An Application of Spatio-temporal Modeling to Finite Population Abundance Prediction

Spatio-temporal models can be used to analyze data collected at various spatial locations throughout multiple time points. However, even with a finite number of spatial locations, there may be a lack of resources to collect data from every spatial location at every time point. We develop a spatio-temporal finite-population block kriging (ST-FPBK) method to predict a quantity of interest, such as a mean or total, across a finite number of spatial locations. This ST-FPBK predictor incorporates an appropriate variance reduction for sampling from a finite population. Through an application to moose surveys in the east-central region of Alaska, we show that the predictor has a substantially smaller standard error compared to a predictor from the purely spatial model that is currently used to analyze moose surveys in the region. We also show how the model can be used to forecast a prediction for abundance in a time point for which spatial locations have not yet been surveyed. A separate simulation study shows that the spatio-temporal predictor is unbiased and that prediction intervals from the ST-FPBK predictor attain appropriate coverage. For ecological monitoring surveys completed with some regularity through time, use of ST-FPBK could improve precision. We also give an R package that ecologists and resource managers could use to incorporate data from past surveys in predicting a quantity from a current survey.

Snapshot Wisconsin: networking community scientists and remote sensing to improve ecological monitoring and management

Biological data collection is entering a new era. Community science, satellite remote sensing (SRS), and local forms of remote sensing (e.g., camera traps and acoustic recordings) have enabled biological data to be collected at unprecedented spatial and temporal scales and resolution. There is growing interest in developing observation networks to collect and synthesize data to improve broad-scale ecological monitoring, but no examples of such networks have emerged to inform decision-making by agencies. Here, we present the implementation of one such jurisdictional observation network (JON), Snapshot Wisconsin, which links synoptic environmental data derived from SRS to biodiversity observations collected continuously from a trail camera network to support management decision-making. We use several examples to illustrate that Snapshot Wisconsin improves the spatial, temporal, and biological resolution and extent of information available to support management, filling gaps associated with traditional monitoring and enabling consideration of new management strategies. JONs like Snapshot Wisconsin further strengthen monitoring inference by contributing novel lines of evidence useful for corroboration or integration. SRS provides environmental context that facilitates inference, prediction, and forecasting, and ultimately helps managers formulate, test, and refine conceptual models for the monitored systems. Although these approaches pose challenges, Snapshot Wisconsin demonstrates that expansive observation networks can be tractably managed by agencies to support decision making, providing a powerful new tool for agencies to better achieve their missions and reshape the nature of environmental decision-making.

Aerial survey estimates of polar bears and their tracks in the Chukchi Sea

Polar bears are of international conservation concern due to climate change but are difficult to study because of low densities and an expansive, circumpolar distribution. In a collaborative U.S.-Russian effort in spring of 2016, we used aerial surveys to detect and estimate the abundance of polar bears on sea ice in the Chukchi Sea. Our surveys used a combination of thermal imagery, digital photography, and human observations. Using spatio-temporal statistical models that related bear and track densities to physiographic and biological covariates (e.g., sea ice extent, resource selection functions derived from satellite tags), we predicted abundance and spatial distribution throughout our study area. Estimates of 2016 abundance ([Formula: see text]) ranged from 3,435 (95% CI: 2,300-5,131) to 5,444 (95% CI: 3,636-8,152) depending on the proportion of bears assumed to be missed on the transect line during Russian surveys (g(0)). Our point estimates are larger than, but of similar magnitude to, a recent estimate for the period 2008-2016 ([Formula: see text]; 95% CI 1,522-5,944) derived from an integrated population model applied to a slightly smaller area. Although a number of factors (e.g., equipment issues, differing platforms, low sample sizes, size of the study area relative to sampling effort) required us to make a number of assumptions to generate estimates, it establishes a useful lower bound for abundance, and suggests high spring polar bear densities on sea ice in Russian waters south of Wrangell Island. With future improvements, we suggest that springtime aerial surveys may represent a plausible avenue for studying abundance and distribution of polar bears and their prey over large, remote areas.

