Highly parallelizable path sampling with minimal rejections using asynchronous replica exchange and infinite swaps.

Capturing rare yet pivotal events poses a significant challenge for molecular simulations. Path sampling provides a unique approach to tackle this issue without altering the potential energy landscape or dynamics, enabling recovery of both thermodynamic and kinetic information. However, despite its exponential acceleration compared to standard molecular dynamics, generating numerous trajectories can still require a long time. By harnessing our recent algorithmic innovations-particularly subtrajectory moves with high acceptance, coupled with asynchronous replica exchange featuring infinite swaps-we establish a highly parallelizable and rapidly converging path sampling protocol, compatible with diverse high-performance computing architectures. We demonstrate our approach on the liquid-vapor phase transition in superheated water, the unfolding of the chignolin protein, and water dissociation. The latter, performed at the ab initio level, achieves comparable statistical accuracy within days, in contrast to a previous study requiring over a year.

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter.

Nonequilibrium states in soft condensed matter require a systematic approach to characterize and model materials, enhancing predictability and applications. Among the tools, X-ray photon correlation spectroscopy (XPCS) provides exceptional temporal and spatial resolution to extract dynamic insight into the properties of the material. However, existing models might overlook intricate details. We introduce an approach for extracting the transport coefficient, denoted as [Formula: see text], from the XPCS studies. This coefficient is a fundamental parameter in nonequilibrium statistical mechanics and is crucial for characterizing transport processes within a system. Our method unifies the Green-Kubo formulas associated with various transport coefficients, including gradient flows, particle-particle interactions, friction matrices, and continuous noise. We achieve this by integrating the collective influence of random and systematic forces acting on the particles within the framework of a Markov chain. We initially validated this method using molecular dynamics simulations of a system subjected to changes in temperatures over time. Subsequently, we conducted further verification using experimental systems reported in the literature and known for their complex nonequilibrium characteristics. The results, including the derived [Formula: see text] and other relevant physical parameters, align with the previous observations and reveal detailed dynamical information in nonequilibrium states. This approach represents an advancement in XPCS analysis, addressing the growing demand to extract intricate nonequilibrium dynamics. Further, the methods presented are agnostic to the nature of the material system and can be potentially expanded to hard condensed matter systems.

Trends in inequalities in the prevalence of dementia in the United States.

This paper presents estimates of the prevalence of dementia in the United States from 2000 to 2016 by age, sex, race and ethnicity, education, and a measure of lifetime earnings, using data on 21,442 individuals aged 65 y and older and 97,629 person-year observations from a nationally representative survey, the Health and Retirement Study (HRS). The survey includes a range of cognitive tests, and a subsample underwent clinical assessment for dementia. We developed a longitudinal, latent-variable model of cognitive status, which we estimated using the Markov Chain Monte Carlo method. This model provides more accurate estimates of dementia prevalence in population subgroups than do previously used methods on the HRS. The age-adjusted prevalence of dementia decreased from 12.2% in 2000 (95% CI, 11.7 to 12.7%) to 8.5% in 2016 (7.9 to 9.1%) in the 65+ population, a statistically significant decline of 3.7 percentage points or 30.1%. Females are more likely to live with dementia, but the sex difference has narrowed. In the male subsample, we found a reduction in inequalities across education, earnings, and racial and ethnic groups; among females, those inequalities also declined, but less strongly. We observed a substantial increase in the level of education between 2000 and 2016 in the sample. This compositional change can explain, in a statistical sense, about 40% of the reduction in dementia prevalence among men and 20% among women, whereas compositional changes in the older population by age, race and ethnicity, and cardiovascular risk factors mattered less.

A Bayesian switching linear dynamical system for estimating seizure chronotypes.

