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

Borcard, Daniel
Legendre, Pierre
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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.
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Grassland Society of Southern Africa

The Grassland Society of Southern Africa (GSSA) is involved and concerned with the science and practice of range and pasture management. This broad field involves primarily the use and conservation of natural resources. It encompasses applied fields such as livestock production, wildlife management, nature conservation, water catchment management and range and mine-dump rehabilitation. The disciplines include, amongst others, ecology, botany zoology, range and pasture science, animal science, soil science and genetics. This collection includes journal articles from the African Journal of Range and Forage Science as well as related articles and reports from throughout the Southern African region.