PARENT SESSION
Special Session 8: Spatial statistics at multiple scales
Organized by: P Legendre and M Fortin
Tuesday, August 9, 8:00 AM - 11:30 AM, Exhibit Hall 210a-e, Level 2, Palais des congrès de Montréal
Using distance-based eigenvector maps (DBEM) in multivariate variation partitioning. Part 2: An adjusted bimultivariate redundancy statistic to replace the traditional but biased R-square.
Legendre, Pierre*,1, Peres-Neto, Pedro1, 1 Département de sciences biologiques, Montréal, Québec, Canada
ABSTRACT- PCNM analysis, which is a form of distance-based eigenvector maps (DBEM), was developed to analyze species-environment relationships at multiple spatial or temporal scales. In this paper, we will first show that canonical variation partitioning provides a correct partitioning of the variation of a response data table Y between sets of environmental and spatial (e.g., PCNM) explanatory variables. Using simulations, we will show that the test of significance used to test the fractions of variation has correct type I error. The power to detect spatial structures depends on the type of spatial structure present in the data and on the representation of the spatial relationships used in the analysis. In our simulations, PCNM base functions had higher power than trend surface analysis or Mantel tests for the detection of spatial autocorrelation in species data. We will derive Miller's (1975) bimultivariate redundancy statistic R2Y∼X which is the canonical equivalent of the coefficient of determination (R2) used in multiple regression. Using simulations, we will show that R2Y∼X provides a biased estimate of the proportion of variation of Y really explained by X. Traditionally, variation partitioning results have been based on this biased form. We will describe an adjusted form of R2Y∼X and show, using simulations, that it provides an unbiased estimate of the X. We will show that variation partitioning can be computed using the adjusted bimultivariate redundancy statistic.
Key words: bimultivariate redundancy statistic, principal coordinates of neighbor matrices, distance-based eigenvector maps, R-square