mantel.correlog {vegan} R Documentation

## Mantel Correlogram

### Description

Function mantel.correlog computes a multivariate Mantel correlogram. Proposed by Sokal (1986) and Oden and Sokal (1986), the method is also described in Legendre and Legendre (1998, pp. 736-738).

### Usage

mantel.correlog(D.eco, D.geo=NULL, XY=NULL, n.class=0, break.pts=NULL,
cutoff=TRUE, r.type="pearson", nperm=999, mult="holm", progressive=TRUE)
## S3 method for class 'mantel.correlog':
plot(x, alpha=0.05, ...)

### Arguments

 D.eco An ecological distance matrix, with class either dist or matrix. D.geo A geographic distance matrix, with class either dist or matrix. Provide either D.geo or XY. Default: D.geo=NULL. XY A file of Cartesian geographic coordinates of the points. Default: XY=NULL. n.class Number of classes. If n.class=0, the Sturge equation will be used unless break points are provided. break.pts Vector containing the break points of the distance distribution. Default: break.pts=NULL. cutoff For the second half of the distance classes, cutoff = TRUE limits the correlogram to the distance classes that include all points. If cutoff = FALSE, the correlogram includes all distance classes. r.type Type of correlation in calculation of the Mantel statistic. Default: r.type="pearson". Other choices are r.type="spearman" and r.type="kendall", as in functions cor and mantel. nperm Number of permutations for the tests of significance. Default: nperm=999. For large data files, permutation tests are rather slow. mult Correct P-values for multiple testing. The correction methods are "holm" (default), "hochberg", "sidak", and other methods available in the p.adjust function: "bonferroni" (best known, but not recommended because it is overly conservative), "hommel", "BH", "BY", "fdr", and "none". progressive Default: progressive=TRUE for progressive correction of multiple-testing, as described in Legendre and Legendre (1998, p. 721). Test of the first distance class: no correction; second distance class: correct for 2 simultaneous tests; distance class k: correct for k simultaneous tests. progressive=FALSE: correct all tests for n.class simultaneous tests. x Output of mantel.correlog. alpha Significance level for the points drawn with black symbols in the correlogram. Default: alpha=0.05. ... Other parameters passed from other functions.

### Details

A correlogram is a graph in which spatial correlation values are plotted, on the ordinate, as a function of the geographic distance classes among the study sites along the abscissa. In a Mantel correlogram, a Mantel correlation (Mantel 1967) is computed between a multivariate (e.g. multi-species) distance matrix of the user's choice and a design matrix representing each of the geographic distance classes in turn. The Mantel statistic is tested through a permutational Mantel test performed by vegan's mantel function.

When a correction for multiple testing is applied, more permutations are necessary than in the no-correction case, to obtain significant p-values in the higher correlogram classes.

The print.mantel.correlog function prints out the correlogram. See examples.

### Value

 mantel.res A table with the distance classes as rows and the class indices, number of distances per class, Mantel statistics (computed using Pearson's r, Spearman's r, or Kendall's tau), and p-values as columns. A positive Mantel statistic indicates positive spatial correlation. An additional column with p-values corrected for multiple testing is added unless mult="none". n.class The n umber of distance classes. break.pts The break points provided by the user or computed by the program. mult The name of the correction for multiple testing. No correction: mult="none". progressive A logical (TRUE, FALSE) value indicating whether or not a progressive correction for multiple testing was requested. n.tests The number of distance classes for which Mantel tests have been computed and tested for significance. call The function call.

### Author(s)

Pierre Legendre, Universite de Montreal

### References

Legendre, P. and L. Legendre. 1998. Numerical ecology, 2nd English edition. Elsevier Science BV, Amsterdam.

Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Res. 27: 209-220.

Oden, N. L. and R. R. Sokal. 1986. Directional autocorrelation: an extension of spatial correlograms to two dimensions. Syst. Zool. 35: 608-617.

Sokal, R. R. 1986. Spatial data analysis and historical processes. 29-43 in: E. Diday et al. [eds.] Data analysis and informatics, IV. North-Holland, Amsterdam.

### Examples

# Mite data from "vegan"
data(mite)
data(mite.xy)
mite.hel <- decostand(mite, "hellinger")
mite.hel.D <- dist(mite.hel)

mite.correlog <- mantel.correlog(mite.hel.D, XY=mite.xy, nperm=99)
summary(mite.correlog)
mite.correlog
plot(mite.correlog)

mite.correlog2 <- mantel.correlog(mite.hel.D, XY=mite.xy, cutoff=FALSE,
r.type="spearman", nperm=99)
summary(mite.correlog2)
mite.correlog2
plot(mite.correlog2)

## Mite correlogram after spatially detrending the mite data
mite.h.det <- resid(lm(as.matrix(mite.hel.D) ~ ., data=mite.xy))
mite.correlog3 <-  mantel.correlog(mite.h.det, XY=mite.xy, nperm=99)
mite.correlog3
plot(mite.correlog3)

[Package vegan version 1.16-32 Index]