A new permutation technique to explore and control for spatial autocorrelation

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.