Epilepsy is a disorder characterized by paroxysmal transitions between multistable states. Dynamical systems have been useful for modeling the paroxysmal nature of seizures. At the same time, intracranial electroencephalography (EEG) recordings have recently discovered that an electrographic measure of epileptogenicity, interictal epileptiform activity, exhibits cycling patterns ranging from ultradian to multidien rhythmicity, with seizures phase-locked to specific phases of these latent cycles. However, many mechanistic questions about seizure cycles remain unanswered. Here, we provide a principled approach to recast the modeling of seizure chronotypes within a statistical dynamical systems framework by developing a Bayesian switching linear dynamical system (SLDS) with variable selection to estimate latent seizure cycles. We propose a Markov chain Monte Carlo algorithm that employs particle Gibbs with ancestral sampling to estimate latent cycles in epilepsy and apply unsupervised learning on spectral features of latent cycles to uncover clusters in cycling tendency. We analyze the largest database of patient-reported seizures in the world to comprehensively characterize multidien cycling patterns among 1,012 people with epilepsy, spanning from infancy to older adulthood. Our work advances knowledge of cycling in epilepsy by investigating how multidien seizure cycles vary in people with epilepsy, while demonstrating an application of an SLDS to frame seizure cycling within a nonlinear dynamical systems framework. It also lays the groundwork for future studies to pursue data-driven hypothesis generation regarding the mechanistic drivers of seizure cycles.

A Dynamic Model for Estimating the Retention Duration of Neutralizing Antibody Titers After Vaccination in a COVID-19 Convalescent Population.

We measured neutralizing antibodies (nAbs) against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a cohort of 235 convalescent patients (representing 384 analytic samples). They were followed for up to 588 days after the first report of onset in Taiwan. A proposed Bayesian approach was used to estimate nAb dynamics in patients postvaccination. This model revealed that the titer reached its peak (1819.70 IU/mL) by 161 days postvaccination and decreased to 154.18 IU/mL by day 360. Thus, the nAb titers declined in 6 months after vaccination. Protection, against variant B.1.1.529 (ie, Omicron) may only occur during the peak period.

Tensor product algorithms for inference of contact network from epidemiological data.

We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The cardinality of this set grows combinatorially with the number of network nodes, which makes this optimisation computationally challenging. For each network, its likelihood is the probability for the observed data to appear during the evolution of the epidemiological process on this network. This probability can be very small, particularly if the network is significantly different from the ground truth network, from which the observed data actually appear. A commonly used stochastic simulation algorithm struggles to recover rare events and hence to estimate small probabilities and likelihoods. In this paper we replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. Since this equation also suffers from the curse of dimensionality, we apply tensor train approximations to overcome it and enable fast and accurate computations. Numerical simulations demonstrate efficient black-box Bayesian inference of the network.

Optimizing spatio-temporal correlation structures for modeling food security in Africa: a simulation-based investigation.

This study investigates the impact of spatio- temporal correlation using four spatio-temporal models: Spatio-Temporal Poisson Linear Trend Model (SPLTM), Poisson Temporal Model (TMS), Spatio-Temporal Poisson Anova Model (SPAM), and Spatio-Temporal Poisson Separable Model (STSM) concerning food security and nutrition in Africa. Evaluating model goodness of fit using the Watanabe Akaike Information Criterion (WAIC) and assessing bias through root mean square error and mean absolute error values revealed a consistent monotonic pattern. SPLTM consistently demonstrates a propensity for overestimating food security, while TMS exhibits a diverse bias profile, shifting between overestimation and underestimation based on varying correlation settings. SPAM emerges as a beacon of reliability, showcasing minimal bias and WAIC across diverse scenarios, while STSM consistently underestimates food security, particularly in regions marked by low to moderate spatio-temporal correlation. SPAM consistently outperforms other models, making it a top choice for modeling food security and nutrition dynamics in Africa. This research highlights the impact of spatial and temporal correlations on food security and nutrition patterns and provides guidance for model selection and refinement. Researchers are encouraged to meticulously evaluate the biases and goodness of fit characteristics of models, ensuring their alignment with the specific attributes of their data and research goals. This knowledge empowers researchers to select models that offer reliability and consistency, enhancing the applicability of their findings.

