# Mantel correlogram Calculates simple Mantel correlograms. ```r mgram(species.d, space.d, breaks, nclass, stepsize, equiprobable = FALSE, nperm = 1000, mrank = FALSE, nboot = 500, pboot = 0.9, cboot = 0.95, alternative = "two.sided", trace = FALSE) ``` ## Arguments - `species.d`: lower-triangular dissimilarity matrix. - `space.d`: lower-triangular matrix of geographic distances. - `breaks`: locations of class breaks. If specified, overrides nclass and stepsize. - `nclass`: number of distance classes. If not specified, Sturge's rule will be used to determine an appropriate number of classes. - `stepsize`: width of each distance class. If not specified, nclass and the range of space.d will be used to calculate an appropriate default. - `equiprobable`: if TRUE, create nclass classes of equal number of distances; if FALSE, create nclass classes of equal width - `nperm`: number of permutations to use. If set to 0, the permutation test will be omitted. - `mrank`: if this is set to FALSE (the default option), Pearson correlations will be used. If set to TRUE, the Spearman correlation (correlation ranked distances) will be used. - `nboot`: number of iterations to use for the bootstrapped confidence limits. If set to 0, the bootstrapping will be omitted. - `pboot`: the level at which to resample the data for the bootstrapping procedure. - `cboot`: the level of the confidence limits to estimate. - `alternative`: default is "two.sided", and returns p-values for H0: rM = 0. The alternative is "one.sided", which returns p-values for H0: rM <= 0. - `trace`: if TRUE, returns progress indicators. ## Details This function calculates Mantel correlograms, and tests the hypothesis that the mean compositional dissimilarity within a distance class differs from the mean of all the other distance classes combined. The Mantel correlogram is essentially a multivariate autocorrelation function. The Mantel r represents the dissimilarity in variable composition (often species composition) at a particular lag distance, and significance is tested in reference to all distance classes. ## Returns Returns an object of class mgram, which is a list with two elements. mgram is a matrix with one row for each distance class and 6 columns: - **lag**: midpoint of the distance class. - **ngroup**: number of distances in that class. - **mantelr**: Mantel r value. - **pval**: p-value for the test chosen. - **llim**: lower bound of confidence limit for mantelr. - **ulim**: upper bound of confidence limit for mantelr. resids is NA for objects calculated by mgram(). ## References Legendre, P. and M. Fortin. 1989. Spatial pattern and ecological analysis. Vegetatio 80:107-138. ## Author(s) Sarah Goslee ## See Also `mantel`, `plot.mgram`, `pmgram` ## Examples ```r # generate a simple surface x <- matrix(1:10, nrow=10, ncol=10, byrow=FALSE) y <- matrix(1:10, nrow=10, ncol=10, byrow=TRUE) z <- x + 3*y image(z) # analyze the pattern of z across space space <- cbind(as.vector(x), as.vector(y)) z <- as.vector(z) space.d <- distance(space, "eucl") z.d <- distance(z, "eucl") z.mgram <- mgram(z.d, space.d, nperm=0) plot(z.mgram) # data(graze) space.d <- dist(graze$sitelocation) forest.d <- dist(graze$forestpct) grasses <- graze[, colnames(graze) %in% c("DAGL", "LOAR10", "LOPE", "POPR")] legumes <- graze[, colnames(graze) %in% c("LOCO6", "TRPR2", "TRRE3")] grasses.bc <- bcdist(grasses) legumes.bc <- bcdist(legumes) # Does the relationship of composition with distance vary for # grasses and legumes? par(mfrow=c(2, 1)) plot(mgram(grasses.bc, space.d, nclass=8)) plot(mgram(legumes.bc, space.d, nclass=8)) ```

mgram function