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]