proxTips: Compute some phylogenetic proximities between tips

In adephylo: Exploratory Analyses for the Phylogenetic Comparative Method

Compute some phylogenetic proximities between tips

Description

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.

Usage

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
)

Arguments

x	a tree of class phylo, phylo4 or phylo4d.
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: - patristic: (inversed sum of) branch length - nNodes: (inversed) number of nodes on the path between the nodes - oriAbouheif: original Abouheif's proximity, with diagonal (see details) - Abouheif: Abouheif's proximity without diagonal (see details) - sumDD: (inversed) sum of direct descendants of all nodes on the path (see details)
f	a function to change a distance into a proximity.
normalize	a character string specifying whether the matrix must be normalized by row (row), column (col), or not (none). Normalization amounts to dividing each row (or column) so that the marginal sum is 1. Hence, default is matrix with each row summing to 1.
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.

Details

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} = \frac{1}{d_{ij}^a} \forall i \neq 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) = \frac{x^TMx}{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).

Value

A matrix of phylogenetic proximities.

Author(s)

Thibaut Jombart [e-mail]

References

== 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.

See Also

distTips which computes several phylogenetic distances between tips.

Examples

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")
}

adephylo documentation built on Oct. 6, 2023, 5:07 p.m.