Example of Mantel test to compare dissimilatry matrices

A Mantel test measures the correlation between two matrices typically containing measures of distance.  A Mantel test is one way of testing for spatial autocorrelation.

 Example of R code:

library("vegan")
library("fields")
library("sp")

 # Random points

 points <- as.matrix(data.frame(longitude=rnorm(20, 3, 2), latitude=rnorm(20, 23, 2)))
caracteristiques <- rnorm(20, 12, 3)

 plot(x=points[,"longitude"], y=points[, "latitude"], pch=19, cex=2*caracteristiques/max(caracteristiques))

 # matrice des distances euclidiennes de caractéristiques
disC <- rdist(x1=caracteristiques)
# Matrice de distances entre les points basée sur la distance terrestre
disL <- spDists(x=points, longlat = TRUE)

 plot(disL, disC)

 MT <- mantel(xdis=disC, ydis=disL, method="pearson", permutations=999)

 MT



# Generate relationship

 caracteristiques <- rnorm(20, points[,"latitude"]*points[,"longitude"], 3)

 plot(x=points[,"longitude"], y=points[, "latitude"], pch=19, cex=2*caracteristiques/max(caracteristiques))

 # matrice des différences de caractéristiques
disC <- rdist(x1=caracteristiques)

 disL <- spDists(x=points, longlat = TRUE)

 plot(disL, disC)

 MT <- mantel(xdis=disC, ydis=disL, method="pearson", permutations=999)

 MT

 # With the package ape

 library("ape")
MT <- mantel.test(m1=disC, m2=disL, nperm = 999, graph = TRUE)



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