arXiv subjects

Julia A. Palacios

Publications and source records attributed to Julia A. Palacios.

At least 19 recordsLinked to original sources

arXiv2026

Phylodynamic inference with the bounded coalescent: a point process perspective

The coalescent is a central framework in population genetics for modelling the ancestral relationships among sampled individuals through a genealogy, represented as a rooted and ranked binary tree. In this model, lineages coalesce at a rate inversely proportional to the effective population size, a time-varying quantity of primary interest. The bounded coalescent conditions genealogies on the time to the most recent common ancestor being bounded above by a fixed time. This model is useful in various contexts, such as phylodynamics of infectious diseases with known introduction times and single-cell lineage tracing in synthetic barcoding experiments. To our knowledge, there is no existing tool that infers variable effective population size trajectories under the bounded coalescent. We view estimation under the bounded coalescent as equivalent to estimation of the intensity function of an inhomogeneous point process. We provide an efficient algorithm for coalescent simulation under the bounded coalescent using point process methods, retaining the exactness of naive rejection sampling while substantially reducing computational cost and avoiding repeated numerical inversion of the bounded cumulative hazard. We then develop a Markov chain Monte Carlo procedure for posterior inference of effective population size trajectories that avoids discretization of the likelihood integrals. In simulations, conditioning on the bound reduces the median sum of squared errors in two of three settings, with less favourable results in the most rapidly varying setting. We illustrate the method using severe acute respiratory syndrome coronavirus 2 sequence data from Washington State.

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arXiv2026

Matrix representations and distance metrics for unlabeled ranked phylogenetic networks

Phylogenetic networks are graphs inferred from molecular sequence data that represent ancestral histories shaped by reticulate processes such as recombination, hybridization, and horizontal gene transfer. We introduce a family of distance metrics for rooted, ranked, unlabeled phylogenetic networks, extending a previously developed distance for ranked trees. Our approach relies on a bijective triangular matrix representation of phylogenetic networks that captures the temporal order of internal events, speciations, and hybridizations. Our metrics, defined as standard matrix norms, allow efficient quantitative comparisons of network topologies, timed networks and networks with differing numbers of hybridizations. Our distance can be used for both isochronous networks where all tips are sampled at one time point, and heterochronous networks where tips are allowed to be sampled at different time points. We show that our metrics capture biologically meaningful differences among evolutionary histories in both simulations and empirical posterior distributions of viral phylogenetic networks. These tools fill a methodological gap, enabling principled comparisons of ranked, unlabeled phylogenetic networks, including ancestral recombination graphs.

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arXiv2025

Coalescent Inference for Epidemics with Latent Periods

Coalescent models are used to study the transmission dynamics of rapidly evolving pathogens from molecular sequence data obtained from infected individuals. However coalescent parameters, such as effective population size, offer limited interpretability for transmission dynamics. In this work, we derive a coalescent model for exposed-infected population dynamics that allows us to infer the number of infected individuals and the effective reproduction number over time from the sample genealogy. The model can be interpreted as a two-deme model in which coalescence is restricted to individuals from different demes (exposed and infected). We propose a new data-augmentation framework with Phase-type distribution for Bayesian inference of epidemiological parameters. We study the performance of our approach on simulations and apply it to re-analyze the 2014 Ebola outbreak in Liberia.

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arXiv2025

The space of multifurcating ranked tree shapes: enumeration, lattice structure, and Markov chains

Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of samples, and a multifurcating genealogy is required. The space of multifurcating genealogical trees, where nodes can have more than two descendants, is largely underexplored in the setting of coalescent inference. In this paper, we examine the space of rooted, ranked, and unlabeled multifurcating trees. We recursively enumerate the space and then construct a partial ordering which induces a lattice on the space of multifurcating ranked tree shapes. The lattice structure lends itself naturally to defining Markov chains that permit exploration on the space of multifurcating ranked tree shapes. Finally, we prove theoretical bounds for the mixing time of two Markov chains defined on the lattice, and we present simulation results comparing the distribution of trees and tree statistics under various coalescent models to the uniform distribution on this tree space.

