SREL Reprint #3644

Solving the sample size problem for resource selection functions

Garrett M. Street1,2, Jonathan R. Potts3, Luca Börger4,5, James C. Beasley6, Stephen Demarais1, John M. Fryxell7, Philip D. McLoughlin8, Kevin L. Monteith9, Christina M. Prokopenko10, Miltinho C. Ribeiro11, Arthur R. Rodgers12, Bronson K. Strickland1, Floris M. van Beest13, David A. Bernasconi6, Larissa T. Beumer13, Guha Dharmarajan6, Samantha P. Dwinnell14, David A. Keiter6, Alexine Keuroghlian15, Levi J. Newediuk10, Júlia Emi F. Oshima11, Olin Rhodes Jr.6, Peter E. Schlichting6, Niels M. Schmidt13, and Eric Vander Wal10

1Department of Wildlife, Fisheries, and Aquaculture, Mississippi State University, Mississippi State, MS, USA 2Quantitative Ecology and Spatial Technologies Laboratory, Mississippi State University,
Mississippi State, MS, USA
3School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
4Department of Biosciences, Swansea University, Swansea, UK
5Centre for Biomathematics, Swansea University, Swansea, UK
6Savannah River Ecology Laboratory, University of Georgia, Aiken, SC, USA
7Department of Integrative Biology, University of Guelph, Guelph, ON, Canada
8Department of Biology, University of Saskatchewan, Saskatoon, SK, Canada
9Haub School of Environment and Natural Resources, University of Wyoming, Laramie, WY, USA
10Department of Biology, Memorial University of Newfoundland, St. John’s, NL, Canada
11Instituto de Biosciências, Universidad Estadual Paulista, Rio Claro, São Paulo, Brazil
12Centre for Northern Forest Ecosystem Research, Ontario Ministry of Natural Resources and Forestry,
ON, Canada
13Department of Bioscience, Aarhus University, Aarhus, Denmark
14Wyoming Cooperative Fish and Wildlife Research Unit, University of Wyoming, Laramie, WY, USA
15IUCN/SSC Peccary Specialist Group, Campo Grande, Brazil

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).
3. 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 demonstrate 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 much fewer than M = 30 animals.
4. We identify several critical steps in implementing these equations, including (a) a priori selection of expected model coefficients and (b) regular sampling of background (pseudoabsence) data within a given definition of availability. We discuss possible methods to identify a priori expectations for habitat selection coefficients, effects of scale on RSF estimation and caveats for rare species applications. We argue that these equations should be a mandatory component for all future RSF studies.

Keywords: bootstrap, habitat selection, p-value, power analysis, resource selection function, sample size, species distribution model, validation

SREL Reprint #3644

Street, G. M., J. R. Potts, L. Börger, J. C. Beasley, S. Demarais, J. M. Fryxell, P. D. McLoughlin, K. L. Monteith, C. M. Prokopenko, M. C. Ribeiro, A. R. Rodgers, B. K. Strickland, F. M. van Beest, D. A. Bernasconi, L. T. Beumer, G. Dharmarajan, S. P. Dwinnell, D. A. Keiter, A. Keuroghlian, L. J. Newediuk, J. E. F. Oshima, O.E. Rhodes Jr., P. E. Schlichting, N. M. Schmidt, and E. Vander Wal. 2021. Solving the sample size problem for resource selection functions. Methods in Ecology and Evolution 12(12): 2421-2431.

This information was provided by the University of Georgia's Savannah River Ecology Laboratory (srel.uga.edu).