Inference of genomic landscapes using ordered Hidden Markov Models with emission densities (oHMMed).

BACKGROUND: Genomes are inherently inhomogeneous, with features such as base composition, recombination, gene density, and gene expression varying along chromosomes. Evolutionary, biological, and biomedical analyses aim to quantify this variation, account for it during inference procedures, and ultimately determine the causal processes behind it. Since sequential observations along chromosomes are not independent, it is unsurprising that autocorrelation patterns have been observed e.g., in human base composition. In this article, we develop a class of Hidden Markov Models (HMMs) called oHMMed (ordered HMM with emission densities, the corresponding R package of the same name is available on CRAN): They identify the number of comparably homogeneous regions within autocorrelated observed sequences. These are modelled as discrete hidden states; the observed data points are realisations of continuous probability distributions with state-specific means that enable ordering of these distributions. The observed sequence is labelled according to the hidden states, permitting only neighbouring states that are also neighbours within the ordering of their associated distributions. The parameters that characterise these state-specific distributions are inferred. RESULTS: We apply our oHMMed algorithms to the proportion of G and C bases (modelled as a mixture of normal distributions) and the number of genes (modelled as a mixture of poisson-gamma distributions) in windows along the human, mouse, and fruit fly genomes. This results in a partitioning of the genomes into regions by statistically distinguishable averages of these features, and in a characterisation of their continuous patterns of variation. In regard to the genomic G and C proportion, this latter result distinguishes oHMMed from segmentation algorithms based in isochore or compositional domain theory. We further use oHMMed to conduct a detailed analysis of variation of chromatin accessibility (ATAC-seq) and epigenetic markers H3K27ac and H3K27me3 (modelled as a mixture of poisson-gamma distributions) along the human chromosome 1 and their correlations. CONCLUSIONS: Our algorithms provide a biologically assumption free approach to characterising genomic landscapes shaped by continuous, autocorrelated patterns of variation. Despite this, the resulting genome segmentation enables extraction of compositionally distinct regions for further downstream analyses.

Adaptive Bayesian variable clustering via structural learning of breast cancer data.

The clustering of proteins is of interest in cancer cell biology. This article proposes a hierarchical Bayesian model for protein (variable) clustering hinging on correlation structure. Starting from a multivariate normal likelihood, we enforce the clustering through prior modeling using angle-based unconstrained reparameterization of correlations and assume a truncated Poisson distribution (to penalize a large number of clusters) as prior on the number of clusters. The posterior distributions of the parameters are not in explicit form and we use a reversible jump Markov chain Monte Carlo based technique is used to simulate the parameters from the posteriors. The end products of the proposed method are estimated cluster configuration of the proteins (variables) along with the number of clusters. The Bayesian method is flexible enough to cluster the proteins as well as estimate the number of clusters. The performance of the proposed method has been substantiated with extensive simulation studies and one protein expression data with a hereditary disposition in breast cancer where the proteins are coming from different pathways.

Detecting Episodic Evolution through Bayesian Inference of Molecular Clock Models.

Molecular evolutionary rate variation is a key aspect of the evolution of many organisms that can be modeled using molecular clock models. For example, fixed local clocks revealed the role of episodic evolution in the emergence of SARS-CoV-2 variants of concern. Like all statistical models, however, the reliability of such inferences is contingent on an assessment of statistical evidence. We present a novel Bayesian phylogenetic approach for detecting episodic evolution. It consists of computing Bayes factors, as the ratio of posterior and prior odds of evolutionary rate increases, effectively quantifying support for the effect size. We conducted an extensive simulation study to illustrate the power of this method and benchmarked it to formal model comparison of a range of molecular clock models using (log) marginal likelihood estimation, and to inference under a random local clock model. Quantifying support for the effect size has higher sensitivity than formal model testing and is straight-forward to compute, because it only needs samples from the posterior and prior distribution. However, formal model testing has the advantage of accommodating a wide range molecular clock models. We also assessed the ability of an automated approach, known as the random local clock, where branches under episodic evolution may be detected without their a priori definition. In an empirical analysis of a data set of SARS-CoV-2 genomes, we find "very strong" evidence for episodic evolution. Our results provide guidelines and practical methods for Bayesian detection of episodic evolution, as well as avenues for further research into this phenomenon.