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arXiv2024

Multiple merger coalescent inference of effective population size

Variation in a sample of molecular sequence data informs about the past evolutionary history of the sample's population. Traditionally, Bayesian modeling coupled with the standard coalescent, is used to infer the sample's bifurcating genealogy and demographic and evolutionary parameters such as effective population size, and mutation rates. However, there are many situations where binary coalescent models do not accurately reflect the true underlying ancestral processes. Here, we propose a Bayesian nonparametric method for inferring effective population size trajectories from a multifurcating genealogy under the $Λ-$coalescent. In particular, we jointly estimate the effective population size and model parameters for the Beta-coalescent model, a special type of $Λ-$coalescent. Finally, we test our methods on simulations and apply them to study various viral dynamics as well as Japanese sardine population size changes over time. The code and vignettes can be found in the phylodyn package.

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arXiv2024

Accounting for reporting delays in real-time phylodynamic analyses with preferential sampling

The COVID-19 pandemic demonstrated that fast and accurate analysis of continually collected infectious disease surveillance data is crucial for situational awareness and policy making. Coalescent-based phylodynamic analysis can use genetic sequences of a pathogen to estimate changes in its effective population size, a measure of genetic diversity. These changes in effective population size can be connected to the changes in the number of infections in the population of interest under certain conditions. Phylodynamics is an important set of tools because its methods are often resilient to the ascertainment biases present in traditional surveillance data (e.g., preferentially testing symptomatic individuals). Unfortunately, it takes weeks or months to sequence and deposit the sampled pathogen genetic sequences into a database, making them available for such analyses. These reporting delays severely decrease precision of phylodynamic methods closer to present time, and for some models can lead to extreme biases. Here we present a method that affords reliable estimation of the effective population size trajectory closer to the time of data collection, allowing for policy decisions to be based on more recent data. Our work uses readily available historic times between sampling and sequencing for a population of interest, and incorporates this information into the sampling model to mitigate the effects of reporting delay in real-time analyses. We illustrate our methodology on simulated data and on SARS-CoV-2 sequences collected in the state of Washington in 2021.

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arXiv2023

CRP-Tree: A phylogenetic association test for binary traits

An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples and it is usually estimated from molecular sequence data at a locus or from other type of genetic data. We propose a model for trait evolution inspired by the Chinese Restaurant Process that includes a parameter that controls the degree of preferential attachment, that is, the tendency of nodes in the tree to subtend from nodes of the same type. This model with no preferential attachment is equivalent to a structured coalescent model with simultaneous migration and coalescence events and serves as a null model. We derive a test for phylogenetic binary trait association with linear computational complexity and empirically demonstrate that it is more powerful than some other methods. We apply our test to study the phylogenetic association of some traits in swordtail fish, breast cancer, yellow fever virus and influenza A H1N1 virus. R package implementation of our methods is available at $\texttt{https://github.com/jyzhang27/CRPTree}$.

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arXiv2021

Statistical Challenges in Tracking the Evolution of SARS-CoV-2

Genomic surveillance of SARS-CoV-2 has been instrumental in tracking the spread and evolution of the virus during the pandemic. The availability of SARS-CoV-2 molecular sequences isolated from infected individuals, coupled with phylodynamic methods, have provided insights into the origin of the virus, its evolutionary rate, the timing of introductions, the patterns of transmission, and the rise of novel variants that have spread through populations. Despite enormous global efforts of governments, laboratories, and researchers to collect and sequence molecular data, many challenges remain in analyzing and interpreting the data collected. Here, we describe the models and methods currently used to monitor the spread of SARS-CoV-2, discuss long-standing and new statistical challenges, and propose a method for tracking the rise of novel variants during the epidemic.

