Inhibitory modulation of action potentials in crayfish motor axons by fluoxetine.

The goal of this report is to explore how K2P channels modulate axonal excitability by using the crayfish ventral superficial flexor preparation. This preparation allows for simultaneous recording of motor nerve extracellular action potentials (eAP) and intracellular excitatory junctional potential (EJP) from a muscle fiber. Previous pharmacological studies have demonstrated the presence of K2P-like channels in crayfish. Fluoxetine (50 µM) was used to block K2P channels in this study. The blocker caused a gradual decline, and eventually complete block, of motor axon action potentials. At an intermediate stage of the block, when the peak-to-peak amplitude of eAP decreased to ∼60%-80% of the control value, the amplitude of the initial positive component of eAP declined at a faster rate than that of the negative peak representing sodium influx. Furthermore, the second positive peak following this sodium influx, which corresponds to the after-hyperpolarizing phase of intracellularly recorded action potentials (iAP), became larger during the intermediate stage of eAP block. Finally, EJP recorded simultaneously with eAP showed no change in amplitude, but did show a significant increase in synaptic delay. These changes in eAP shape and EJP delay are interpreted as the consequence of depolarized resting membrane potential after K2P channel block. In addition to providing insights to possible functions of K2P channels in unmyelinated axons, results presented here also serve as an example of how changes in eAP shape contain information that can be used to infer alterations in intracellular events. This type of eAP-iAP cross-inference is valuable for gaining mechanistic insights here and may also be applicable to other model systems.

Evolutionary shift detection with ensemble variable selection.

Abrupt environmental changes can lead to evolutionary shifts in trait evolution. Identifying these shifts is an important step in understanding the evolutionary history of phenotypes. The detection performances of different methods are influenced by many factors, including different numbers of shifts, shift sizes, where a shift occurs on a tree, and the types of phylogenetic structure. Furthermore, the model assumptions are oversimplified, so are likely to be violated in real data, which could cause the methods to fail. We perform simulations to assess the effect of these factors on the performance of shift detection methods. To make the comparisons more complete, we also propose an ensemble variable selection method (R package ELPASO) and compare it with existing methods (R packages [Formula: see text]1ou and PhylogeneticEM). The performances of methods are highly dependent on the selection criterion. [Formula: see text]1ou+pBIC is usually the most conservative method and it performs well when signal sizes are large. [Formula: see text]1ou+BIC is the least conservative method and it performs well when signal sizes are small. The ensemble method provides more balanced choices between those two methods. Moreover, the performances of all methods are heavily impacted by measurement error, tree reconstruction error and shifts in variance.

SPADE4: Sparsity and Delay Embedding Based Forecasting of Epidemics.

Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify the population into compartments according to health status and model the dynamics of these compartments using dynamical systems. However, these predefined systems may not capture the true dynamics of the epidemic due to the complexity of the disease transmission and human interactions. In order to overcome this drawback, we propose Sparsity and Delay Embedding based Forecasting (SPADE4) for predicting epidemics. SPADE4 predicts the future trajectory of an observable variable without the knowledge of the other variables or the underlying system. We use random features model with sparse regression to handle the data scarcity issue and employ Takens' delay embedding theorem to capture the nature of the underlying system from the observed variable. We show that our approach outperforms compartmental models when applied to both simulated and real data.

When can we reconstruct the ancestral state? Beyond Brownian motion.

Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a necessary and sufficient condition, called the big bang condition, for the existence of an accurate reconstruction method under discrete trait evolution models and the Brownian motion model. In this paper, we extend this result to a wide range of continuous trait evolution models. In particular, we consider a general setting where continuous traits evolve along the tree according to stochastic processes that satisfy some regularity conditions. We verify these conditions for popular continuous trait evolution models including Ornstein-Uhlenbeck, reflected Brownian Motion, bounded Brownian Motion, and Cox-Ingersoll-Ross.

Striving for personal growth matters: The relationship between personal growth initiative, teacher engagement and instructional quality.

