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A new permutation technique to explore and control for spatial autocorrelation

Radersma, Reinder LU and Sheldon, Ben C. (2015) In Methods in Ecology and Evolution 6(9). p.1026-1033
Abstract
1. Permutation tests are important in ecology and evolution as they enable robust analysis of small sample sizes and control for various forms of dependencies among observations. A common source of dependence is spatial autocorrelation. Accounting for spatial autocorrelation is often crucial, because many ecological and evolutionary processes are spatially restricted, such as gene flow, dispersal, mate choice, inter-and intraspecific competition, mutualism and predation. 2. Here we discuss various ways of controlling for spatial autocorrelation in permutation tests; we highlight their particular properties and assumptions and introduce a new permutation technique which explores and controls for spatial autocorrelation: the floating grid... (More)
1. Permutation tests are important in ecology and evolution as they enable robust analysis of small sample sizes and control for various forms of dependencies among observations. A common source of dependence is spatial autocorrelation. Accounting for spatial autocorrelation is often crucial, because many ecological and evolutionary processes are spatially restricted, such as gene flow, dispersal, mate choice, inter-and intraspecific competition, mutualism and predation. 2. Here we discuss various ways of controlling for spatial autocorrelation in permutation tests; we highlight their particular properties and assumptions and introduce a new permutation technique which explores and controls for spatial autocorrelation: the floating grid permutation technique (FGPT). 3. The FGPT is a method to randomize observations with known geographical locations. Within the randomization process, the probability an observation is assigned to any of the spatial locations is a negative function of the distance between its original and assigned location. The slope of this function depends on a preset parameter, and by exploring its parameter space, non-random ecological and evolutionary processes can be both assessed and controlled at multiple spatial scales. 4. We show that the FGPT has acceptable type-I-error rates. We applied the FGPT to simulated univariate and bivariate data sets in which both negative and positive spatial autocorrelation were present. In comparison with a method that uses eigenvector decomposition to separate negative from positive spatial autocorrelation, the FGPT performed better for negative spatial autocorrelation alone, equal for positive spatial autocorrelation alone and equal or slightly worse for simultaneous negative and positive spatial autocorrelation. For the bivariate data, it performed equally to a bootstrapping technique in which sampling probabilities were weighted by distance. The FGPT benefits from a large flexibility for application to bivariate (e.g. dyadic interactions) and multivariate observations (e.g. genetic marker-based relatedness measures) and has a large freedom in the choice of test statistic. It also has the potential to identify two spatial autocorrelation patterns, even if both result in positive spatial autocorrelation, given that they operate at different spatial scales. 5. The Floating Grid Permutation Technique is available as the R-package fgpt in CRAN. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
bootstrap, point pattern, population stratification, randomization, R-package, SNPs, spatial autocorrelation, spatial distribution, spatially restricted
in
Methods in Ecology and Evolution
volume
6
issue
9
pages
1026 - 1033
publisher
British Ecology Society / John Wiley & Sons, Inc.
external identifiers
  • wos:000362916100006
  • scopus:84941805514
ISSN
2041-210X
DOI
10.1111/2041-210X.12390
language
English
LU publication?
yes
id
3d97d7e2-b9ec-45dd-a0b4-73603541cf23 (old id 8206050)
date added to LUP
2015-11-26 15:30:17
date last changed
2017-01-01 06:04:43
@article{3d97d7e2-b9ec-45dd-a0b4-73603541cf23,
  abstract     = {1. Permutation tests are important in ecology and evolution as they enable robust analysis of small sample sizes and control for various forms of dependencies among observations. A common source of dependence is spatial autocorrelation. Accounting for spatial autocorrelation is often crucial, because many ecological and evolutionary processes are spatially restricted, such as gene flow, dispersal, mate choice, inter-and intraspecific competition, mutualism and predation. 2. Here we discuss various ways of controlling for spatial autocorrelation in permutation tests; we highlight their particular properties and assumptions and introduce a new permutation technique which explores and controls for spatial autocorrelation: the floating grid permutation technique (FGPT). 3. The FGPT is a method to randomize observations with known geographical locations. Within the randomization process, the probability an observation is assigned to any of the spatial locations is a negative function of the distance between its original and assigned location. The slope of this function depends on a preset parameter, and by exploring its parameter space, non-random ecological and evolutionary processes can be both assessed and controlled at multiple spatial scales. 4. We show that the FGPT has acceptable type-I-error rates. We applied the FGPT to simulated univariate and bivariate data sets in which both negative and positive spatial autocorrelation were present. In comparison with a method that uses eigenvector decomposition to separate negative from positive spatial autocorrelation, the FGPT performed better for negative spatial autocorrelation alone, equal for positive spatial autocorrelation alone and equal or slightly worse for simultaneous negative and positive spatial autocorrelation. For the bivariate data, it performed equally to a bootstrapping technique in which sampling probabilities were weighted by distance. The FGPT benefits from a large flexibility for application to bivariate (e.g. dyadic interactions) and multivariate observations (e.g. genetic marker-based relatedness measures) and has a large freedom in the choice of test statistic. It also has the potential to identify two spatial autocorrelation patterns, even if both result in positive spatial autocorrelation, given that they operate at different spatial scales. 5. The Floating Grid Permutation Technique is available as the R-package fgpt in CRAN.},
  author       = {Radersma, Reinder and Sheldon, Ben C.},
  issn         = {2041-210X},
  keyword      = {bootstrap,point pattern,population stratification,randomization,R-package,SNPs,spatial autocorrelation,spatial distribution,spatially restricted},
  language     = {eng},
  number       = {9},
  pages        = {1026--1033},
  publisher    = {British Ecology Society / John Wiley & Sons, Inc.},
  series       = {Methods in Ecology and Evolution},
  title        = {A new permutation technique to explore and control for spatial autocorrelation},
  url          = {http://dx.doi.org/10.1111/2041-210X.12390},
  volume       = {6},
  year         = {2015},
}