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).
Usage
1 2 3 4 
Arguments
D.eco 
An ecological distance matrix, with class
either 
D.geo 
A geographic distance matrix, with class either

XY 
A file of Cartesian geographic coordinates of the
points. Default: 
n.class 
Number of classes. If 
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: 
cutoff 
For the second half of the distance classes,

r.type 
Type of correlation in calculation of the Mantel
statistic. Default: 
nperm 
Number of permutations for the tests of
significance. Default: 
mult 
Correct Pvalues for multiple testing. The correction
methods are 
progressive 
Default: 
x 
Output of 
alpha 
Significance level for the points drawn with black
symbols in the correlogram. Default: 
... 
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. multispecies) 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 nocorrection case, to obtain significant pvalues 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
pvalues as columns. A positive Mantel statistic indicates positive
spatial correlation. An additional column with pvalues corrected for
multiple testing is added unless 
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: 
progressive 
A logical ( 
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, Université de Montréal
References
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: 209220.
Oden, N. L. and R. R. Sokal. 1986. Directional autocorrelation: an extension of spatial correlograms to two dimensions. Syst. Zool. 35: 608617.
Sokal, R. R. 1986. Spatial data analysis and historical processes. 2943 in: E. Diday et al. [eds.] Data analysis and informatics, IV. NorthHolland, Amsterdam.
Sturges, H. A. 1926. The choice of a class interval. Journal of the American Statistical Association 21: 65–66.
Examples
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# 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.
