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The sex ratio is nearly equal in most organisms, while several ecological and evolutionary factors skew the sex ratio. We evaluated the sex ratios of 12 species in the freshwater snail genus Semisulcospira in and around Lake Biwa. We found highly female-biased sex ratios in all 12 species. The sex ratios were nearly equal or slightly female-biased in the smaller shell-size classes, while they were highly female-biased in the larger size classes. We also found that females were significantly larger in most of these species. Further, the species with a larger size difference between the sexes tended to exhibit a more female-biased sex ratio. Considering the general correlation between shell size and age, this pattern can be explained by longer lifespans in females, shaping the observed female-biased sex ratios. We also found that some Semisulcospira species showed female-biased sex ratios in all shell size classes. This pattern suggests that the distinct longevity hypothesis can not solely explain the observed biased sex ratios. We discussed the possible contributions of the sampling errors and selfish genetic elements to the observed biased sex ratios. This study provides essential information to disentangle the mechanisms of the biased sex ratio in the Semisulcospira snails. [ABSTRACT FROM AUTHOR]

The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially in terms of approximating the invariant distribution. The triangle inequality framework employed in this paper is a convenient approach to estimate the long-time sampling error of the numerical methods. Using the triangle inequality framework, we show that the long-time error of the discrete random batch method is |$O(\sqrt {\tau } + e^{-\lambda t})$|⁠ , where |$\tau $| is the time step and |$\lambda $| is the convergence rate, which does not depend on the time step |$\tau $| or the number of particles |$N$|⁠. Our results also apply to the McKean–Vlasov process, which is the mean-field limit of the interacting particle system as the number of particles |$N\rightarrow \infty $|⁠. [ABSTRACT FROM AUTHOR]

When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population‐size‐independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue. [ABSTRACT FROM AUTHOR]

Motivation Mixed molecular data combines continuous and categorical features of the same samples, such as OMICS profiles with genotypes, diagnoses, or patient sex. Like all high-dimensional molecular data, it is prone to incorrect values that can stem from various sources for example the technical limitations of the measurement devices, errors in the sample preparation, or contamination. Most anomaly detection algorithms identify complete samples as outliers or anomalies. However, in most cases, not all measurements of those samples are erroneous but only a few one-dimensional features within the samples are incorrect. These one-dimensional data errors are continuous measurements that are either located outside or inside the normal ranges of their features but in both cases show atypical values given all other continuous and categorical features in the sample. Additionally, categorical anomalies can occur for example when the genotype or diagnosis was submitted wrongly. Results We introduce ADMIRE (Anomaly Detection using MIxed gRaphical modEls), a novel approach for the detection and correction of anomalies in mixed high-dimensional data. Hereby, we focus on the detection of single (one-dimensional) data errors in the categorical and continuous features of a sample. For that the joint distribution of continuous and categorical features is learned by mixed graphical models, anomalies are detected by the difference between measured and model-based estimations and are corrected using imputation. We evaluated ADMIRE in simulation and by screening for anomalies in one of our own metabolic datasets. In simulation experiments, ADMIRE outperformed the state-of-the-art methods of Local Outlier Factor, stray, and Isolation Forest. Availability and implementation All data and code is available at https://github.com/spang-lab/adadmire. ADMIRE is implemented in a Python package called adadmire which can be found at https://pypi.org/project/adadmire. [ABSTRACT FROM AUTHOR]

We present a generalized estimator for the autocorrelation function, S-ACF, which is an extended version of the standard estimator of the autocorrelation function (ACF). S-ACF is a versatile definition that can robustly and efficiently extract periodicity and signal shape information from a time series, independent of the time sampling and with minimal assumptions about the underlying process. Calculating the autocorrelation of irregularly sampled time series becomes possible by generalizing the lag of the standard estimator of the ACF to a real parameter and introducing the notion of selection and weight functions. We show that the S-ACF reduces to the standard ACF estimator for regularly sampled time series. Using a large number of synthetic time series, we demonstrate that the performance of the S-ACF is as good or better than commonly used Gaussian and rectangular kernel estimators, and is comparable to a combination of interpolation and the standard estimator. We apply the S-ACF to astrophysical data by extracting rotation periods for the spotted star KIC 5110407, and compare our results to Gaussian process (GP) regression and Lomb–Scargle (LS) periodograms. We find that the S-ACF periods typically agree better with those from GP regression than from LS periodograms, especially in cases where there is evolution in the signal shape. The S-ACF has a wide range of potential applications and should be useful in quantitative science disciplines where irregularly sampled time series occur. A python implementation of the S-ACF is available under the MIT license. [ABSTRACT FROM AUTHOR]

