Abouheif's test based on Moran's I
The test of Abouheif (1999) is designed to detect phylogenetic
autocorrelation in a quantitative trait. Pavoine et al. (2008) have
shown that this tests is in fact a Moran's I test using a particular
phylogenetic proximity between tips (see details). The function
abouheif.moran performs basically Abouheif's test for several traits
at a time, but it can incorporate other phylogenetic proximities as well.
abouheif.moran(x, W = NULL, method = c("oriAbouheif", "patristic", "nNodes",
"Abouheif", "sumDD"), f = function(x) { 1/x }, nrepet = 999,
alter = c("greater", "less", "two-sided"))x |
a data frame with continuous variables, or a phylo4d
object (i.e. containing both a tree, and tip data). In the latter case,
|
W |
a n by n matrix (n being the number rows in x)
of phylogenetic proximities, as produced by |
method |
a character string (full or unambiguously abbreviated)
specifying the type of proximity to be used. By default, the proximity used
is that of the original Abouheif's test. See details in
|
f |
a function to turn a distance into a proximity (see
|
nrepet |
number of random permutations of data for the randomization test |
alter |
a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided" |
Note that the original Abouheif's proximity (Abouheif, 1999; Pavoine
et al. 2008) unifies Moran's I and Geary'c tests (Thioulouse et
al. 1995).
abouheif.moran can be used in two ways:
- providing a data.frame
of traits (x) and a matrix of phylogenetic proximities (W)
- providing a phylo4d object (x) and specifying the
type of proximity to be used (method).
W is a squared symmetric matrix whose terms are all positive or
null.
W is firstly transformed in frequency matrix A by dividing it by the
total sum of data matrix :
a_ij = W_ij / (sum_i sum_j W_ij)
The neighbouring weights is defined by the matrix D = diag(d_1,d_2, …) where d_i = sum_j W_ij. For each vector x of the data frame x, the test is based on the Moran statistic t(x)Ax where x is D-centred.
Returns an object of class krandtest (randomization tests
from ade4), containing one Monte Carlo test for each trait.
Original code from ade4 (gearymoran function) by Sebastien Ollier
Adapted and maintained by Thibaut Jombart <tjombart@imperial.ac.uk>.
Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.
- gearymoran from the ade4 package
-
Moran.I from the ape package for the classical Moran's I
test.
if(require(ade4)&& require(ape) && require(phylobase)){
## load data
data(ungulates)
tre <- read.tree(text=ungulates$tre)
x <- phylo4d(tre, ungulates$tab)
## Abouheif's tests for each trait
myTests <- abouheif.moran(x)
myTests
plot(myTests)
## a variant using another proximity
plot(abouheif.moran(x, method="nNodes") )
## Another example
data(maples)
tre <- read.tree(text=maples$tre)
dom <- maples$tab$Dom
## Abouheif's tests for each trait (equivalent to Cmean)
W1 <- proxTips(tre,method="oriAbouheif")
abouheif.moran(dom,W1)
## Equivalence with moran.idx
W2 <- proxTips(tre,method="Abouheif")
abouheif.moran(dom,W2)
moran.idx(dom,W2)
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