Solving the sample size problem for resource selection functions

Abstract

1. Sample size sufficiency is a critical consideration for estimating resource selection functions (RSFs) 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 RSF-based studies misleading if large sample sizes were truly insufficient, or unpublishable if small sample sizes were sufficient but failed to meet reviewer expectations.2. We provide the first comprehensive solution for RSF 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 3 biologically meaningful quantities: habitat selection strength, variation in individual selection 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).

Heterogeneity in risk‐sensitive allocation of somatic reserves in a long‐lived mammal

“…We randomly selected 2 locations/day for each sheep to create a balanced sample size across individuals. We excluded sheep with fewer than 30 GPS locations during a season (Street et al, 2021). We calculated seasonal home ranges as 75% kernel density utilization distributions using a 250‐m resolution for each sheep using the adehabitatHR package (Calenge, 2006).…”

Mitigating pseudoreplication and bias in resource selection functions with autocorrelation-informed weighting

“…In other words, increasing the rate of animal locations should cause the confidence intervals estimated using IID RSFs to become narrower (because increasing autocorrelation in the data causes pseudoreplication) but have no effect on weighted RSF confidence intervals (because autocorrelation is explicitly modeled and accounted for). Third, we can demonstrate that the amount of spatial auto-correlation in habitat covariates—which is known to influence RSF parameter estimates (Northrup et al ., 2013, Street et al ., 2021)—also influences differences between weighted RSF and IID RSF parameter estimates. In this case, as more consecutive locations occur within a single habitat type, the average weights of locations in the habitat type with frequent triangulation failure become larger, allowing the model to reduce the influence of the habitat-specific sampling intervals on parameter estimates.…”

Guidelines for Telemetry Studies on Snow Leopards

“…However, this approach ignores the principle of reduction, puts animals at higher risk levels than necessary, and jeopardizes limited resources [14]. For example, empirical and mathematical evidence suggest that, with respect to resource selection (a) common subject for telemetry studies; [23]), reasonably precise and accurate estimates of population-level parameters may be generated from far fewer individuals than is typically assumed, particularly if resource selection is strong and landscapes are complex [24], as is likely the case for snow leopards across much of their distribution. Nonetheless, a standard baseline of scientific rigor in research will require that any valid collar-based study deploys collars on multiple individuals.…”

“…Except for idiosyncratic and extraordinary circumstances where the objective is to describe or monitor the behavior of a single individual, even a pilot study will require that at least two individuals are monitored. Researchers interested in resource selection can use the closed-form expressions of Street et al [24] to estimate how many animals and location fixes are necessary to detect expected selection patterns. Given the substantial effort required for capturing individuals of most felid species, it is reasonable to expect that inference at ecological scales of interest to research and conservation will require a multi-year effort to acquire sufficient sample sizes.…”