Biology subjects

Terhorst, J.

Publications and source records attributed to Terhorst, J..

At least 19 recordsLinked to original sources

bioRxiv2026

Linkage disequilibrium moderates how evolving genetic background shapes variant-level architecture

Evolutionary theory offers a unifying explanation for the genetics of complex traits and diseases by modeling how a trait and its genetic basis are maintained by evolutionary forces. A growing body of evidence suggests that linkage disequilibrium (LD) couples a variant's evolution to that of the genetic background it resides on. However, widely used single-variant theories omit this coupling between variants and the background, or hold the background fixed. We close this gap by developing a model of linkage LD evolution accounting for stabilizing selection, recombination, and genetic drift. The model deduces the genetic architecture of individual variants subject to the co-evolving genetic background. More efficient selection in larger populations is partially offset by slower decay of existing LD and increased generation of new LD. Conversely, noisier LD in smaller populations exposes the variants to episodes of stronger selection. We ask whether ancestry differences in the relationship between effect-size magnitude and minor allele frequency require different selection strengths or can arise from differences in demographic history alone. Stabilizing selection needs to be more than three times stronger in Africans than in Europeans under the constant-size demography, whereas an Out-of-Africa demography alone can explain most of the observed frequency-dependence gap. As this example indicates, selection strength is in general not identifiable from the frequency--effect-size relationship alone, because different combinations of selection and demographic history can produce the same pattern in data with further redundancy added by LD.

genetics↗

bioRxiv2026

Computing coalescence rates for complex demographies and sampling configurations

Inference of population history from genetic data relies, implicitly or explicitly, on the distribution of coalescence times, because population size changes, migration, and admixture all leave characteristic signatures in genealogies. The distribution of pairwise coalescent rates in particular has emerged as a popular target for demographic inference methods. However, pairwise coalescent rates have limited power to resolve recent history, because recent coalescences in samples of size two are rare. In this article, we introduce demestats, a software library for computing first-coalescence and cross-coalescence rate functions for structured demographic models specified in the demes format. The method computes the instantaneous rate at which the first coalescence event occurs conditional on no prior coalescence for arbitrary sampling configurations, combines exact calculations with mean-field approximations for larger samples, and is differentiable with respect to model parameters. In simulations, these statistics recover recent population size change and recent migration more accurately than pairwise summaries. Applied to tree sequences inferred from the 1000 Genomes Project, we provide new insight into the rate of recent expansion in human populations.

evolutionary biology↗

bioRxiv2026

Parameterizing the genetic architecture under stabilizing selection

Across many complex traits, genetic variants with larger effect sizes tend to occur at lower frequencies, which is often interpreted as a signature of stabilizing selection. In statistical genetics, the so-called -model captures this relationship by assuming that effect size variance is inversely proportional to heterozygosity raised to a power 0 [<=] [<=] 1. Although empirically useful, the -model is phenomenological rather than mechanistic and lacks a direct population-genetic interpretation. In this paper, we derive an alternative to the -model based on evolutionary theory. Our approach yields a linear mixed model in which the frequency dependence of effect size emerges naturally as a function of interpretable evolutionary quantities describing mutational variance, selection intensity, and coupling between the focal and selected traits. These quantities enter through two identifiable variance components that can be estimated by restricted maximum likelihood (REML). The resulting framework links a fitness-landscape model to standard mixed-model methodology, enabling both inference on evolutionary parameters and downstream prediction by best linear unbiased prediction (BLUP). In forward simulations, the model accurately recovers the focal-trait variance and generally improves genetic prediction relative to conventional -model baselines.

genetics↗

bioRxiv2026

Model selection in ADMIXTURE can be inconsistent: proof of the K=2 phenomenon

STRUCTURE and ADMIXTURE are two popular methods for detecting population structure in genetic data. They model observed genotypes as mixtures of latent ancestral populations, and the inferred admixture proportions can be used to visualize and summarize population structure. A key parameter in these models is the number of ancestral populations, K. Selecting K is a challenging problem. Perhaps the most widely used method is Evannos {Delta}K, which selects K based on the second-order change in log-likelihood as K increases. However, practitioners have often noted that {Delta}K often favors overly small K, frequently returning K = 2 even when more meaningful substructure is present. In this paper, we provide a theoretical explanation for this phenomenon: we prove that, under certain conditions, the {Delta}K method can be inconsistent, meaning that it can fail to identify the true number of populations even with infinite data.