The grapheme-valued Wright-Fisher diffusion with mutation.

In Athreya et al. (2021), models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an example of a simple neutral population genetics model for which this dynamics is a Markovian diffusion that can be characterized as the solution of a martingale problem. In particular, we consider a Markov chain in the space of finite graphs that resembles a Moran model with resampling and mutation. We encode the finite graphs as graphemes, which can be represented as a triple consisting of a vertex set (or more generally, a topological space), an adjacency matrix, and a sampling (Borel) measure. We equip the space of graphons with convergence of sample subgraph densities and show that the grapheme-valued Markov chain converges to a grapheme-valued diffusion as the number of vertices goes to infinity. We show that the grapheme-valued diffusion has a stationary distribution that is linked to the Griffiths-Engen-McCloskey (GEM) distribution. In a companion paper (Greven et al. 2023), we build up a general theory for obtaining grapheme-valued diffusions via genealogies of models in population genetics.

Impact of new direct-acting antiviral therapy on the prevalence and undiagnosed proportion of chronic hepatitis C infection.

BACKGROUND: Patients with chronic hepatitis C (CHC) can be cured with the new highly effective interferon-free combination treatments (DAA) that were approved in 2014. However, CHC is a largely silent disease, and many individuals are unaware of their infections until the late stages of the disease. The impact of wider access to effective treatments and improved awareness of the disease on the number of infections and the number of patients who remain undiagnosed is not known in Canada. Such evidence can guide the development of strategies and interventions to reduce the burden of CHC and meet World Health Organization's (WHO) 2030 elimination targets. The purpose of this study is to use a back-calculation framework informed by provincial population-level health administrative data to estimate the prevalence of CHC and the proportion of cases that remain undiagnosed in the three most populated provinces in Canada: British Columbia (BC), Ontario and Quebec. METHODS: We have conducted a population-based retrospective analysis of health administrative data for the three provinces to generate the annual incidence of newly diagnosed CHC cases, decompensated cirrhosis (DC), hepatocellular carcinoma (HCC) and HCV treatment initiations. For each province, the data were stratified in three birth cohorts: individuals born prior to 1945, individuals born between 1945 and 1965 and individuals born after 1965. We used a back-calculation modelling approach to estimate prevalence and the undiagnosed proportion of CHC. The historical prevalence of CHC was inferred through a calibration process based on a Bayesian Markov chain Monte Carlo (MCMC) algorithm. The algorithm constructs the historical prevalence of CHC for each cohort by comparing the model-generated outcomes of the annual incidence of the CHC-related health events against the data set of observed diagnosed cases generated in the retrospective analysis. RESULTS: The results show a decreasing trend in both CHC prevalence and undiagnosed proportion in BC, Ontario and Quebec. In 2018, CHC prevalence was estimated to be 1.23% (95% CI: .96%-1.62%), .91% (95% CI: .82%-1.04%) and .57% (95% CI: .51%-.64%) in BC, Ontario and Quebec respectively. The CHC undiagnosed proportion was assessed to be 35.44% (95% CI: 27.07%-45.83%), 34.28% (95% CI: 26.74%-41.62%) and 46.32% (95% CI: 37.85%-52.80%) in BC, Ontario and Quebec, respectively, in 2018. Also, since the introduction of new DAA treatment in 2014, CHC prevalence decreased from 1.39% to 1.23%, .97% to .91% and .65% to .57% in BC, Ontario and Quebec respectively. Similarly, the CHC undiagnosed proportion decreased from 38.78% to 35.44%, 38.70% to 34.28% and 47.54% to 46.32% in BC, Ontario and Quebec, respectively, from 2014 to 2018. CONCLUSIONS: We estimated that the CHC prevalence and undiagnosed proportion have declined for all three provinces since the new DAA treatment has been approved in 2014. Yet, our findings show that a significant proportion of HCV cases remain undiagnosed across all provinces highlighting the need to increase investment in screening. Our findings provide essential evidence to guide decisions about current and future HCV strategies and help achieve the WHO goal of eliminating hepatitis C in Canada by 2030.

