Using spatiotemporal statistical models to estimate animal abundance and infer ecological dynamics from survey counts

Abstract

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal (Phoca largha) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.

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

“…We chose a reflective boundary condition for considering dispersal probability across the edge of our study area (Conn et al, 2015;Williams et al, 2017). As most elements of the shortterm movement probability are zero, the annual dispersal probability can be efficiently calculated by sparse matrix implementation.…”

Estimating occupancy and abundance using aerial images with imperfect detection

“…Aerial images improve perception bias, but not necessarily availability bias (Bayliss & Yeomans, ; Frederick, Hylton, Heath, & Ruane, ; Gibbs, Woodward, Hunter, & Hutchinson, ; Leonard & Fish, ). For example, many seabirds and marine mammals are virtually certain to be detected in images if they are at the surface of the water, but animals may be diving beneath the surface of the water and unavailable to be photographed (Buckland et al., ; Conn et al., ). Aerial images alone typically do not provide sufficient information for estimating availability, and auxiliary information is usually required to estimate absolute abundance.…”

“…Aerial images alone typically do not provide sufficient information for estimating availability, and auxiliary information is usually required to estimate absolute abundance. For example, activity budgets or time spent diving underwater can be estimated from telemetry devices including VHF transmitters, satellite‐linked transmitters, or time‐depth recorders (Bechet et al., ; Conn et al., ; Heide‐Jørgensen, Laidre, Borchers, Samarra, & Stern, ). Often, aerial image data are easily obtainable, but auxiliary data may be more challenging to acquire due to financial, logistical, or regulatory constraints, precluding estimation of availability.…”

Black swans in space: modeling spatiotemporal processes with extremes

“…, Conn et al. ). Spatiotemporal models have also been widely used in other disciplines, including applications to weather, remote sensing, human disease dynamics, and crime (Cressie and Wikle ).…”