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Density-dependent feedback is recognized as important regulatory mechanisms of population size. Considering the spatial scales over which such feedback operates has advanced our theoretical understanding of metapopulation dynamics. Yet, metapopulation models are rarely fit to time-series data and tend to omit details of the natural history and behavior of long-lived, highly mobile species such as colonial mammals and birds. Seabird metapopulations consist of breeding colonies that are connected across large spatial scales, within a heterogeneous marine environment that is increasingly affected by anthropogenic disturbance. Currently, we know little about the strength and spatial scale of density-dependent regulation and connectivity between colonies. Thus, many important seabird conservation and management decisions rely on outdated assumptions of closed populations that lack density-dependent regulation. We investigated metapopulation dynamics and connectivity in an exemplar seabird species, the Northern gannet (Morus bassanus), using more than a century of census data of breeding colonies distributed across the Northeast Atlantic. We developed and fitted these data to a novel hierarchical Bayesian state-space model, to compare increasingly complex scenarios of metapopulation regulation through lagged, local, regional, and global density dependence, as well as different mechanisms for immigration. Models with conspecific attraction fit the data better than the equipartitioning of immigrants. Considering local and regional density dependence jointly improved model fit slightly, but importantly, future colony size projections based on different mechanistic regulatory scenarios varied widely: a model with local and regional dynamics estimated a lower metapopulation capacity (645,655 Apparently Occupied Site [AOS]) and consequently higher present saturation (63%) than a model with local density dependence (1,367,352 AOS, 34%). Our findings suggest that metapopulation regulation in the gannet is more complex than traditionally assumed, and highlight the importance of using models that consider colony connectivity and regional dynamics for conservation management applications guided by precautionary principles. Our study advances our understanding of metapopulation dynamics in long-lived colonial species and our approach provides a template for the development of metapopulation models for colonially living birds and mammals. connectivity, conspecific attraction, dispersal, immigration, latent process, long-term population monitoring, marine conservation, metapopulation dynamics, Monte Carlo Markov Chain, Morus bassanus, Northern gannet, regulatory feedback

A daily stochastic spatiotemporal precipitation generator that yields spatially consistent gridded quantitative precipitation realizations is described. The methodology relies on a latent Gaussian process to drive precipitation occurrence and a probability integral transformed Gaussian process for intensity. At individual locations, the model reduces to a Markov chain for precipitation occurrence and a gamma distribution for precipitation intensity, allowing statistical parameters to be included in a generalized linear model framework. Statistical parameters are modeled as spatial Gaussian processes, which allows for interpolation to locations where there are no direct observations via kriging. One advantage of such a model for the statistical parameters is that stochastic generator parameters are immediately available at any location, with the ability to adapt to spatially varying precipitation characteristics. A second advantage is that parameter uncertainty, generally unavailable with deterministic interpolators, can be immediately quantified at all locations. The methodology is illustrated on two data sets, the first in Iowa and the second over the Pampas region of Argentina. In both examples, the method is able to capture the local and domain aggregated precipitation behavior fairly well at a wide range of time scales, including daily, monthly, and annually. Key Points Transformed Gaussian processes give realistic spatial precipitation realizations Modelling parameters as processes produces uncertainty estimates at any location Simulations and parameters are available at locations without observational data

Background Modern developments in single-cell sequencing technologies enable broad insights into cellular state. Single-cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden our understanding of cellular heterogeneity in tissues and organs. Analysis of these sparse, high-dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-dimensional embeddings for filtered and normalized single-cell data. However, methods have yet to be developed for unfiltered and unnormalized count data that estimate uncertainty in the low-dimensional space. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-dimensional nonlinear structure in scRNA-seq data. Results Gene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student’s t-distribution to estimate a manifold that is robust to technical and biological noise found in normalized scRNA-seq data. We compare our approach to common dimension reduction tools across a diverse set of scRNA-seq data sets to highlight our model’s ability to enable important downstream tasks such as clustering, inferring cell developmental trajectories, and visualizing high throughput experiments on available experimental data. Conclusion We show that our adaptive robust statistical approach to estimate a nonlinear manifold is well suited for raw, unfiltered gene counts from high-throughput sequencing technologies for visualization, exploration, and uncertainty estimation of cell states.

