Is the Mantel correlogram powerful enough to be useful in ecological analysis? A simulation study

The Mantel correlogram is an elegant way to compute a correlogram for multivariate data. However, recent papers raised concerns about the power of the Mantel test itself. Hence the question: Is the Mantel correlogram powerful enough to be useful? To explore this issue, we compared the performances o...

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Bibliographic Details
Published in:Ecology (Durham) 2012-06, Vol.93 (6), p.1473-1481
Main Authors: Borcard, Daniel, Legendre, Pierre
Format: Article
Language:English
Subjects:
Animal and plant ecology
Animal, plant and microbial ecology
autocorrelation
Biological and medical sciences
Coefficients
Comparative analysis
Computer Simulation
Correlations
correlogram
data analysis
Data ranges
Data sampling
Datasets
Ecological genetics
Ecology
Ecosystem
Environmental Monitoring - methods
Fundamental and applied biological sciences. Psychology
Geary
General aspects
Mantel
Mantels
mathematical models
Models, Biological
Models, Statistical
Moran
multiscale ordination
Multivariate analysis
multivariate variogram
Simulation
simulation study
spatial correlation
Statistical variance
Statistics
Synecology
variance
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Summary:The Mantel correlogram is an elegant way to compute a correlogram for multivariate data. However, recent papers raised concerns about the power of the Mantel test itself. Hence the question: Is the Mantel correlogram powerful enough to be useful? To explore this issue, we compared the performances of the Mantel correlogram to those of other methods, using numerical simulations based on random, normally distributed data. For a single response variable, we compared it to the Moran and Geary correlograms. Type I error rates of the three methods were correct. Power of the Mantel correlogram was nearly as high as that of the univariate methods. For the multivariate case, the test of the multivariate variogram developed in the context of multiscale ordination is in fact a Mantel test, so that the power of the two methods is the same by definition. We devised an alternative permutation test based on the variance, which yielded similar results. Overall, the power of the Mantel test was high, the method successfully detecting spatial correlation at rates similar to the permutation test of the variance statistic in multivariate variograms. We conclude that the Mantel correlogram deserves its place in the ecologist's toolbox.
ISSN:0012-9658
1939-9170
DOI:10.1890/11-1737.1