death models to infer these growth rate differences across space. We apply our model (SDevo) to a sample of hepatocellular carcinomas and infer that these tumor peripheries grow 2-6 times faster than their interiors. 2) Tumors experience differential growth rates over time as they acquire new driver mutations and invade their surrounding tissues, and these growth dynamics similarly leave characteristic signatures in their phylogenies. We employ Bayesian skyline models to dissect tumor growth dynamics from a dataset of diverse cancers and reveal variation in cancer growth rates over time. As cancer sequencing continues to proliferate, phylodynamic approaches are poised to reveal new quantitative insights into cancer growth dynamics across time and space. Citation Format: Maya Lewinsohn, Trevor Bedford, Nicola F. Müller, Alison Feder. Bayesian phylodynamics to quantify cancer growth across space and time [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr IA016.

Moment Closure for a Birth-Death Model of Antimicrobial Heteroresistance

Developing predictive Antimicrobial Resistance (AMR) models supporting optimal treatment design to combat ”superbugs” poses a significant challenge for mathematical biology. Birth-Death (BD) processes constitute an intuitive and flexible approach for modelling biological systems’ stochastic dynamics that is regaining attention due to the advances in computational techniques. This work presents a multivariate BD model of antimicrobial heteroresistance, a phenotype in which a bacterial isolate contains many subpopulations with heterogeneous antimicrobial responses. The model includes Lotka-Volterra competition between subpopulations, leading to an infinite coupled system of equations for the moment dynamics of the BD process. Then, a moment closure is proposed by assuming a log-normal distribution for a univariate BD process approximating the total population behaviour. The results are compared with stochastic simulations of the multivariate BD process during a typical time-kill assay.