Solving the sample size problem for resource selection functions

Sample size sufficiency is a critical consideration for estimating resource selection functions (RSFs) from GPS-based animal telemetry. Cited thresholds include number of captured animals and as many relocations per N possible. These render RSF-based studies misleading if large sample sizes were truly insufficient, or unpublishable small sufficient but failed to meet reviewer expectations. We provide the first comprehensive solution RSF by deriving closed-form mathematical expressions M required model outputs given degree precision. The needed depend on just 3 biologically meaningful quantities: habitat strength, variation in individual novel measure landscape complexity, which we define rigorously. are calculable any environmental dataset at spatial scale applicable study involving (including sessile organisms). validate our analytical solutions using globally relevant empirical data including 5,678,623 GPS locations 511 10 species (omnivores, carnivores herbivores living boreal, temperate tropical forests, montane woodlands, swamps Arctic tundra). Our analytic show that must decline with increasing strength this insensitive definition availability used analysis. results demonstrate most effects utilization distribution (i.e. those conditions greatest absolute magnitude selection) can often be estimated much fewer than animals. identify several steps implementing these equations, (a) priori expected coefficients (b) regular sampling background (pseudoabsence) within availability. discuss possible methods expectations coefficients, estimation caveats rare applications. argue equations should mandatory component all future studies.