Unit information Dirichlet process prior.

Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis.

Joint structure learning and causal effect estimation for categorical graphical models.

The scope of this paper is a multivariate setting involving categorical variables. Following an external manipulation of one variable, the goal is to evaluate the causal effect on an outcome of interest. A typical scenario involves a system of variables representing lifestyle, physical and mental features, symptoms, and risk factors, with the outcome being the presence or absence of a disease. These variables are interconnected in complex ways, allowing the effect of an intervention to propagate through multiple paths. A distinctive feature of our approach is the estimation of causal effects while accounting for uncertainty in both the dependence structure, which we represent through a directed acyclic graph (DAG), and the DAG-model parameters. Specifically, we propose a Markov chain Monte Carlo algorithm that targets the joint posterior over DAGs and parameters, based on an efficient reversible-jump proposal scheme. We validate our method through extensive simulation studies and demonstrate that it outperforms current state-of-the-art procedures in terms of estimation accuracy. Finally, we apply our methodology to analyze a dataset on depression and anxiety in undergraduate students.

Topical hidden genome: discovering latent cancer mutational topics using a Bayesian multilevel context-learning approach.

Inferring the cancer-type specificities of ultra-rare, genome-wide somatic mutations is an open problem. Traditional statistical methods cannot handle such data due to their ultra-high dimensionality and extreme data sparsity. To harness information in rare mutations, we have recently proposed a formal multilevel multilogistic "hidden genome" model. Through its hierarchical layers, the model condenses information in ultra-rare mutations through meta-features embodying mutation contexts to characterize cancer types. Consistent, scalable point estimation of the model can incorporate 10s of millions of variants across thousands of tumors and permit impressive prediction and attribution. However, principled statistical inference is infeasible due to the volume, correlation, and noninterpretability of mutation contexts. In this paper, we propose a novel framework that leverages topic models from computational linguistics to effectuate dimension reduction of mutation contexts producing interpretable, decorrelated meta-feature topics. We propose an efficient MCMC algorithm for implementation that permits rigorous full Bayesian inference at a scale that is orders of magnitude beyond the capability of existing out-of-the-box inferential high-dimensional multi-class regression methods and software. Applying our model to the Pan Cancer Analysis of Whole Genomes dataset reveals interesting biological insights including somatic mutational topics associated with UV exposure in skin cancer, aging in colorectal cancer, and strong influence of epigenome organization in liver cancer. Under cross-validation, our model demonstrates highly competitive predictive performance against blackbox methods of random forest and deep learning.

The multivariate Bernoulli detector: change point estimation in discrete survival analysis.

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffers from biased estimation. Therefore, we propose the multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from nonconjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

Latent classification model for censored longitudinal binary outcome.

Latent classification model is a class of statistical methods for identifying unobserved class membership among the study samples using some observed data. In this study, we proposed a latent classification model that takes a censored longitudinal binary outcome variable and uses its changing pattern over time to predict individuals' latent class membership. Assuming the time-dependent outcome variables follow a continuous-time Markov chain, the proposed method has two primary goals: (1) estimate the distribution of the latent classes and predict individuals' class membership, and (2) estimate the class-specific transition rates and rate ratios. To assess the model's performance, we conducted a simulation study and verified that our algorithm produces accurate model estimates (ie, small bias) with reasonable confidence intervals (ie, achieving approximately 95% coverage probability). Furthermore, we compared our model to four other existing latent class models and demonstrated that our approach yields higher prediction accuracies for latent classes. We applied our proposed method to analyze the COVID-19 data in Houston, Texas, US collected between January first 2021 and December 31st 2021. Early reports on the COVID-19 pandemic showed that the severity of a SARS-CoV-2 infection tends to vary greatly by cases. We found that while demographic characteristics explain some of the differences in individuals' experience with COVID-19, some unaccounted-for latent variables were associated with the disease.

