The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor ) in Colorado, USA.
In spatial generalized linear mixed models (SGLMMs), covariates that are spatially smooth are often collinear with spatially smooth random effects. This phenomenon is known as spatial confounding and has been studied primarily in the case where the spatial support of the process being studied is discrete (e.g., areal spatial data). In this case, the most common approach suggested is restricted spatial regression (RSR) in which the spatial random effects are constrained to be orthogonal to the fixed effects. We consider spatial confounding and RSR in the geostatistical (continuous spatial support) setting. We show that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. We propose a posterior predictive approach to alleviating this potential problem and discuss the appropriateness of RSR in a variety of situations. We illustrate RSR and SGLMM approaches through simulation studies and an analysis of malaria frequencies in The Gambia, Africa. Copyright © 2015 John Wiley & Sons, Ltd.
Contemporary ecologists often find themselves with an overwhelming amount of data to analyze. For example, it is now possible to collect nearly continuous spatiotemporal data on animal locations via global positioning systems and other satellite telemetry technology. In addition, there is a wealth of readily available environmental data via geographic information systems and remote sensing. We present a modeling framework that utilizes these forms of data and builds on previous research pertaining to the quantitative analysis of animal movement. This approach provides additional insight into the environmental drivers of residence and movement as well as resource selection while accommodating path uncertainty. The methods are demonstrated in an application involving mule deer movement in the La Sal Range, Utah, USA. Supplemental materials for this article are available online.
Abstract. Ecological data often exhibit spatial pattern, which can be modeled as autocorrelation. Conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models are network-based models (also known as graphical models) specifically designed to model spatially autocorrelated data based on neighborhood relationships. We identify and discuss six different types of practical ecological inference using CAR and SAR models, including: (1) model selection, (2) spatial regression, (3) estimation of autocorrelation, (4) estimation of other connectivity parameters, (5) spatial prediction, and (6) spatial smoothing. We compare CAR and SAR models, showing their development and connection to partial correlations. Special cases, such as the intrinsic autoregressive model (IAR), are described. Conditional autoregressive and SAR models depend on weight matrices, whose practical development uses neighborhood definition and row-standardization. Weight matrices can also include ecological covariates and connectivity structures, which we emphasize, but have been rarely used. Trends in harbor seals (Phoca vitulina) in southeastern Alaska from 463 polygons, some with missing data, are used to illustrate the six inference types. We develop a variety of weight matrices and CAR and SAR spatial regression models are fit using maximum likelihood and Bayesian methods. Profile likelihood graphs illustrate inference for covariance parameters. The same data set is used for both prediction and smoothing, and the relative merits of each are discussed. We show the nonstationary variances and correlations of a CAR model and demonstrate the effect of row-standardization. We include several take-home messages for CAR and SAR models, including (1) choosing between CAR and IAR models, (2) modeling ecological effects in the covariance matrix, (3) the appeal of spatial smoothing, and (4) how to handle isolated neighbors. We highlight several reasons why ecologists will want to make use of autoregressive models, both directly and in hierarchical models, and not only in explicit spatial settings, but also for more general connectivity models.
Multiple factors complicate the analysis of animal telemetry location data. Recent advancements address issues such as temporal autocorrelation and telemetry measurement error, but additional challenges remain. Difficulties introduced by complicated error structures or barriers to animal movement can weaken inference. We propose an approach for obtaining resource selection inference from animal location data that accounts for complicated error structures, movement constraints, and temporally autocorrelated observations. We specify a model for telemetry data observed with error conditional on unobserved true locations that reflects prior knowledge about constraints in the animal movement process. The observed telemetry data are modeled using a flexible distribution that accommodates extreme errors and complicated error structures. Although constraints to movement are often viewed as a nuisance, we use constraints to simultaneously estimate and account for telemetry error. We apply the model to simulated data, showing that it outperforms common ad hoc approaches used when confronted with measurement error and movement constraints. We then apply our framework to an Argos satellite telemetry data set on harbor seals (Phoca vitulina) in the Gulf of Alaska, a species that is constrained to move within the marine environment and adjacent coastlines.
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