mantel  R Documentation 
Function mantel
finds the Mantel statistic as a matrix
correlation between two dissimilarity matrices, and function
mantel.partial
finds the partial Mantel statistic as the
partial matrix correlation between three dissimilarity matrices. The
significance of the statistic is evaluated by permuting rows and
columns of the first dissimilarity matrix.
mantel(xdis, ydis, method="pearson", permutations=999, strata = NULL,
na.rm = FALSE, parallel = getOption("mc.cores"))
mantel.partial(xdis, ydis, zdis, method = "pearson", permutations = 999,
strata = NULL, na.rm = FALSE, parallel = getOption("mc.cores"))
xdis , ydis , zdis 
Dissimilarity matrices or 
method 
Correlation method, as accepted by 
permutations 
a list of control values for the permutations
as returned by the function 
strata 
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. 
na.rm 
Remove missing values in calculation of Mantel correlation. Use this option with care: Permutation tests can be biased, in particular if two matrices had missing values in matching positions. 
parallel 
Number of parallel processes or a predefined socket
cluster. With 
Mantel statistic is simply a correlation between entries of two
dissimilarity matrices (some use cross products, but these are
linearly related). However, the significance cannot be directly
assessed, because there are N(N1)/2
entries for just N
observations. Mantel developed asymptotic test, but here we use
permutations of N
rows and columns of dissimilarity
matrix. Only the first matrix (xdist
) will be permuted, and
the second is kept constant. See permutations
for
additional details on permutation tests in Vegan.
Partial Mantel statistic uses partial correlation
conditioned on the third matrix. Only the first matrix is permuted so
that the correlation structure between second and first matrices is
kept constant. Although mantel.partial
silently accepts other
methods than "pearson"
, partial correlations will probably be
wrong with other methods.
Borcard & Legendre (2012) warn against using partial Mantel test and
recommend instead Mantel correlogram
(mantel.correlog
).
The function uses cor
, which should accept
alternatives pearson
for product moment correlations and
spearman
or kendall
for rank correlations.
The function returns a list of class mantel
with following
components:
Call 
Function call. 
method 
Correlation method used, as returned by

statistic 
The Mantel statistic. 
signif 
Empirical significance level from permutations. 
perm 
A vector of permuted values. The distribution of
permuted values can be inspected with 
permutations 
Number of permutations. 
control 
A list of control values for the permutations
as returned by the function 
Jari Oksanen
Borcard, D. & Legendre, P. (2012) Is the Mantel correlogram powerful enough to be useful in ecological analysis? A simulation study. Ecology 93: 14731481.
Legendre, P. and Legendre, L. (2012) Numerical Ecology. 3rd English Edition. Elsevier.
mantel.correlog
.
## Is vegetation related to environment?
data(varespec)
data(varechem)
veg.dist < vegdist(varespec) # BrayCurtis
env.dist < vegdist(scale(varechem), "euclid")
mantel(veg.dist, env.dist)
mantel(veg.dist, env.dist, method="spear")
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