mgram {ecodist}

Mantel correlogram

Description

Calculates simple Mantel correlograms.

Usage

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.

Value

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().

Author(s)

Sarah Goslee

References

Legendre, P. and M. Fortin. 1989. Spatial pattern and ecological analysis. Vegetatio 80:107-138.

See Also

mantel, plot.mgram, pmgram

Examples

# 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))