Previous studies on the relationship between job insecurity and depressive symptoms have mainly focused on the stressor-to-strain effect from job insecurity to depressive symptoms, on rather secure and healthy employees, and on rank-order relationships. This is not entirely in line with stress theories suggesting intraindividual and reciprocal relationships between high levels of stressors and strain. In reply, this study investigated whether high levels of job insecurity were related to subsequent high levels of depressive symptoms, and vice versa. Cross-lagged dual process latent Markov model analysis with 3-wave data (time lags of 2 and 3 years) from a representative sample of the Norwegian working force (N = 2,539) revealed 5 latent states of job insecurity and 6 latent states of depressive symptoms. As hypothesized, a reciprocal relationship between the “high job insecurity” state and the “depressed” state was found: Previously highly job-insecure employees were more likely to be depressed at the next measurement point (OR = 42.54), and employees labeled as depressed were more likely to experience high job insecurity later on (OR = 69.92). This study contributes to stress theory by demonstrating that stressors and strain may relate differently depending on the level of stressor and strain experienced.

Quantification of precipitation extremes is important for flood planning purposes, and a common measure of extreme events is the r-year return level. We present a method for producing maps of precipitation return levels and uncertainty measures and apply it to a region in Colorado. Separate hierarchical models are constructed for the intensity and the frequency of extreme precipitation events. For intensity, we model daily precipitation above a high threshold at 56 weather stations with the generalized Pareto distribution. For frequency, we model the number of exceedances at the stations as binomial random variables. Both models assume that the regional extreme precipitation is driven by a latent spatial process characterized by geographical and climatological covariates. Effects not fully described by the covariates are captured by spatial structure in the hierarchies. Spatial methods were improved by working in a space with climatological coordinates. Inference is provided by a Markov chain Monte Carlo algorithm and spatial interpolation method, which provide a natural method for estimating uncertainty.

Background Along the southern shoreline of Lake Malawi, the incidence of schistosomiasis is increasing with snails of the genera Bulinus and Biomphalaria transmitting urogenital and intestinal schistosomiasis, respectively. Since the underlying distribution of snails is partially known, often being focal, developing pragmatic spatial models that interpolate snail information across under-sampled regions is required to understand and assess current and future risk of schistosomiasis. Methods A secondary geospatial analysis of recently collected malacological and environmental survey data was undertaken. Using a Bayesian Poisson latent Gaussian process model, abundance data were fitted for Bulinus and Biomphalaria . Interpolating the abundance of snails along the shoreline (given their relative distance along the shoreline) was achieved by smoothing, using extracted environmental rainfall, land surface temperature (LST), evapotranspiration, normalised difference vegetation index (NDVI) and soil type covariate data for all predicted locations. Our adopted model used a combination of two-dimensional (2D) and one dimensional (1D) mapping. Results A significant association between normalised difference vegetation index (NDVI) and abundance of Bulinus spp. was detected (log risk ratio − 0.83, 95% CrI − 1.57, − 0.09). A qualitatively similar association was found between NDVI and Biomphalaria sp. but was not statistically significant (log risk ratio − 1.42, 95% CrI − 3.09, 0.10). Analyses of all other environmental data were considered non-significant. Conclusions The spatial range in which interpolation of snail distributions is possible appears < 10km owing to fine-scale biotic and abiotic heterogeneities. The forthcoming challenge is to refine geospatial sampling frameworks with future opportunities to map schistosomiasis within actual or predicted snail distributions. In so doing, this would better reveal local environmental transmission possibilities. Graphical Abstract

Hidden Markov models (HMMs) are a useful tool for capturing the behavior of overdispersed, autocorrelated data. These models have been applied to many different problems, including speech recognition, precipitation modeling, and gene finding and profiling. Typically, HMMs are applied to individual stochastic processes; HMMs for simultaneously modeling multiple processes-as in the longitudinal data setting-have not been widely studied. In this article I present a new class of models, mixed HMMs (MHMMs), where I use both covariates and random effects to capture differences among processes. I define the models using the framework of generalized linear mixed models and discuss their interpretation. I then provide algorithms for parameter estimation and illustrate the properties of the estimators via a simulation study. Finally, to demonstrate the practical uses of MHMMs, I provide an application to data on lesion counts in multiple sclerosis patients. I show that my model, while parsimonious, can describe the heterogeneity among such patients.

