# mantel.correlog: Mantel Correlogram In vegan: Community Ecology Package

## 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``` ```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 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.

## 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, 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: 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ``` # 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. ```

vegan documentation built on Dec. 2, 2017, 1:06 a.m.