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

Area of Science:

• Ecology
• Spatial Statistics
• Multivariate Data Analysis

Background:

• The Mantel correlogram is a method for analyzing multivariate spatial data.
• Concerns have been raised regarding the statistical power of the Mantel test.
• The utility of the Mantel correlogram in ecological research is questioned.

Purpose of the Study:

• To evaluate the statistical power of the Mantel correlogram.
• To compare its performance against alternative methods for spatial correlation analysis.
• To determine if the Mantel correlogram is a sufficiently powerful tool for ecological applications.

Main Methods:

• Numerical simulations using random, normally distributed data.
• Comparison of Mantel correlogram with Moran and Geary correlograms for univariate data.
• Assessment of multivariate variogram tests and a novel permutation test based on variance.

Main Results:

• The Mantel test exhibited correct Type I error rates across comparisons.
• The Mantel correlogram demonstrated high statistical power, nearly matching univariate methods.
• In multivariate scenarios, its power was equivalent to related multiscale ordination techniques and a variance-based permutation test.

Conclusions:

• The Mantel correlogram is a powerful method for detecting spatial correlation.
• Its performance is comparable to established univariate and multivariate techniques.
• The Mantel correlogram is a reliable and recommended tool for ecological spatial analysis.