Energetic trade-offs in migration decision-making, reproductive effort and subsequent parental care in a long-distance migratory bird.

Migratory species trade-off long-distance movement with survival and reproduction, but the spatio-temporal scales at which these decisions occur are relatively unknown. Technological and statistical advances allow fine-scale study of animal decision-making, improving our understanding of possible causes and therefore conservation management. We quantified effects of reproductive preparation during spring migration on subsequent breeding outcomes, breeding outcomes on autumn migration characteristics and autumn migration characteristics on subsequent parental survival in Greenland white-fronted geese (Anser albifrons flavirostris). These are long-distance migratory birds with an approximately 50% population decline from 1999 to 2022. We deployed GPS-acceleration devices on adult females to quantify up to 5 years of individual decision-making throughout the annual cycle. Weather and habitat-use affected time spent feeding and overall dynamic body acceleration (i.e. energy expenditure) during spring and autumn. Geese that expended less energy and fed longer during spring were more likely to successfully reproduce. Geese with offspring expended more energy and fed for less time during autumn, potentially representing adverse fitness consequences of breeding. These behavioural comparisons among Greenland white-fronted geese improve our understanding of fitness trade-offs underlying abundance. We provide a reproducible framework for full annual cycle modelling using location and behaviour data, applicable to similarly studied migratory animals.

Associations between rurality and regional differences in sociodemographic factors and the 1918-20 influenza and 2020-21 COVID-19 pandemics in Missouri counties: An ecological study.

This study compares pandemic experiences of Missouri's 115 counties based on rurality and sociodemographic characteristics during the 1918-20 influenza and 2020-21 COVID-19 pandemics. The state's counties and overall population distribution have remained relatively stable over the last century, which enables identification of long-lasting pandemic attributes. Sociodemographic data available at the county level for both time periods were taken from U.S. census data and used to create clusters of similar counties. Counties were also grouped by rural status (RSU), including fully (100%) rural, semirural (1-49% living in urban areas), and urban (>50% of the population living in urban areas). Deaths from 1918 through 1920 were collated from the Missouri Digital Heritage database and COVID-19 cases and deaths were downloaded from the Missouri COVID-19 dashboard. Results from sociodemographic analyses indicate that, during both time periods, average farm value, proportion White, and literacy were the most important determinants of sociodemographic clusters. Furthermore, the Urban/Central and Southeastern regions experienced higher mortality during both pandemics than did the North and South. Analyses comparing county groups by rurality indicated that throughout the 1918-20 influenza pandemic, urban counties had the highest and rural had the lowest mortality rates. Early in the 2020-21 COVID-19 pandemic, urban counties saw the most extensive epidemic spread and highest mortality, but as the epidemic progressed, cumulative mortality became highest in semirural counties. Additional results highlight the greater effects both pandemics had on county groups with lower rates of education and a lower proportion of Whites in the population. This was especially true for the far southeastern counties of Missouri ("the Bootheel") during the COVID-19 pandemic. These results indicate that rural-urban and socioeconomic differences in health outcomes are long-standing problems that continue to be of significant importance, even though the overall quality of health care is substantially better in the 21st century.

Excursions in the Bayesian treatment of model error.

Advances in observational and computational assets have led to revolutions in the range and quality of results in many science and engineering settings. However, those advances have led to needs for new research in treating model errors and assessing their impacts. We consider two settings. The first involves physically-based statistical models that are sufficiently manageable to allow incorporation of a stochastic "model error process". In the second case we consider large-scale models in which incorporation of a model error process and updating its distribution is impractical. Our suggestion is to treat dimension-reduced model output as if it is observational data, with a data model that incorporates a bias component to represent the impacts of model error. We believe that our suggestions are valuable quantitative, yet relatively simple, ways to extract useful information from models while including adjustment for model error. These ideas are illustrated and assessed using an application inspired by a classical oceanographic problem.

An illustration of model agnostic explainability methods applied to environmental data.