BACKGROUND: Teachers' instructional quality is critical to student learning and development. However, the affordance of different aspects of instructional quality remains underexplored. AIMS: This study explores the relationship between teachers' personal growth initiative (PGI) and teacher engagement and instructional quality. SAMPLE: The data were collected from 998 teachers (82.9% female, average years of teaching experience = 15.25, SD = 10.29) from China. METHODS: The participants completed an anonymous online survey questionnaire that examined their PGI, work engagement and self-reported instructional quality. Structural equation modelling and bootstrapping were performed to determine the differentiated associations between PGI and each aspect of the teachers' self-reported instructional quality. RESULTS: The results confirmed the critical role of PGI in teacher engagement and self-reported instructional quality. To varying degrees, the dimensions of teacher engagement, except for cognitive engagement, mediated the association between PGI and self-reported instructional quality. CONCLUSIONS: The teachers' self-reported data showed that their motivation for personal growth played an important role in improving their instructional quality. The teachers' emotional engagement and social engagement with colleagues were positively related to classroom management, and their social engagement with students was associated with a supportive climate.

Inferring Phenotypic Trait Evolution on Large Trees With Many Incomplete Measurements.

Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This generally necessitates data imputation or integration, and existing control techniques typically scale poorly as the number of taxa increases. We propose an inference technique that integrates out missing measurements analytically and scales linearly with the number of taxa by using a post-order traversal algorithm under a multivariate Brownian diffusion (MBD) model to characterize trait evolution. We further exploit this technique to extend the MBD model to account for sampling error or non-heritable residual variance. We test these methods to examine mammalian life history traits, prokaryotic genomic and phenotypic traits, and HIV infection traits. We find computational efficiency increases that top two orders-of-magnitude over current best practices. While we focus on the utility of this algorithm in phylogenetic comparative methods, our approach generalizes to solve long-standing challenges in computing the likelihood for matrix-normal and multivariate normal distributions with missing data at scale.

When can we reconstruct the ancestral state? A unified theory.

Ancestral state reconstruction is one of the most important tasks in evolutionary biology. Conditions under which we can reliably reconstruct the ancestral state have been studied for both discrete and continuous traits. However, the connection between these results is unclear, and it seems that each model needs different conditions. In this work, we provide a unifying theory on the consistency of ancestral state reconstruction for various types of trait evolution models. Notably, we show that for a sequence of nested trees with bounded heights, the necessary and sufficient conditions for the existence of a consistent ancestral state reconstruction method under discrete models, the Brownian motion model, and the threshold model are equivalent. When tree heights are unbounded, we provide a simple counter-example to show that this equivalence is no longer valid.

Ancestral state reconstruction with large numbers of sequences and edge-length estimation.

Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and edge lengths are known. In some scenarios the tree topology might be reasonably well known for the taxa under study. When sequence length is much smaller than the number of species, however, edge lengths are not likely to be accurately estimated. We study the consistency of the maximum likelihood and empirical Bayes estimators of the ancestral state of discrete traits in such settings under a star tree. We prove that the likelihood-based reconstruction is consistent under symmetric models but can be inconsistent under non-symmetric models. We show, however, that a simple consistent estimator for the ancestral states is available under non-symmetric models. The results illustrate that likelihood methods can unexpectedly have undesirable properties as the number of sequences considered gets very large. Broader implications of the results are discussed.

Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the US

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multi-model ensemble forecast that combined predictions from dozens of different research groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naive baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-week horizon 3-5 times larger than when predicting at a 1-week horizon. This project underscores the role that collaboration and active coordination between governmental public health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks. Significance StatementThis paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the US. Results show high variation in accuracy between and within stand-alone models, and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public health action.

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model.

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a 2-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value.

Multi-task learning improves ancestral state reconstruction.

We consider the ancestral state reconstruction problem where we need to infer phenotypes of ancestors using observations from present-day species. For this problem, we propose a multi-task learning method that uses regularized maximum likelihood to estimate the ancestral states of various traits simultaneously. We then show both theoretically and by simulation that this method improves the estimates of the ancestral states compared to the maximum likelihood method. The result also indicates that for the problem of ancestral state reconstruction under the Brownian motion model, the maximum likelihood method can be improved.

Consistency and convergence rate of phylogenetic inference via regularization.

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.

Computational methods for birth-death processes.

Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers in which only jumps to adjacent states are allowed. BDPs can be used to easily parameterize a rich variety of probability distributions on the non-negative integers, and straightforward conditions guarantee that these distributions are proper. BDPs also provide a mechanistic interpretation - birth and death of actual particles or organisms - that has proven useful in evolution, ecology, physics, and chemistry. Although the theoretical properties of general BDPs are well understood, traditionally statistical work on BDPs has been limited to the simple linear (Kendall) process. Aside from a few simple cases, it remains impossible to find analytic expressions for the likelihood of a discretely-observed BDP, and computational difficulties have hindered development of tools for statistical inference. But the gap between BDP theory and practical methods for estimation has narrowed in recent years. There are now robust methods for evaluating likelihoods for realizations of BDPs: finite-time transition, first passage, equilibrium probabilities, and distributions of summary statistics that arise commonly in applications. Recent work has also exploited the connection between continuously- and discretely-observed BDPs to derive EM algorithms for maximum likelihood estimation. Likelihood-based inference for previously intractable BDPs is much easier than previously thought and regression approaches analogous to Poisson regression are straightforward to derive. In this review, we outline the basic mathematical theory for BDPs and demonstrate new tools for statistical inference using data from BDPs.

Birth/birth-death processes and their computable transition probabilities with biological applications.

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Phase transition on the convergence rate of parameter estimation under an Ornstein-Uhlenbeck diffusion on a tree.

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges because of the intrinsic correlation between the observations produced by the shared evolutionary history, thus violating the standard independence assumption of large-sample theory. For instance (Ho and Ané, Ann Stat 41:957-981, 2013) recently proved that the mean (also known in this context as selection optimum) of an Ornstein-Uhlenbeck process on a tree cannot be estimated consistently from an increasing number of tip observations if the tree height is bounded. Here, using a fruitful connection to the so-called reconstruction problem in probability theory, we study the convergence rate of parameter estimation in the unbounded height case. For the mean of the process, we provide a necessary and sufficient condition for the consistency of the maximum likelihood estimator (MLE) and establish a phase transition on its convergence rate in terms of the growth of the tree. In particular we show that a loss of [Formula: see text]-consistency (i.e., the variance of the MLE becomes [Formula: see text], where n is the number of tips) occurs when the tree growth is larger than a threshold related to the phase transition of the reconstruction problem. For the covariance parameters, we give a novel, efficient estimation method which achieves [Formula: see text]-consistency under natural assumptions on the tree. Our theoretical results provide practical suggestions for the design of comparative data collection.

A Relaxed Directional Random Walk Model for Phylogenetic Trait Evolution.

Understanding the processes that give rise to quantitative measurements associated with molecular sequence data remains an important issue in statistical phylogenetics. Examples of such measurements include geographic coordinates in the context of phylogeography and phenotypic traits in the context of comparative studies. A popular approach is to model the evolution of continuously varying traits as a Brownian diffusion process acting on a phylogenetic tree. However, standard Brownian diffusion is quite restrictive and may not accurately characterize certain trait evolutionary processes. Here, we relax one of the major restrictions of standard Brownian diffusion by incorporating a nontrivial estimable mean into the process. We introduce a relaxed directional random walk (RDRW) model for the evolution of multivariate continuously varying traits along a phylogenetic tree. Notably, the RDRW model accommodates branch-specific variation of directional trends while preserving model identifiability. Furthermore, our development of a computationally efficient dynamic programming approach to compute the data likelihood enables scaling of our method to large data sets frequently encountered in phylogenetic comparative studies and viral evolution. We implement the RDRW model in a Bayesian inference framework to simultaneously reconstruct the evolutionary histories of molecular sequence data and associated multivariate continuous trait data, and provide tools to visualize evolutionary reconstructions. We demonstrate the performance of our model on synthetic data, and we illustrate its utility in two viral examples. First, we examine the spatiotemporal spread of HIV-1 in central Africa and show that the RDRW model uncovers a clearer, more detailed picture of the dynamics of viral dispersal than standard Brownian diffusion. Second, we study antigenic evolution in the context of HIV-1 resistance to three broadly neutralizing antibodies. Our analysis reveals evidence of a continuous drift at the HIV-1 population level towards enhanced resistance to neutralization by the VRC01 monoclonal antibody over the course of the epidemic. [Brownian Motion; Diffusion Processes; Phylodynamics; Phylogenetics; Phylogeography; Trait Evolution.].