evolutionary biology↗

bioRxiv2026

Global patterns of natural selection inferred using ancient DNA

Ancient DNA has revolutionized our understanding of human history, and is now yielding important insights into evolution and natural selection. However, studies of selection using ancient DNA have largely been limited to Europe, excluding populations in other parts of the world. While many selective pressures were local to specific populations others, for example those related to the development of agriculture, may have been universal. By studying a broader range of global populations, we can identify examples of local adaption but also more general principles of adaptation to climatic, social and technological changes. We therefore leverage ancient DNA to test for selection in 7244 individuals from 13 ancient and 19 present-day populations across five regions: Europe, East Asia, South Asia, Africa and the Americas. In each region, we tested for selection using multiple approaches that account for complex demographic histories. We identify 31 genome-wide significant signals of selection, including both known and novel loci. We find a high degree of shared signal across regions, suggesting extensive parallel or shared adaptation. Using a novel admixture-aware time series method, we find that the strength of selection on many variants changed over time, for example decreasing selection at LCT in Europe and increasing selection at ADH1B in East Asia over the past few thousand years. Finally, we developed a test for polygenic selection on complex traits by modeling the frequencies of trait-associated alleles identified in GWAS. We tested for selection jointly across regions, avoiding the confounding effect of population stratification by excluding the European or East Asian GWAS population from the selection test. We find evidence for directional selection on pigmentation and immune traits, and that strong stabilizing selection on female waist-hip ratio was universal across human populations suggesting a fundamental constraint on human morphology.

genomics↗

bioRxiv2024

Faster inference of complex demographic models from large allele frequency spectra

We present O_SCPLOWMOMIC_SCPLOW3, a new method for inferring complex demographic models using genetic variation data sampled from many populations. O_SCPLOWMOMIC_SCPLOW3 features many improvements over its predecessor O_SCPLOWMOMIC_SCPLOW2 (Kamm, Terhorst, Durbin, et al., 2020), including support for continuous migration, just-in-time compilation, and execution on GPUs; a standardized interface for specifying demographic models; and a novel importance sampling strategy that enables it to efficiently analyze data from a large number of samples. Together, these improvements lead to speedups of as much as 1000x over existing state-of-the-art methods such as {partial}a{partial}i, O_SCPLOWMOMENTSC_SCPLOW, and O_SCPLOWMOMIC_SCPLOW2. We illustrate the usefulness of our method by revisiting a model of archaic admixture using a large, recent dataset containing hundreds of human genomes from many populations.

evolutionary biology↗

bioRxiv2024

A geographic history of human genetic ancestry

Describing the distribution of genetic variation across individuals is a fundamental goal of population genetics. In humans, traditional approaches for describing population genetic variation often rely on discrete genetic ancestry labels, which, despite their utility, can obscure the complex, multifaceted nature of human genetic history. These labels risk oversimplifying ancestry by ignoring its temporal depth and geographic continuity, and may therefore conflate notions of race, ethnicity, geography, and genetic ancestry. Here, we present a method that capitalizes on the rich genealogical information encoded in genomic tree sequences to infer the geographic locations of the shared ancestors of a sample of sequenced individuals. We use this method to infer the geographic history of genetic ancestry of a set of human genomes sampled from Europe, Asia, and Africa, accurately recovering major population movements on those continents. Our findings demonstrate the importance of defining the spatial-temporal context of genetic ancestry to describing human genetic variation and caution against the oversimplified interpretations of genetic data prevalent in contemporary discussions of race and ancestry.

genetics↗

bioRxiv2024

Accelerated Bayesian inference of population size history from recombining sequence data

I present O_SCPLOWPHLASHC_SCPLOW, a new Bayesian method for inferring population history from whole genome sequence data. O_SCPLOWPHLASHC_SCPLOW is population history learning by averaging sampled histories: it works by drawing random, low-dimensional projections of the coalescent intensity function from the posterior distribution of a O_SCPLOWPSMCC_SCPLOW-like model, and averaging them together to form an accurate and adaptive size history estimator. On simulated data, O_SCPLOWPHLASHC_SCPLOW tends to be faster and have lower error than several competing methods including O_SCPLOWSMCC_SCPLOW++, O_SCPLOWMSMCC_SCPLOW2, and FO_SCPLOWITC_SCPLOWCO_SCPLOWOALC_SCPLOW. Moreover, it provides a full posterior distribution over population size history, leading to automatic uncertainty quantification of the point estimates, as well to new Bayesian testing procedures for detecting population structure and ancient bottlenecks. On the technical side, the key advance is a novel algorithm for computing the score function (gradient of the log-likelihood) of a coalescent hidden Markov model: when there are M hidden states, the algorithm requires. [O](M 2) time and. [O](1) memory per decoded position, the same cost as evaluating the log-likelihood itself using the naive forward algorithm. This algorithm is combined with a hand-tuned implementation that fully leverages the power of modern GPU hardware, and the entire method has been released as an easy-to-use Python software package.