Spatial-temporal Bayesian accelerated failure time models for survival endpoints with applications to prostate cancer registry data.

Prostate cancer is the most common cancer after non-melanoma skin cancer and the second leading cause of cancer deaths in US men. Its incidence and mortality rates vary substantially across geographical regions and over time, with large disparities by race, geographic regions (i.e., Appalachia), among others. The widely used Cox proportional hazards model is usually not applicable in such scenarios owing to the violation of the proportional hazards assumption. In this paper, we fit Bayesian accelerated failure time models for the analysis of prostate cancer survival and take dependent spatial structures and temporal information into account by incorporating random effects with multivariate conditional autoregressive priors. In particular, we relax the proportional hazards assumption, consider flexible frailty structures in space and time, and also explore strategies for handling the temporal variable. The parameter estimation and inference are based on a Monte Carlo Markov chain technique under a Bayesian framework. The deviance information criterion is used to check goodness of fit and to select the best candidate model. Extensive simulations are performed to examine and compare the performances of models in different contexts. Finally, we illustrate our approach by using the 2004-2014 Pennsylvania Prostate Cancer Registry data to explore spatial-temporal heterogeneity in overall survival and identify significant risk factors.

Impacts on Atlantic Killifish from Neurotoxicants: Genes, Behavior, and Population-Relevant Outcomes.

Molecular, cellular, and organismal alterations are important descriptors of toxic effects, but our ability to extrapolate and predict ecological risks is limited by the availability of studies that link measurable end points to adverse population relevant outcomes such as cohort survival and growth. In this study, we used laboratory gene expression and behavior data from two populations of Atlantic killifish Fundulus heteroclitus [one reference site (SCOKF) and one PCB-contaminated site (NBHKF)] to inform individual-based models simulating cohort growth and survival from embryonic exposures to environmentally relevant concentrations of neurotoxicants. Methylmercury exposed SCOKF exhibited brain gene expression changes in the si:ch211-186j3.6, si:dkey-21c1.4, scamp1, and klhl6 genes, which coincided with changes in feeding and swimming behaviors, but our models simulated no growth or survival effects of exposures. PCB126-exposed SCOKF had lower physical activity levels coinciding with a general upregulation in nucleic and cellular brain gene sets (BGS) and downregulation in signaling, nucleic, and cellular BGS. The NBHKF, known to be tolerant to PCBs, had altered swimming behaviors that coincided with 98% fewer altered BGS. Our models simulated PCB126 decreased growth in SCOKF and survival in SCOKF and NBHKF. Overall, our study provides a unique demonstration linking molecular and behavioral data to develop quantitative, testable predictions of ecological risk.

A stable sensory map emerges from a dynamic equilibrium of neurons with unstable tuning properties.

Recent long-term measurements of neuronal activity have revealed that, despite stability in large-scale topographic maps, the tuning properties of individual cortical neurons can undergo substantial reformatting over days. To shed light on this apparent contradiction, we captured the sound response dynamics of auditory cortical neurons using repeated 2-photon calcium imaging in awake mice. We measured sound-evoked responses to a set of pure tone and complex sound stimuli in more than 20,000 auditory cortex neurons over several days. We found that a substantial fraction of neurons dropped in and out of the population response. We modeled these dynamics as a simple discrete-time Markov chain, capturing the continuous changes in responsiveness observed during stable behavioral and environmental conditions. Although only a minority of neurons were driven by the sound stimuli at a given time point, the model predicts that most cells would at least transiently become responsive within 100 days. We observe that, despite single-neuron volatility, the population-level representation of sound frequency was stably maintained, demonstrating the dynamic equilibrium underlying the tonotopic map. Our results show that sensory maps are maintained by shifting subpopulations of neurons "sharing" the job of creating a sensory representation.