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of N possible states. The states are loosely connected to behavioral modes that manifest themselves at the temporal resolution at which observations are made. Due to advances in tag technology and tracking with digital video recordings, data can be collected at increasingly fine temporal resolutions. Yet, inferences at time scales cruder than those at which data are collected and, which correspond to larger-scale behavioral processes, are not yet answered via HMMs. We include additional hierarchical structures to the basic HMM framework, incorporating multiple Markov chains at various time scales. The hierarchically structured HMMs allow for behavioral inferences at multiple time scales and can also serve as a means to avoid coarsening data. Our proposed framework is one of the first that models animal behavior simultaneously at multiple time scales, opening new possibilities in the area of animal movement and behavior modeling. We illustrate the application of hierarchically structured HMMs in two real-data examples: (i) vertical movements of harbor porpoises observed in the field, and (ii) garter snake movement data collected as part of an experimental design.

Background The bidirectional association of HIV/AIDS and Tuberculosis (TB) presents significant global health challenges. However, the relationship between these dual epidemics and the heterogeneity in their mortality rate patterns have not been properly addressed. Therefore, the aim of this study was to cluster and model the joint trajectories of HIV/AIDS and TB mortality rates from 1990 to 2021 worldwide. Methods In this longitudinal study, the HIV/AIDS and TB mortality rates data for 204 countries from 1990 to 2021 were obtained from the global burden of disease database. The longitudinal k-means clustering approach was utilized to categorize countries into homogeneous subgroups based on the joint patterns of HIV/AIDS and TB mortality rates. Subsequently, the Bayesian multi-process nonlinear Latent Growth Model (LGM) was conducted to concurrently estimate the patterns of HIV/AIDS and TB mortality rates. Results The average global TB mortality rates dropped from 30.61 to 13.34 per 100,000 between 1990 and 2021. Meanwhile, the average HIV/AIDS mortality rates rose from 10.94 to 48.42 per 100,000 by 2000 before declining to 16.90 per 100,000 in 2021. The Bayesian multi-process nonlinear LGM indicated that the intercepts for the overall HIV/AIDS and TB models were 11.168 and 30.184, and the slopes were 16.104 and − 1.040, respectively. This suggests that the initial HIV/AIDS and TB mortality rates were 11.168 and 30.184 persons per 100,000, and the rates of change were 16.104 and − 1.040 persons per 100,000 every five years. However, the strength and direction of the rate of change were dependent on the factor loading scores, as they exhibited a nonlinear trend. Finally, the 204 countries were clustered into three distinct subgroups, each with different intercepts and slopes. Cluster A demonstrated the lowest HIV/AIDS and TB mortality rates throughout the study, while Cluster C exhibited the highest mortality rates. Conclusions Although the overall global HIV/AIDS and TB mortality rates have declined, Southern African countries continue to bear a significant burden of HIV/AIDS and TB, with no significant reduction observed in TB mortality rates from 1990 to 2021. Therefore, prioritizing these countries is crucial to achieving the Sustainable Development Goals (SDGs) of eradicating the global HIV/AIDS and TB epidemics by 2030 and 2035, respectively.

A multimodal cyclic-label dequantized Gaussian process latent variable model (mCDGP) for visual emotion recognition is presented in this paper. Although the emotion is followed by various emotion models that describe cyclic interactions between them, they should be represented as precise labels respecting the emotions’ continuity. Traditional feature integration approaches, however, are incapable of reflecting circular structures to the common latent space. To address this issue, mCDGP uses the common latent space and the cyclic-label dequantization by maximizing the probability function utilizing the cyclic-label feature as one of the observed features. The likelihood maximization problem provides limits to preserve the emotions’ circular structures. Then mCDGP increases the number of dimensions of the common latent space by translating the rough label to the detailed one by label dequantization, with a focus on emotion continuity. Furthermore, label dequantization improves the ability to express label features by retaining circular structures, making accurate visual emotion recognition possible. The main contribution of this paper is the implementation of feature integration through the use of cyclic-label dequantization.