Solving the Sample Size Problem for Resource Selection Analysis

Abstract

Sample size sufficiency is a critical consideration for conducting Resource-Selection Analyses (RSAs) from GPS-based animal telemetry. Cited thresholds for sufficiency include a number of captured animals M ≥ 30 and as many relocations per animal N as possible. These thresholds render many RSA-based studies misleading if large sample sizes were truly insufficient, or unpublishable if small sample sizes were sufficient but failed to meet reviewer expectations. We provide the first comprehensive solution for RSA sample size by deriving closed-form mathematical expressions for the number of animals M and the number of relocations per animal N required for model outputs to a given degree of precision. The sample sizes needed depend on just 2 biologically meaningful quantities: habitat selection strength and a novel measure of landscape complexity, which we define rigorously. The mathematical expressions are calculable for any environmental dataset at any spatial scale and are applicable to any study involving resource selection (including sessile organisms). We validate our analytical solutions using globally relevant empirical data including 5,678,623 GPS locations from 511 animals from 10 species (omnivores, carnivores, and herbivores living in boreal, temperate, and tropical forests, montane woodlands, swamps, and arctic tundra). Our analytic expressions show that the required M and N must decline with increasing selection strength and increasing landscape complexity, and this decline is insensitive to the definition of availability used in the analysis. Our results contradict conventional wisdom by demonstrating that the most biologically relevant effects on the utilization distribution (i.e. those landscape conditions with the greatest absolute magnitude of resource selection) can often be estimated with far fewer data than is commonly assumed. We identify several critical steps in implementing these equations, including (i) a priori selection of expected model coefficients, and (ii) sampling intensity for background (absence/pseudo-absence) data within a given definition of availability. We show that random sampling of background data violates the underlying mathematics of RSA, leading to incorrect values for necessary M and N and potentially incorrect RSA model outputs. We argue that these equations should be a mandatory component for all future RSA studies.

Roost Sites Influence Habitat Selection of Sandhill Cranes (Antigone canadensis tabida) in Arizona and California

“…While our sample size of Sandhill Cranes is small, based on Street et al . (2021) findings we feel the analysis conducted is appropriate and provides reliable inference to what habitats are important to LCRVP cranes particularly given the overall population size.…”

“…However, Street et al . (2021) found through their analysis that the most biologically relevant effects can often be estimated with only a few marked animals. They argue that it is feasible and demonstrable that consistent findings can be achieved with as few as 100 locations per animal and a minimum of two marked animals.…”

Integrated animal movement and spatial capture–recapture models: Simulation, implementation, and inference

“…In our simulations, there were approximately n = 28 individuals captured on average 12 times (which is equivalent to having 12 relocations per individual) in the scenarios with σ det = 0.1 and approximately n = 25 individuals captured on average five times when σ det = 0.05. Street et al ( 2021 ) showed that the required sample size in resource selection analyses is dependent on the strength of the selection and the landscape variation. Therefore, with additional habitat covariates or more complex movement models, auxiliary location data may become necessary to tease out the habitat selection coefficients.…”

“…This initial simulation study shows that the integrated Langevin–SCR model performs well under a specific set of conditions. Moving forward, there are some other questions that should be investigated such as the effect of landscape variation on required sample sizes (Street et al, 2021 ) and on the optimal grid layout (Dupont et al, 2020 ). It would also be valuable to directly compare the Langevin–SCR model to previous SCR–RSF models to evaluate potential strengths and weaknesses.…”