Solving the sample size problem for resource selection functions

TY - JOUR

T1 - Solving the sample size problem for resource selection functions

AU - Street, Garrett M.

AU - Potts, Jonathan R.

AU - Börger, Luca

AU - Beasley, James C.

AU - Demarais, Stephen

AU - Fryxell, John M.

AU - McLoughlin, Philip D.

AU - Monteith, Kevin L.

AU - Prokopenko, Christina M.

AU - Ribeiro, Miltinho C.

AU - Rodgers, Arthur R.

AU - Strickland, Bronson K.

AU - van Beest, Floris M.

AU - Bernasconi, David A.

AU - Beumer, Larissa T.

AU - Dharmarajan, Guha

AU - Dwinnell, Samantha P.

AU - Keiter, David A.

AU - Keuroghlian, Alexine

AU - Newediuk, Levi J.

AU - Oshima, Júlia Emi F.

AU - Rhodes, Olin

AU - Schlichting, Peter E.

AU - Schmidt, Niels M.

AU - Vander Wal, Eric

N1 - Publisher Copyright: © 2021 British Ecological Society

PY - 2021/12

Y1 - 2021/12

N2 - 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 (Formula presented.) 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. 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). 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 (Formula presented.) animals. 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.

AB - 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 (Formula presented.) 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. 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). 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 (Formula presented.) animals. 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.

KW - bootstrap

KW - habitat selection

KW - p-value

KW - power analysis

KW - resource selection function

KW - sample size

KW - species distribution model

KW - validation

UR - http://www.scopus.com/inward/record.url?scp=85113732445&partnerID=8YFLogxK

U2 - 10.1111/2041-210X.13701

DO - 10.1111/2041-210X.13701

M3 - Journal article

AN - SCOPUS:85113732445

SN - 2041-210X

VL - 12

SP - 2421

EP - 2431

JO - Methods in Ecology and Evolution

JF - Methods in Ecology and Evolution

IS - 12

ER -