Statistical evidence for common ancestry: Application to primates.

Since Darwin, biologists have come to recognize that the theory of descent from common ancestry (CA) is very well supported by diverse lines of evidence. However, while the qualitative evidence is overwhelming, we also need formal methods for quantifying the evidential support for CA over the alternative hypothesis of separate ancestry (SA). In this article, we explore a diversity of statistical methods using data from the primates. We focus on two alternatives to CA, species SA (the separate origin of each named species) and family SA (the separate origin of each family). We implemented statistical tests based on morphological, molecular, and biogeographic data and developed two new methods: one that tests for phylogenetic autocorrelation while correcting for variation due to confounding ecological traits and a method for examining whether fossil taxa have fewer derived differences than living taxa. We overwhelmingly rejected both species and family SA with infinitesimal P values. We compare these results with those from two companion papers, which also found tremendously strong support for the CA of all primates, and discuss future directions and general philosophical issues that pertain to statistical testing of historical hypotheses such as CA.

A linear-time algorithm for Gaussian and non-Gaussian trait evolution models.

We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.

Interactive effects of nurse-experienced time pressure and burnout on patient safety: a cross-sectional survey.

BACKGROUND: Global nursing shortages have exacerbated time pressure and burnout among nurses. Despite the well-established correlation between burnout and patient safety, no studies have addressed how time pressure among nurses and patient safety are related and whether burnout moderates such a relation. OBJECTIVES: This study investigated how time pressure and the interaction of time pressure and nursing burnout affect patient safety. DESIGN-SETTING PARTICIPANTS: This cross-sectional study surveyed 458 nurses in 90 units of two medical centres in northern Taiwan. METHODS: Nursing burnout was measured by the Maslach Burnout Inventory-Human Service Scale. Patient safety was inversely measured by six items on frequency of adverse events. Time pressure was measured by five items. Regressions were used for the analysis. RESULTS: While the results of regression analyses suggest that time pressure did not significantly affect patient safety (beta=-.01, p>.05), time pressure and burnout had an interactive effect on patient safety (beta=-.08, p<.05). Specifically, for nurses with high burnout (n=223), time pressure was negatively related to patient safety (beta=-.10, p<.05). CONCLUSION: Time pressure adversely affected patient safety for nurses with a high level of burnout, but not for nurses with a low level of burnout.

A test for measuring gustatory function.

OBJECTIVES/HYPOTHESIS: The purpose of this study was to determine the usefulness of edible taste strips for measuring human gustatory function. STUDY DESIGN: The physical properties of edible taste strips were examined to determine their potential for delivering threshold and suprathreshold amounts of taste stimuli to the oral cavity. Taste strips were then assayed by fluorescence to analyze the uniformity and distribution of bitter tastant in the strips. Finally, taste recognition thresholds for sweet taste were examined to determine whether or not taste strips could detect recognition thresholds that were equal to or better than those obtained from aqueous tests. METHODS: Edible strips were prepared from pullulan-hydroxypropyl methylcellulose solutions that were dried to a thin film. The maximal amount of a tastant that could be incorporated in a 2.54 cm2 taste strip was identified by including representative taste stimuli for each class of tastant (sweet, sour, salty, bitter, and umami) during strip formation. Distribution of the bitter tastant quinine hydrochloride in taste strips was assayed by fluorescence emission spectroscopy. The efficacy of taste strips for evaluating human gustatory function was examined by using a single series ascending method of limits protocol. Sucrose taste recognition threshold data from edible strips was then compared with results that were obtained from a standard "sip and spit" recognition threshold test. RESULTS: Edible films that formed from a pullulan-hydroxypropyl methylcellulose polymer mixture can be used to prepare clear, thin strips that have essentially no background taste and leave no physical presence after release of tastant. Edible taste strips could uniformly incorporate up to 5% of their composition as tastant. Taste recognition thresholds for sweet taste were over one order of magnitude lower with edible taste strips when compared with an aqueous taste test. CONCLUSION: Edible taste strips are a highly sensitive method for examining taste recognition thresholds in humans. This new means of presenting taste stimuli should have widespread applications for examining human taste function in the laboratory, in the clinic, or at remote locations.