Historically, two primary criticisms statisticians have of machine learning and deep neural models is their lack of uncertainty quantification and the inability to do inference (i.e., to explain what inputs are important). Explainable AI has developed in the last few years as a sub-discipline of computer science and machine learning to mitigate these concerns (as well as concerns of fairness and transparency in deep modeling). In this article, our focus is on explaining which inputs are important in models for predicting environmental data. In particular, we focus on three general methods for explainability that are model agnostic and thus applicable across a breadth of models without internal explainability: "feature shuffling", "interpretable local surrogates", and "occlusion analysis". We describe particular implementations of each of these and illustrate their use with a variety of models, all applied to the problem of long-lead forecasting monthly soil moisture in the North American corn belt given sea surface temperature anomalies in the Pacific Ocean.

Joint use of location and acceleration data reveals influences on transitions among habitats in wintering birds.

Quantifying relationships between animal behavior and habitat use is essential to understanding animal decision-making. High-resolution location and acceleration data allows unprecedented insights into animal movement and behavior. These data types allow researchers to study the complex linkages between behavioral plasticity and habitat distribution. We used a novel Markov model in a Bayesian framework to quantify the influence of behavioral state frequencies and environmental variables on transitions among landcover types through joint use of location and tri-axial accelerometer data. Data were collected from 56 greater white-fronted geese (Anser albifrons frontalis) across seven ecologically distinct winter regions over two years in midcontinent North America. We showed that goose decision-making varied across landcover types, ecoregions, and abiotic conditions, and was influenced by behavior. We found that time spent in specific behaviors explained variation in the probability of transitioning among habitats, revealing unique behavioral responses from geese among different habitats. Combining GPS and acceleration data allowed unique study of potential influences of an ongoing large-scale range shift in the wintering distribution of a migratory bird across midcontinent North America. We anticipate that behavioral adaptations among variable landscapes is a likely mechanism explaining goose use of highly variable ecosystems during winter in ways which optimize their persistence.

Time-varying effects of local weather on behavior and probability of breeding deferral in two Arctic-nesting goose populations.

Arctic-nesting geese face energetic challenges during spring migration, including ecological barriers and weather conditions (e.g., precipitation and temperature), which in long-lived species can lead to a trade-off to defer reproduction in favor of greater survival. We used GPS location and acceleration data collected from 35 greater white-fronted geese of the North American midcontinent and Greenland populations at spring migration stopovers, and novel applications of Bayesian dynamic linear models to test daily effects of minimum temperature and precipitation on energy expenditure (i.e., overall dynamic body acceleration, ODBA) and proportion of time spent feeding (PTF), then examined the daily and additive importance of ODBA and PTF on probability of breeding deferral using stochastic antecedent models. We expected distinct responses in behavior and probability of breeding deferral between and within populations due to differences in stopover area availability. Time-varying coefficients of weather conditions were variable between ODBA and PTF, and often did not show consistent patterns among birds, indicating plasticity in how individuals respond to conditions. An increase in antecedent ODBA was associated with a slightly increased probability of deferral in midcontinent geese but not Greenland geese. Probability of deferral decreased with increased PTF in both populations. We did not detect any differentially important time periods. These results suggest either that movements and behavior throughout spring migration do not explain breeding deferral or that ecological linkages between bird decisions during spring and subsequent breeding deferral were different between populations and across migration but occurred at different time scales than those we examined.

Artificial Intelligence to Aid Glaucoma Diagnosis and Monitoring: State of the Art and New Directions.

Recent developments in the use of artificial intelligence in the diagnosis and monitoring of glaucoma are discussed. To set the context and fix terminology, a brief historic overview of artificial intelligence is provided, along with some fundamentals of statistical modeling. Next, recent applications of artificial intelligence techniques in glaucoma diagnosis and the monitoring of glaucoma progression are reviewed, including the classification of visual field images and the detection of glaucomatous change in retinal nerve fiber layer thickness. Current challenges in the direct application of artificial intelligence to further our understating of this disease are also outlined. The article also discusses how the combined use of mathematical modeling and artificial intelligence may help to address these challenges, along with stronger communication between data scientists and clinicians.

Ecological Dynamics: Integrating Empirical, Statistical, and Analytical Methods.