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arXiv2021

Enumeration of binary trees compatible with a perfect phylogeny

Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy--a rooted, binary, timed tree, with tips corresponding to individual sequences. Under the infinitely-many-sites mutation model, mutations are randomly superimposed along the branches of the genealogy, so that every mutation occurs at a chromosomal site that has not previously mutated; if a mutation occurs at an interior branch, then all individuals descending from that branch carry the mutation. The implication is that observed patterns of molecular variation from this model impose combinatorial constraints on the hidden state space of genealogies. In particular, observed molecular variation can be represented in the form of a perfect phylogeny, a tree structure that fully encodes the mutational differences among sequences. For a sample of n sequences, a perfect phylogeny might not possess n distinct leaves, and hence might be compatible with many possible binary tree structures that could describe the evolutionary relationships among the n sequences. Here, we investigate enumerative properties of the set of binary ranked and unranked tree shapes that are compatible with a perfect phylogeny, and hence, the binary ranked and unranked tree shapes conditioned on an observed pattern of mutations under the infinitely-many-sites mutation model. We provide a recursive enumeration of these shapes. We consider both perfect phylogenies that can be represented as binary and those that are multifurcating. The results have implications for computational aspects of the statistical inference of evolutionary parameters that underlie sets of molecular sequences.

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arXiv2021

The Tajima heterochronous n-coalescent: inference from heterochronously sampled molecular data

The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, it is well understood that inference under this model does not scale well with sample size. Here, we build on recent work based on a lower resolution coalescent process, the Tajima coalescent, to model longitudinal samples. While the Kingman coalescent models the ancestry of labeled individuals, the heterochronous Tajima coalescent models the ancestry of individuals labeled by their sampling time. We propose a new inference scheme for the reconstruction of effective population size trajectories based on this model with the potential to improve computational efficiency. Modeling of longitudinal samples is necessary for applications (e.g. ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter identifiability). We propose an efficient algorithm to calculate the likelihood and employ a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of heterochronous Tajima's genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and applications.

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arXiv2021

Scalable Bayesian change point detection with spike and slab priors

We study the use of spike and slab priors for consistent estimation of the number of change points and their locations. Leveraging recent results in the variable selection literature, we show that an estimator based on spike and slab priors achieves optimal localization rate in the multiple offline change point detection problem. Based on this estimator, we propose a Bayesian change point detection method, which is one of the fastest Bayesian methodologies, and it is more robust to misspecification of the error terms than the competing methods. We demonstrate through empirical work the good performance of our approach vis-a-vis some state-of-the-art benchmarks.

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arXiv2021

Statistical summaries of unlabelled evolutionary trees and ranked hierarchical clustering trees

Rooted and ranked binary trees are mathematical objects of great importance used to model hierarchical data and evolutionary relationships with applications in many fields including evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explore the posterior distribution of trees via Markov Chain Monte Carlo methods, however assessing uncertainty and summarizing distributions or samples of such trees remains challenging. While labelled phylogenetic trees have been extensively studied, relatively less literature exists for unlabelled trees which are increasingly useful, for example when one seeks to summarize samples of trees obtained with different methods, or from different samples and environments, and wishes to assess stability and generalizability of these summaries. In our paper, we exploit recently proposed distance metrics of unlabelled ranked binary trees and unlabelled ranked genealogies (equipped with branch lengths) to define the Frechet mean and variance as summaries of these tree distributions. We provide an efficient combinatorial optimization algorithm for computing the Frechet mean from a sample of or distribution on unlabelled ranked tree shapes and unlabelled ranked genealogies. We show the applicability of our summary statistics for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020.

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arXiv2020

An adjacent-swap Markov chain on coalescent trees

The standard coalescent is widely used in evolutionary biology and population genetics to model the ancestral history of a sample of molecular sequences as a rooted and ranked binary tree. In this paper, we present a representation of the space of ranked trees as a space of constrained ordered matched pairs. We use this representation to define ergodic Markov chains on labeled and unlabeled ranked tree shapes analogously to transposition chains on the space of permutations. We show that an adjacent-swap chain on labeled and unlabeled ranked tree shapes has mixing time at least of order $n^3$, and at most of order $n^{4}$. Bayesian inference methods rely on Markov chain Monte Carlo methods on the space of trees. Thus, it is important to define good Markov chains which are easy to simulate and for which rates of convergence can be studied.

