Compute some phylogenetic proximities between tips
The function proxTips computes a given proximity between a set of
tips of a phylogeny. A vector of tips is supplied: proximities between all
possible pairs of these tips are computed. The proximities are computed
from the shortest path between the tips.
proxTips(x, tips = "all", method = c("patristic", "nNodes", "oriAbouheif",
"Abouheif", "sumDD"), f = function(x) { 1/x }, normalize = c("row",
"col", "none"), symmetric = TRUE, useC = TRUE)x |
|
tips |
A vector of integers identifying tips by their numbers, or a vector of characters identifying tips by their names. Distances will be computed between all possible pairs of tips. |
method |
a character string (full or abbreviated without ambiguity)
specifying the method used to compute proximities; possible values are: |
f |
a function to change a distance into a proximity. |
normalize |
a character string specifying whether the matrix must be
normalized by row ( |
symmetric |
a logical stating whether M must be coerced to be symmetric (TRUE, default) or not. This is achieved by taking (denoting N the matrix of proximities before re-symmetrization): M = 0.5 * (N + N^{T}) Note that x^{T}Ny = x^{T}My, but the latter has the advantage of using a bilinear symmetric form (more appropriate for optimization purposes). |
useC |
a logical indicating whether computations of distances (before transformation into proximities) should be performed using compiled C code (TRUE, default), or using a pure R version (FALSE). C version is several orders of magnitude faster, and R version is kept for backward compatibility. |
Proximities are computed as the inverse (to the power a) of a
phylogenetic distance (computed by distTips. Denoting
D=[d_{ij}] a matrix of phylogenetic distances, the proximity matrix
M=[m_{ij}] is computed as:
m_{ij} = (1/d_{ij})^a for all i different from j
and
m_{ii} = 0
Several distances can be used, defaulting to the sum of branch lengths (see
argument method). Proximities are not true similarity measures,
since the proximity of a tip with itself is always set to zero.
The obtained matrix of phylogenetic proximities (M) defines a bilinear
symmetric form when M is symmetric (default):
f(x,y) = x^{T}My
In general, M is not a metric because it is not positive-definite. Such a matrice can be used to measure phylogenetic autocorrelation (using Moran's index):
I(x) = (x^{T}Mx)/(var(x))
or to compute lag vectors (Mx) used in autoregressive models, like:
x = Mx + ... + e
where '...' is the non-autoregressive part of the model, and 'e' are residuals.
Abouheif proximity refers to the phylogenetic proximity underlying
the test of Abouheif (see references). Let P be the set of all the nodes in
the path going from node1 to node2. Let DDP be the number of
direct descendants from each node in P. Then, the so-called 'Abouheif'
distance is the inverse of the product of all terms in DDP.
oriAbouheif returns a matrix with non-null diagonal elements, as
formulated in Pavoine et al. (2008). This matrix is bistochastic (all
marginal sums equal 1), but this bilinear symmetric form does not give rise
to a Moran's index, since it requires a null diagonal. Abouheif
contains Abouheif's proximities but has a null diagonal, giving rise to a
Moran's index.
sumDD refers to a phylogenetic proximity quite similar to that of
Abouheif. We consider the same sets P and DDP. But instead of taking the
inverse of the product of all terms in DDP, this proximity computes the
inverse of the sum of all terms in DDP. This matrix was denoted 'M' in
Pavoine et al. (2008), who reported that it is related to May's index
(May, 1990).
A matrix of phylogenetic proximities.
Thibaut Jombart tjombart@imperial.ac.uk
== About Moran's index with various proximities ==
Pavoine,
S.; Ollier, S.; Pontier, D.; Chessel, D. (2008) Testing for phylogenetic
signal in life history variable: Abouheif's test revisited.
Theoretical Population Biology: 73, 79-91.
== About regression on phylogenetic lag vector ==
Cheverud, J. M.; Dow,
M. M.; Leutenegger, W. (1985) The quantitative assessment of phylogentic
constaints in comparative analyses: sexual dimorphism in body weights among
primates. Evolution 39, 1335-1351.
Cheverud, J. M.; Dow, M. M. (1985) An autocorrelation analysis of genetic
variation due to lineal fission in social groups of Rhesus macaques.
American Journal of Phyisical Anthropology 67, 113-121.
== Abouheif's original paper ==
Abouheif, E. (1999) A method for testing
the assumption of phylogenetic independence in comparative data.
Evolutionary Ecology Research, 1, 895-909.
== May's index ==
May, R.M. (1990) Taxonomy as destiny. Nature
347, 129-130.
distTips which computes several phylogenetic
distances between tips.
if(require(ape) & require(phylobase)){
## make a tree
x <- as(rtree(10),"phylo4")
plot(x, show.node=TRUE)
axisPhylo()
## compute different distances
proxTips(x, 1:5)
proxTips(x, 1:5, "nNodes")
proxTips(x, 1:5, "Abouheif")
proxTips(x, , "sumDD")
## see what one proximity looks like
M <- proxTips(x)
obj <- phylo4d(x,as.data.frame(M))
table.phylo4d(obj,symbol="sq")
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