vegan (version 2.6-8)

mantel.correlog: 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 (2012, pp. 819--821) and tested and compared in Borcard and Legendere (2012).

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 mantel.correlog
plot(x, alpha=0.05, ...)

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.

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 Sturges equation will be used unless break points are provided.

break.pts

Vector containing the break points of the distance distribution. Provide (n.class+1) breakpoints, that is, a list with a beginning and an ending point. 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.

Author

Pierre Legendre, Université de Montréal

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.

Borcard and Legendre (2012) show that the testing method in the Mantel correlogram has correct type I error and power, contrary to the simple and partial Mantel tests so often used by ecologists and geneticists in spatial analysis (see mantel.partial). They also show that the test in Mantel correlograms is the same test as used by Wagner (2004) in multiscale ordination (mso), and that it is closely related to the Geary’s \(c\) test in univariate correlograms.

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.

References

Borcard, D. & P. Legendre. 2012. Is the Mantel correlogram powerful enough to be useful in ecological analysis? A simulation study. Ecology 93: 1473-1481.

Legendre, P. and L. Legendre. 2012. Numerical ecology, 3rd 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.

Sturges, H. A. 1926. The choice of a class interval. Journal of the American Statistical Association 21: 65–66.

Wagner, H.H. 2004. Direct multi-scale ordination with canonical correspondence analysis. Ecology 85: 342-351.

Examples

# Mite data available in "vegan"
data(mite)        
data(mite.xy)  
mite.hel <- decostand(mite, "hellinger")

# Detrend the species data by regression on the site coordinates
mite.hel.resid <- resid(lm(as.matrix(mite.hel) ~ ., data=mite.xy))

# Compute the detrended species distance matrix
mite.hel.D <- dist(mite.hel.resid)

# Compute Mantel correlogram with cutoff, Pearson statistic
mite.correlog <- mantel.correlog(mite.hel.D, XY=mite.xy, nperm=49)
summary(mite.correlog)
mite.correlog   
# or: print(mite.correlog)
# or: print.mantel.correlog(mite.correlog)
plot(mite.correlog)

# Compute Mantel correlogram without cutoff, Spearman statistic
mite.correlog2 <- mantel.correlog(mite.hel.D, XY=mite.xy, cutoff=FALSE, 
   r.type="spearman", nperm=49)
summary(mite.correlog2)
mite.correlog2
plot(mite.correlog2)

# NOTE: 'nperm' argument usually needs to be larger than 49.
# It was set to this low value for demonstration purposes.