evolutionary biology↗

bioRxiv2022

Identifiability and inference of phylogenetic birth-death models

Recent theoretical work on phylogenetic birth-death models offers differing viewpoints on whether they can be estimated using lineage-through-time data. Louca and Pennell (2020) showed that the class of models with continuously differentiable rate functions is nonidentifiable: any such model is consistent with an infinite collection of alternative models, which are statistically indistinguishable regardless of how much data are collected. Legried and Terhorst (2022a) qualified this grave result by showing that identifiability is restored if only piecewise constant rate functions are considered. Here, we contribute new theoretical results to this discussion, in both the positive and negative directions. Our main result is to prove that models based on piecewise polynomial rate functions of any order and with any (finite) number of pieces are statistically identifiable. In particular, this implies that spline-based models with an arbitrary number of knots are identifiable. The proof is simple and self-contained, relying mainly on basic algebra. We complement this positive result with a negative one, which shows that even when identifiability holds, rate function estimation is still a difficult problem. To illustrate this, we prove some rates-of-convergence results for hypothesis testing using birth-death models. These results are information-theoretic lower bounds which apply to all potential estimators.

evolutionary biology↗

bioRxiv2022

The solution path of the Li-Stephens haplotype copying model

The Li-Stephens (LS) haplotype copying model forms the basis of a number of important statistical inference procedures in genetics. LS is a probabilistic generative model which supposes that a sampled chromosome is an imperfect mosaic of other chromosomes found in a population. In the frequentist setting which is the focus of this paper, the output of LS is a "copying path" through chromosome space. The behavior of LS depends crucially on two user-specified parameters,{theta} and{rho} , which are respectively interpreted as the rates of mutation and recombination. However, because LS is not based on a realistic model of ancestry, the precise connection between these parameters and the biological phenomena they represent is unclear. Here, we offer an alternative perspective, which considers{theta} and{rho} as tuning parameters, and seeks to understand their impact on the LS output. We derive an algorithm which, for a given dataset, efficiently partitions the ({theta}, {rho}) plane into regions where the output of the algorithm is constant, thereby enumerating all possible solutions to the LS model at one go. We extend this approach to the "diploid LS" model commonly used for phasing. We demonstrate the usefulness of our method by studying the effects changing of{theta} and{rho} when using LS for common bioinformatic tasks. Our findings indicate that using the conventional (i.e., population-scaled) values for{theta} and{rho} produces near optimal results for imputation, but may systematically inflate switch error in the case of phasing diploid genotypes.

genetics↗

bioRxiv2022

Direct detection of natural selection in Bronze Age Britain

We developed a novel method for efficiently estimating time-varying selection coefficients from genome-wide ancient DNA data. In simulations, our method accurately recovers selective trajectories, and is robust to mis-specification of population size. We applied it to a large dataset of ancient and present-day human genomes from Britain, and identified seven loci with genome-wide significant evidence of selection in the past 4500 years. Almost all of them are related to increased vitamin D or calcium levels, and we conclude that lack of vitamin D and consequent low calcium was consistently the most important selective pressure in Britain since the Bronze Age. However, the strength of selection on individual loci varied substantially over time, suggesting that cultural or environmental factors moderated the genetic response to this pressure. Of 28 complex anthropometric and metabolic traits, skin pigmentation was the only one with significant evidence of polygenic selection, further underscoring the importance of phenotypes related to vitamin D. Our approach illustrates the power of ancient DNA to characterize selection in human populations and illuminates the recent evolutionary history of Britain.

evolutionary biology↗

bioRxiv2022

Variational phylodynamic inference using pandemic-scale data

The ongoing global pandemic has sharply increased the amount of data available to researchers in epidemiology and public health. Unfortunately, few existing analysis tools are capable of exploiting all of the information contained in a pandemic-scale data set, resulting in missed opportunities for improved surveillance and contact tracing. In this paper, we develop the variational Bayesian skyline (VBSKY), a method for fitting Bayesian phylodynamic models to very large pathogen genetic data sets. By combining recent advances in phylodynamic modeling, scalable Bayesian inference and differentiable programming, along with a few tailored heuristics, VBSKY is capable of analyzing thousands of genomes in a few minutes, providing accurate estimates of epidemiologically relevant quantities such as the effective reproduction number and overall sampling effort through time. We illustrate the utility of our method by performing a rapid analysis of a large number of SARS-CoV-2 genomes, and demonstrate that the resulting estimates closely track those derived from alternative sources of public health data.