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression using information theory match the leading terms in Keeton's expression from an analysis of moments. This approximate agreement was previously only known numerically and was somewhat mysterious. Second, we show that the uncertainty in single NS runs approximately equals the standard deviation in repeated NS runs. While intuitive, this was previously taken for granted. We close by investigating our results and their assumptions in several numerical examples, including cases in which NS uncertainties increase without bound. [ABSTRACT FROM AUTHOR]

Motivation Genes evolve under processes such as gene duplication and loss (GDL), so that gene family trees are multi-copy, as well as incomplete lineage sorting (ILS); both processes produce gene trees that differ from the species tree. The estimation of species trees from sets of gene family trees is challenging, and the estimation of rooted species trees presents additional analytical challenges. Two of the methods developed for this problem are STRIDE, which roots species trees by considering GDL events, and Quintet Rooting (QR), which roots species trees by considering ILS. Results We present DISCO+QR, a new approach to rooting species trees that first uses DISCO to address GDL and then uses QR to perform rooting in the presence of ILS. DISCO+QR operates by taking the input gene family trees and decomposing them into single-copy trees using DISCO and then roots the given species tree using the information in the single-copy gene trees using QR. We show that the relative accuracy of STRIDE and DISCO+QR depend on the properties of the dataset (number of species, genes, rate of gene duplication, degree of ILS and gene tree estimation error), and that each provides advantages over the other under some conditions. Availability and implementation DISCO and QR are available in github. Supplementary information Supplementary data are available at Bioinformatics Advances online. [ABSTRACT FROM AUTHOR]

In sample surveys that collect information on skewed variables, it is often desirable to assess the influence of sample units on the sampling error of survey-weighted estimators of finite population parameters. The conditional bias is an attractive measure of influence that accounts for the sampling design and the estimation method. It is defined as the design expectation of the sampling error conditional on a given unit being selected in the sample. The estimation of the conditional bias is relatively straightforward for simple sampling designs and estimators. However, for complex designs or complex estimators, it may be tedious to derive an explicit expression for the conditional bias. In those complex surveys, variance estimation is often achieved through replication methods such as the bootstrap. Bootstrap methods of variance estimation are typically implemented by producing a set of bootstrap weights that is provided to users along with the survey data. In this article, we show how to use these bootstrap weights to obtain an estimator of the conditional bias. Our bootstrap estimator is evaluated in a simulation study and illustrated using data from the Canadian Survey of Household Spending. [ABSTRACT FROM AUTHOR]

Background: Laboratory sampling is a significant source of error in feed testing. Proficiency testing programs such as the Association of American Feed Control Officials Proficiency Testing Program are an effectivemeans of assessing error in and among analyticalmethods. However, all proficiency test items are comminuted and blended to control variability among items, effectivelyminimizing sampling error. Currently there is nomechanismformonitoring sampling error among laboratories. Objective: The objective of this work was to investigate the feasibility of a proficiency testing program for laboratory sampling methods and provide insight into a program to advance the performance of sampling in laboratories. Methods: The study involved the fabrication of identical feed test items from feed ingredients and shipping the uncomminuted materials to volunteer laboratories. The volunteer laboratories followed in-house procedures for selecting test portions for routine feed tests. Tests on all the test portions for a single analyte were performed by a single laboratory, so that the variability in test results could be attributed to laboratory sampling processes to select test portions. Results: The average RSD, %, for Item A and Item B, respectively, were as follows: protein, 5.08 and 5.23; non-protein nitrogen, 8.90 and 16.6; crude fat, 3.45 and 5.67; vitamin A, 33.9 and 26.9; calcium, 21.9 and 23.6; zinc, 17.9 and 27.9; and copper, 17.4 and 27.9. Conclusion: This study suggests that a proficiency testing program for laboratory sampling is feasible with manual manufacture of the test items, and data can be used to monitor laboratory sampling proficiency and also to compare the performance of different laboratory sampling methods. Highlights: The data illustrates that each analyte has unique distributional and compositional heterogeneity, thus unique sampling error, even when multiple analytes are determined from a single test portion. [ABSTRACT FROM AUTHOR]