Estimating range expansion of wildlife in heterogeneous landscapes: A spatially explicit state-space matrix model coupled with an improved numerical integration technique

Dispersal as well as population growth is a key demographic process that determines population dynamics. However, determining the effects of environmental covariates on dispersal from spatial-temporal abundance proxy data is challenging owing to the complexity of model specification for directional dispersal permeability and the extremely high computational loads for numerical integration. In this paper, we present a case study estimating how environmental covariates affect the dispersal of Japanese sika deer by developing a spatially explicit state-space matrix model coupled with an improved numerical integration technique (Markov chain Monte Carlo with particle filters). In particular, we explored the environmental drivers of inhomogeneous range expansion, characteristic of animals with short dispersal. Our model framework successfully reproduced the complex population dynamics of sika deer, including rapid changes in densely populated areas and distribution fronts within a decade. Furthermore, our results revealed that the inhomogeneous range expansion of sika deer seemed to be primarily caused by the dispersal process (i.e., movement barriers in fragmented forests) rather than population growth. Our state-space matrix model enables the inference of population dynamics for a broad range of organisms, even those with low dispersal ability, in heterogeneous landscapes, and could address many pressing issues in conservation biology and ecosystem management.

Black swans in space: modeling spatiotemporal processes with extremes

In ecological systems, extremes can happen in time, such as population crashes, or in space, such as rapid range contractions. However, current methods for joint inference about temporal and spatial dynamics (e.g., spatiotemporal modeling with Gaussian random fields) may perform poorly when underlying processes include extreme events. Here we introduce a model that allows for extremes to occur simultaneously in time and space. Our model is a Bayesian predictive-process GLMM (generalized linear mixed-effects model) that uses a multivariate-t distribution to describe spatial random effects. The approach is easily implemented with our flexible R package glmmfields. First, using simulated data, we demonstrate the ability to recapture spatiotemporal extremes, and explore the consequences of fitting models that ignore such extremes. Second, we predict tree mortality from mountain pine beetle (Dendroctonus ponderosae) outbreaks in the U.S. Pacific Northwest over the last 16 yr. We show that our approach provides more accurate and precise predictions compared to traditional spatiotemporal models when extremes are present. Our R package makes these models accessible to a wide range of ecologists and scientists in other disciplines interested in fitting spatiotemporal GLMMs, with and without extremes.

A geostatistical state-space model of animal densities for stream networks

Population dynamics are often correlated in space and time due to correlations in environmental drivers as well as synchrony induced by individual dispersal. Many statistical analyses of populations ignore potential autocorrelations and assume that survey methods (distance and time between samples) eliminate these correlations, allowing samples to be treated independently. If these assumptions are incorrect, results and therefore inference may be biased and uncertainty underestimated. We developed a novel statistical method to account for spatiotemporal correlations within dendritic stream networks, while accounting for imperfect detection in the surveys. Through simulations, we found this model decreased predictive error relative to standard statistical methods when data were spatially correlated based on stream distance and performed similarly when data were not correlated. We found that increasing the number of years surveyed substantially improved the model accuracy when estimating spatial and temporal correlation coefficients, especially from 10 to 15 yr. Increasing the number of survey sites within the network improved the performance of the nonspatial model but only marginally improved the density estimates in the spatiotemporal model. We applied this model to brook trout data from the West Susquehanna Watershed in Pennsylvania collected over 34 yr from 1981 to 2014. We found the model including temporal and spatiotemporal autocorrelation best described young of the year (YOY) and adult density patterns. YOY densities were positively related to forest cover and negatively related to spring temperatures with low temporal autocorrelation and moderately high spatiotemporal correlation. Adult densities were less strongly affected by climatic conditions and less temporally variable than YOY but with similar spatiotemporal correlation and higher temporal autocorrelation.

The basis function approach for modeling autocorrelation in ecological data

Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many seemingly disparate statistical methods used to account for autocorrelation can be expressed as regression models that include basis functions. Basis functions also enable ecologists to modify a wide range of existing ecological models in order to account for autocorrelation, which can improve inference and predictive accuracy. Furthermore, understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of collinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.

An integrated data model to estimate spatiotemporal occupancy, abundance, and colonization dynamics

Ecological invasions and colonizations occur dynamically through space and time. Estimating the distribution and abundance of colonizing species is critical for efficient management or conservation. We describe a statistical framework for simultaneously estimating spatiotemporal occupancy and abundance dynamics of a colonizing species. Our method accounts for several issues that are common when modeling spatiotemporal ecological data including multiple levels of detection probability, multiple data sources, and computational limitations that occur when making fine-scale inference over a large spatiotemporal domain. We apply the model to estimate the colonization dynamics of sea otters (Enhydra lutris) in Glacier Bay, in southeastern Alaska.