evolutionary biology↗

bioRxiv2021

A class of identifiable birth-death models

In a striking result, Louca and Pennell (2020) recently proved that a large class of phylogenetic birth-death models are statistically unidentifiable from lineage-through-time (LTT) data: any pair of sufficiently smooth birth and death rate functions is "congruent" to an infinite collection of other rate functions, all of which have the same likelihood for any LTT vector of any dimension. As Louca and Pennell argue, this fact has distressing implications for the thousands of studies that have utilized birth-death models to study evolution. In this paper, we qualify their finding by proving that an alternative and widely used class of birth-death models is indeed identifiable. Specifically, we show that piecewise constant birth-death models can, in principle, be consistently estimated and distinguished from one another, given a sufficiently large extant time tree and some knowledge of the present-day population. Subject to mild regularity conditions, we further show that any unidentifiable birth-death model class can be arbitrarily closely approximated by a class of identifiable models. The sampling requirements needed for our results to hold are explicit, and are expected to be satisfied in many contexts such as the phylodynamic analysis of a global pandemic.

evolutionary biology↗

bioRxiv2021

Rates of convergence in the two-island andisolation-with-migration models

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and demands new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

genetics↗

bioRxiv2021

Robust detection of natural selection using a probabilistic model of tree imbalance

Neutrality tests such as Tajimas D (Tajima, 1989) and Fay and Wus H (Fay and Wu, 2000) are standard implements in the population genetics toolbox. One of their most common uses is to scan the genome for signals of natural selection. However, it is well understood that deviance measures like D and H are confounded by other evolutionary forces--in particular, population expansion--that may be unrelated to selection. Because they are not model-based, it is not clear how to deconfound these statistics in a principled way. In this paper we derive new likelihood-based methods for detecting natural selection which are robust to confounding by fluctuations in effective population size. At the core of our method is a novel proba-bilistic model of tree imbalance, which generalizes Kingmans coales-cent to allow certain aberrant tree topologies to arise more frequently than is expected under neutrality. We derive a frequency spectrum-based estimator which can be used in place of D, and also extend to the case where genealogies are first estimated. We benchmark our meth-ods on real and simulated data, and provide an open source software implementation.

genetics↗

bioRxiv2020

Exact decoding of the sequentially Markov coalescent

In statistical genetics, the sequentially Markov coalescent (SMC) is an important framework for approximating the distribution of genetic variation data under complex evolutionary models. Methods based on SMC are widely used in genetics and evolutionary biology, with significant applications to genotype phasing and imputation, recombination rate estimation, and inferring population history. SMC allows for likelihood-based inference using hidden Markov models (HMMs), where the latent variable represents a genealogy. Because genealogies are continuous, while HMMs are discrete, SMC requires discretizing the space of trees in a way that is complicated and can lead to bias. In this work, we propose a method that circumvents this requirement, enabling SMC-based inference to be performed in the natural setting of a continuous state space. We derive fast, exact methods for frequentist and Bayesian inference using SMC. Compared to existing methods, ours requires minimal user intervention or parameter tuning, no numerical optimization or E-M, and is faster and more accurate.

genetics↗

bioRxiv2019

U-PASS: unified power analysis and forensics for qualitative traits in genetic association studies

SummaryDespite the availability of existing calculators for statistical power analysis in genetic association studies, there has not been a model-invariant and test-independent tool that allows for both planning of prospective studies and systematic review of reported findings. In this work, we develop a web-based application U-PASS (Unified Power analysis of ASsociation Studies), implementing a unified framework for the analysis of common association tests for binary qualitative traits. The application quantifies the shared asymptotic power limits of the common association tests, and visualizes the fundamental statistical trade-off between risk allele frequency (RAF) and odds ratio (OR). The application also addresses the applicability of asymptotics-based power calculations in finite samples, and provides guidelines for single- SNP-based association tests. In addition to designing prospective studies, U-PASS enables researchers to retrospectively assess the statistical validity of previously reported associations.\n\nAvailability and implementationU-PASS is available as a web-based R Shiny application at https://power.stat.lsa.umich.edu. Source code is available at https://github.com/Pill-GZ/U-PASS.\n\nContactgaozheng@umich.edu\n\nSupplementary informationSupplementary data are available in the application.

genetics↗

bioRxiv2018

Efficiently inferring the demographic history of many populations with allele count data

The sample frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than previously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed \"basal Eurasian\" admixture event in human history. We implement and release our method in a new open-source software package momi2.

evolutionary biology↗