Understanding ecological processes and predicting long-term dynamics are ongoing challenges in ecology. To address these challenges, we suggest an approach combining mathematical analyses and Bayesian hierarchical statistical modeling with diverse data sources. Novel mathematical analysis of ecological dynamics permits a process-based understanding of conditions under which systems approach equilibrium, experience large oscillations, or persist in transient states. This understanding is improved by combining ecological models with empirical observations from a variety of sources. Bayesian hierarchical models explicitly couple process-based models and data, yielding probabilistic quantification of model parameters, system characteristics, and associated uncertainties. We outline relevant tools from dynamical analysis and hierarchical modeling and argue for their integration, demonstrating the value of this synthetic approach through a simple predator-prey example.

Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data.

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. Recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications.

A hierarchical spatiotemporal analog forecasting model for count data.

Analog forecasting is a mechanism-free nonlinear method that forecasts a system forward in time by examining how past states deemed similar to the current state moved forward. Previous applications of analog forecasting has been successful at producing robust forecasts for a variety of ecological and physical processes, but it has typically been presented in an empirical or heuristic procedure, rather than as a formal statistical model. The methodology presented here extends the model-based analog method of McDermott and Wikle (Environmetrics, 27, 2016, 70) by placing analog forecasting within a fully hierarchical statistical framework that can accommodate count observations. Using a Bayesian approach, the hierarchical analog model is able to quantify rigorously the uncertainty associated with forecasts. Forecasting waterfowl settling patterns in the northwestern United States and Canada is conducted by applying the hierarchical analog model to a breeding population survey dataset. Sea surface temperature (SST) in the Pacific Ocean is used to help identify potential analogs for the waterfowl settling patterns.

A two-species occupancy model accommodating simultaneous spatial and interspecific dependence.

Occupancy models are popular for estimating the probability a site is occupied by a species of interest when detection is imperfect. Occupancy models have been extended to account for interacting species and spatial dependence but cannot presently allow both factors to act simultaneously. We propose a two-species occupancy model that accommodates both interspecific and spatial dependence. We use a point-referenced multivariate hierarchical spatial model to account for both spatial and interspecific dependence. We model spatial random effects with predictive process models and use probit regression to improve efficiency of posterior sampling. We model occupancy probabilities of red fox (Vulpes vulpes) and coyote (Canis latrans) with camera trap data collected from six mid-Atlantic states in the eastern United States. We fit four models comprising a fully factorial combination of spatial and interspecific dependence to two-thirds of camera trapping sites and validated models with the remaining data. Red fox and coyotes each exhibited spatial dependence at distances > 0.8 and 0.4 km, respectively, and exhibited geographic variation in interspecific dependence. Consequently, predictions from the model assuming simultaneous spatial and interspecific dependence best matched test data observations. This application highlights the utility of simultaneously accounting for spatial and interspecific dependence.

Modeling complex phenotypes: generalized linear models using spectrogram predictors of animal communication signals.

A major goal of evolutionary biology is to understand the dynamics of natural selection within populations. The strength and direction of selection can be described by regressing relative fitness measurements on organismal traits of ecological significance. However, many important evolutionary characteristics of organisms are complex, and have correspondingly complex relationships to fitness. Secondary sexual characteristics such as mating displays are prime examples of complex traits with important consequences for reproductive success. Typically, researchers atomize sexual traits such as mating signals into a set of measurements including pitch and duration, in order to include them in a statistical analysis. However, these researcher-defined measurements are unlikely to capture all of the relevant phenotypic variation, especially when the sources of selection are incompletely known. In order to accommodate this complexity we propose a Bayesian dimension-reduced spectrogram generalized linear model that directly incorporates representations of the entire phenotype (one-dimensional acoustic signal) into the model as a predictor while accounting for multiple sources of uncertainty. The first stage of dimension reduction is achieved by treating the spectrogram as an "image" and finding its corresponding empirical orthogonal functions. Subsequently, further dimension reduction is accomplished through model selection using stochastic search variable selection. Thus, the model we develop characterizes key aspects of the acoustic signal that influence sexual selection while alleviating the need to extract higher-level signal traits a priori. This facet of our approach is fundamental and has the potential to provide additional biological insight, as is illustrated in our analysis.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling.

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Hierarchical spatiotemporal matrix models for characterizing invasions.

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.