Failure of individuals to voluntarily observe regulations and recommendations around mitigating COVID-19 (e.g. social distancing; frequent handwashing) is often cited as a reason why some countries struggled to curtail the spread of the virus. Understanding the factors that are associated with people's willingness to comply with COVID-19 regulations and recommendations is an important step in helping policy makers and health officials reduce the impact of this (and future) pandemics. In the current study we examined this question in one of the countries hardest hit by the pandemic: Spain. A large, representative survey (N = 2100) revealed that several factors were positively associated with willingness to comply to COVID-19 regulations and recommendations. In decreasing order of predictive value, these were: (i) perceptions of whether friends and family were complying (i.e. norms), (ii) trust in science as a basis for lawmaking, (iii) perceived effectiveness of regulations and (iv) perception of risk of infection. These results point to the importance of influencing social norms as the primary way to improve adherence to the health regulations of COVID-19; more important than intrapsychic considerations such as efficacy and risk. [ABSTRACT FROM AUTHOR]

In the search for life in the Universe, exoplanets represent numerous natural experiments in planet formation, evolution, and the emergence of life. This raises the fascinating prospect of evaluating cosmic life on a statistical basis. One key statistic is the occurrence rate of life-bearing worlds, f L, the 'frequency of life' term in the famous Drake Equation. Measuring f L would give profound insight into how common life is and may help us to constrain origin-of-life theories. I propose f L as the goal for the DRAKE mission (Dedicated Research for Advancing Knowledge of Exobiology): a transit spectroscopy survey of M-dwarf habitable zone terrestrial planets. I investigate how the uncertainty on the observed value of f L scales with sample size. I determine that sampling error dominates over observational error and that the uncertainty is a function of the observed f L value. I show that even small sample sizes can provide significant constraints on f L, boding well for the transit spectroscopy approach. I perform a feasibility study of the DRAKE mission using a nominal instrument design and mission plan. Due to low observing efficiencies, DRAKE may need to be incorporated into a wider-ranging deep-space or lunar observatory. A 50-planet survey could constrain f L to ≤ 0.06 (at 95 per cent confidence) if the sample f L  = 0, or 0.03–0.2 if the sample f L  = 0.1. This can be achieved (on average) in 10 yr using a 17-m telescope with an unrestricted field-of-regard. DRAKE is a viable approach to attempting the first experimental measurement of f L. [ABSTRACT FROM AUTHOR]

Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly quantifying the uncertainty of the (noisy) sample estimate regarding the true value in the population, is currently still limited. This article proposes and evaluates several strategies to compute valid differentially private confidence intervals for the median. Instead of computing a differentially private point estimate and deriving its uncertainty, we directly estimate the interval bounds and discuss why this approach is superior if ensuring privacy is important. We also illustrate that addressing both sources of uncertainty—the error from sampling and the error from protecting the output—simultaneously should be preferred over simpler approaches that incorporate the uncertainty in a sequential fashion. We evaluate the performance of the different algorithms under various parameter settings in extensive simulation studies and demonstrate how the findings could be applied in practical settings using data from the 1940 Decennial Census. [ABSTRACT FROM AUTHOR]

Secondary contact between species often results in the formation of a hybrid zone, with the eventual fates of the hybridizing species dependent on evolutionary and ecological forces. We examine this process in the Amazon Basin by conducting the first genomic and phenotypic characterization of the hybrid zone formed after secondary contact between two obligate army‐ant‐followers: the White‐breasted Antbird (Rhegmatorhina hoffmannsi) and the Harlequin Antbird (Rhegmatorhina berlepschi). We found a major geographic displacement (∼120 km) between the mitochondrial and nuclear clines, and we explore potential hypotheses for the displacement, including sampling error, genetic drift, and asymmetric cytonuclear incompatibilities. We cannot exclude roles for sampling error and genetic drift in contributing to the discordance; however, the data suggest expansion and unidirectional introgression of hoffmannsi into the distribution of berlepschi. [ABSTRACT FROM AUTHOR]

