Mantel Correlogram
mantel.correlog.RdFunction 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
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, ...)Arguments
- D.eco
An ecological distance matrix, with class either
distormatrix.- D.geo
A geographic distance matrix, with class either
distormatrix. Provide eitherD.geoorXY. 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 = TRUElimits the correlogram to the distance classes that include all points. Ifcutoff = FALSE, the correlogram includes all distance classes.- r.type
Type of correlation in calculation of the Mantel statistic. Default:
r.type="pearson". Other choices arer.type="spearman"andr.type="kendall", as in functionscorandmantel.- 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 thep.adjustfunction:"bonferroni"(best known, but not recommended because it is overly conservative),"hommel","BH","BY","fdr", and"none".- progressive
Default:
progressive=TRUEfor 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 forn.classsimultaneous 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.
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: 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.
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)
#> Length Class Mode
#> mantel.res 65 -none- numeric
#> n.class 1 -none- numeric
#> break.pts 14 -none- numeric
#> mult 1 -none- character
#> n.tests 1 -none- numeric
#> call 4 -none- call
mite.correlog
#>
#> Mantel Correlogram Analysis
#>
#> Call:
#>
#> mantel.correlog(D.eco = mite.hel.D, XY = mite.xy, nperm = 49)
#>
#> class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
#> D.cl.1 0.514182 358.000000 0.135713 0.02 0.02 *
#> D.cl.2 1.242546 650.000000 0.118174 0.02 0.04 *
#> D.cl.3 1.970910 796.000000 0.037820 0.20 0.20
#> D.cl.4 2.699274 696.000000 -0.098605 0.02 0.08 .
#> D.cl.5 3.427638 500.000000 -0.112682 0.02 0.10 .
#> D.cl.6 4.156002 468.000000 -0.107603 0.02 0.12
#> D.cl.7 4.884366 364.000000 -0.022264 0.08 0.16
#> D.cl.8 5.612730 326.000000 NA NA NA
#> D.cl.9 6.341094 260.000000 NA NA NA
#> D.cl.10 7.069458 184.000000 NA NA NA
#> D.cl.11 7.797822 130.000000 NA NA NA
#> D.cl.12 8.526186 66.000000 NA NA NA
#> D.cl.13 9.254550 32.000000 NA NA NA
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 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)
#> Length Class Mode
#> mantel.res 65 -none- numeric
#> n.class 1 -none- numeric
#> break.pts 14 -none- numeric
#> mult 1 -none- character
#> n.tests 1 -none- numeric
#> call 6 -none- call
mite.correlog2
#>
#> Mantel Correlogram Analysis
#>
#> Call:
#>
#> mantel.correlog(D.eco = mite.hel.D, XY = mite.xy, cutoff = FALSE, r.type = "spearman", nperm = 49)
#>
#> class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
#> D.cl.1 0.514182 358.000000 0.134229 0.02 0.02 *
#> D.cl.2 1.242546 650.000000 0.121270 0.02 0.04 *
#> D.cl.3 1.970910 796.000000 0.035413 0.08 0.08 .
#> D.cl.4 2.699274 696.000000 -0.095899 0.02 0.08 .
#> D.cl.5 3.427638 500.000000 -0.118692 0.02 0.10 .
#> D.cl.6 4.156002 468.000000 -0.117148 0.02 0.12
#> D.cl.7 4.884366 364.000000 -0.031123 0.06 0.14
#> D.cl.8 5.612730 326.000000 0.026064 0.12 0.18
#> D.cl.9 6.341094 260.000000 0.050573 0.04 0.18
#> D.cl.10 7.069458 184.000000 0.057017 0.02 0.20
#> D.cl.11 7.797822 130.000000 0.036195 0.14 0.24
#> D.cl.12 8.526186 66.000000 -0.054242 0.08 0.32
#> D.cl.13 9.254550 32.000000 -0.066677 0.04 0.28
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
plot(mite.correlog2)
# NOTE: 'nperm' argument usually needs to be larger than 49.
# It was set to this low value for demonstration purposes.