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arXiv2020

Adaptive preferential sampling in phylodynamics

Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that represents the sample ancestral relationships. The basic assumption is that coalescent events occur at a rate inversely proportional to the effective population size $N_{e}(t)$, a time-varying measure of genetic diversity. When the sampling process (collection of samples over time) depends on $N_{e}(t)$, the coalescent and the sampling processes can be jointly modeled to improve estimation of $N_{e}(t)$. Failing to do so can lead to bias due to model misspecification. However, the way that the sampling process depends on the effective population size may vary over time. We introduce an approach where the sampling process is modeled as an inhomogeneous Poisson process with rate equal to the product of $N_{e}(t)$ and a time-varying coefficient, making minimal assumptions on their functional shapes via Markov random field priors. We provide scalable algorithms for inference, show the model performance vis-a-vis alternative methods in a simulation study, and apply our model to SARS-CoV-2 sequences from Los Angeles and Santa Clara counties. The methodology is implemented and available in the R package adapref.

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arXiv2019

Sequential importance sampling for multi-resolution Kingman-Tajima coalescent counting

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state-space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data. We analyse the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population to illustrate the settings in which it is advantageous to employ coarser resolutions.

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arXiv2018

Exact Limits of Inference in Coalescent Models

Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost of estimating parameters from these models usually compels researchers to select a subset of the available data or to rely on non-sufficient summary statistics for statistical inference. We consider the problem of recovering the true population size history from two possible alternatives on the basis of coalescent time data. We give exact expressions for the probability of selecting the correct alternative in a variety of biologically interesting cases as a function of the separation between the alternative size histories, the number of individuals, loci, and the sampling times. The results are applied to human population history. This work has significant implications for optimal design when the inferential goal is to test scientific hypotheses about population size trajectories in coalescent models with and without recombination.

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arXiv2016

phylodyn: an R package for phylodynamic simulation and inference

We introduce phylodyn, an R package for phylodynamic analysis based on gene genealogies. The package main functionality is Bayesian nonparametric estimation of effective population size fluctuations over time. Our implementation includes several Markov chain Monte Carlo-based methods and an integrated nested Laplace approximation-based approach for phylodynamic inference that have been developed in recent years. Genealogical data describe the timed ancestral relationships of individuals sampled from a population of interest. Here, individuals are assumed to be sampled at the same point in time (isochronous sampling) or at different points in time (heterochronous sampling); in addition, sampling events can be modeled with preferential sampling, which means that the intensity of sampling events is allowed to depend on the effective population size trajectory. We assume the coalescent and the sequentially Markov coalescent processes as generative models of genealogies. We include several coalescent simulation functions that are useful for testing our phylodynamics methods via simulation studies. We compare the performance and outputs of various methods implemented in phylodyn and outline their strengths and weaknesses. R package phylodyn is available at https://github.com/mdkarcher/phylodyn.

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arXiv2015

Quantifying and mitigating the effect of preferential sampling on phylodynamic inference

Phylodynamics seeks to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. One way to accomplish this task formulates an observed sequence data likelihood exploiting a coalescent model for the sampled individuals' genealogy and then integrating over all possible genealogies via Monte Carlo or, less efficiently, by conditioning on one genealogy estimated from the sequence data. However, when analyzing sequences sampled serially through time, current methods implicitly assume either that sampling times are fixed deterministically by the data collection protocol or that their distribution does not depend on the size of the population. Through simulation, we first show that, when sampling times do probabilistically depend on effective population size, estimation methods may be systematically biased. To correct for this deficiency, we propose a new model that explicitly accounts for preferential sampling by modeling the sampling times as an inhomogeneous Poisson process dependent on effective population size. We demonstrate that in the presence of preferential sampling our new model not only reduces bias, but also improves estimation precision. Finally, we compare the performance of the currently used phylodynamic methods with our proposed model through clinically-relevant, seasonal human influenza examples.

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