The adoption of a multivariate perspective of selection implies the existence of multivariate adaptive peaks and pervasive correlational selection that promotes co‐adaptation between traits. However, to test for the ubiquity of correlational selection in nature, we must first have a sense of how well can we estimate multivariate nonlinear selection (i.e., the γ‐matrix) in the face of sampling error. To explore the sampling properties of estimated γ‐matrices, we simulated inidividual traits and fitness under a wide range of sample sizes, using different strengths of correlational selection and of stabilizing selection, combined with different number of traits under selection, different amounts of residual variance in fitness, and distinct patterns of selection. We then ran nonlinear regressions with these simulated datasets to simulate γ‐matrices after adding random error to individual fitness. To test how well could we detect the imposed pattern of correlational selection at different sample sizes, we measured the similarity between simulated and imposed γ‐matrices. We show that detection of the pattern of correlational selection is highly dependent on the total strength of selection on traits and on the amount of residual variance in fitness. Minimum sample size needs to be at least 500 to precisely estimate the pattern of correlational selection. Furthermore, a pattern of selection in which different sets of traits contribute to different functions is the easiest to diagnose, even when using a large number of traits (10 traits), but with sample sizes in the order of 1000 individuals. Consequently, we recommend working with sets of traits from distinct functional complexes and fitness proxies less prone to effects of environmental and demographic stochasticity to test for correlational selection with lower sample sizes. [ABSTRACT FROM AUTHOR]

Background: Vitamin A test results have historically been notorious for poor repeatability and reproducibility. This problem has been discussed at length in Association of American Feed Control Officials Laboratory Methods and Services Committee meetings. Objective: The objective of this work was to assess the effect of test portion mass on the repeatability of vitamin A test results. Methods: The study was conducted in two parts. In Part I, fundamental sampling error (FSE) was determined experimentally through replicated (n = 16) vitamin A testing of three animal feed materials. The testing followed rigorous test portion selection for 10 g and 100 g test portions. In Part II, FSE calculations were made (1) using theoretical equations based on vitamin A as a liberated analyte and (2) on representing the particles in feed materials. Particle size characterization of vitamin A ingredients was estimated by microscopy and further evaluated by particle size analysis. Results: RSDs, % for vitamin A determinations ranged from 10.5-24.7, and 2.26-10.7 for 10 g and 100 g test portions, respectively. FSE calculated for Ingredient A ranged from 18.3-101% and 5.79-32.0% for 10 g and 100 g test portions, respectively, and for Ingredient B, ranged from 10.2-56.2% and 3.21-17.8% for 10 g and 100 g test portions, respectively. Conclusion: Test portion mass has a substantial impact on FSE and is an important factor in controlling the random error in vitamin A testing. FSE equations are useful to approximate minimum test portion mass. Highlights: Vitamin A method development should use theoretical predictions and experimental verification to guide test portion mass. Strategies to deal with the larger test portion masses will be key to validating new methods. [ABSTRACT FROM AUTHOR]

We introduce Bilby-MCMC , a Markov chain Monte Carlo sampling algorithm tuned for the analysis of gravitational waves from merging compact objects. Bilby-MCMC provides a parallel-tempered ensemble Metropolis-Hastings sampler with access to a block-updating proposal library including problem-specific and machine learning proposals. We demonstrate that learning proposals can produce over a 10-fold improvement in efficiency by reducing the autocorrelation time. Using a variety of standard and problem-specific tests, we validate the ability of the Bilby-MCMC sampler to produce independent posterior samples and estimate the Bayesian evidence. Compared to the widely used Dynesty nested sampling algorithm, Bilby-MCMC is less efficient in producing independent posterior samples and less accurate in its estimation of the evidence. However, we find that posterior samples drawn from the Bilby-MCMC sampler are more robust: never failing to pass our validation tests. Meanwhile, the Dynesty sampler fails the difficult-to-sample Rosenbrock likelihood test, over constraining the posterior. For CBC problems, this highlights the importance of cross-sampler comparisons to ensure results are robust to sampling error. Finally, Bilby-MCMC can be embarrassingly and asynchronously parallelized making it highly suitable for reducing the analysis wall-time using a High Throughput Computing environment. Bilby-MCMC may be a useful tool for the rapid and robust analysis of gravitational-wave signals during the advanced detector era and we expect it to have utility throughout astrophysics. [ABSTRACT FROM AUTHOR]