adephylo (version 1.1-16)

orthogram: Orthonormal decomposition of variance

Description

This function performs the orthonormal decomposition of variance of a quantitative variable on an orthonormal basis. It also returns the results of five non parametric tests associated to the variance decomposition. It thus provides tools (graphical displays and test) for analysing phylogenetic, pattern in one quantitative trait. This implementation replace the (deprecated) version from the ade4 package.

Usage

orthogram(
  x,
  tre = NULL,
  orthobas = NULL,
  prox = NULL,
  nrepet = 999,
  posinega = 0,
  tol = 1e-07,
  cdot = 1.5,
  cfont.main = 1.5,
  lwd = 2,
  nclass,
  high.scores = 0,
  alter = c("greater", "less", "two-sided")
)

Value

If (high.scores = 0), returns an object of class 'krandtest'

(randomization tests) corresponding to the five non parametric tests.

If (high.scores > 0), returns a list containg :

w

: an object of class 'krandtest' (randomization tests)

scores.order

: a vector which terms give labels of vectors that explain the larger part of variance

Arguments

x

a numeric vector corresponding to the quantitative variable

tre

a tree of class phylo, phylo4 or phylo4d.

orthobas

an object of class 'orthobasis'

prox

a matrix of phylogenetic proximities as returned by proxTips.

nrepet

an integer giving the number of permutations

posinega

a parameter for the ratio test. If posinega > 0, the function computes the ratio test.

tol

a tolerance threshold for orthonormality condition

cdot

a character size for points on the cumulative decomposition display

cfont.main

a character size for titles

lwd

a character size for dash lines

nclass

a single number giving the number of cells for the histogram

high.scores

a single number giving the number of vectors to return. If > 0, the function returns labels of vectors that explains the larger part of variance.

alter

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided"

Author

Original code: Sebastien Ollier and Daniel Chessel.

Current maintainer: Stephane Dray <[e-mail]>

Details

Several orthonormal bases can be used. By default, basis is constructed from a partition of tips according to tree topology (as returned by treePart); for this, the argument tre must be provided. Alternatively, one can provide an orthonormal basis as returned by orthobasis.phylo/me.phylo (argument orthobas), or provide a proximity matrix from which an orthobasis based on Moran's eigenvectors will be constructed (argument prox).

The function computes the variance decomposition of a quantitative vector x on an orthonormal basis B. The variable is normalized given the uniform weight to eliminate problem of scales. It plots the squared correlations \(R^{2}\) between x and vectors of B (variance decomposition) and the cumulated squared correlations \(SR^{2}\) (cumulative decomposition). The function also provides five non parametric tests to test the existence of autocorrelation. The tests derive from the five following statistics :

- R2Max=\(\max(R^{2})\). It takes high value when a high part of the variability is explained by one score.
- SkR2k=\(\sum_{i=1}^{n-1}(iR^{2}_i)\). It compares the part of variance explained by internal nodes to the one explained by end nodes.
- Dmax=\(\max_{m=1,...,n-1}(\sum_{j=1}^{m}R^{2}_j - \)\( \frac{m}{n-1})\). It examines the accumulation of variance for a sequence of scores.
- SCE=\(\sum_{m=1}^{n-1} (\sum_{j=1}^{m}R^{2}_j - \)\( \frac{m}{n-1})^{2}\). It examines also the accumulation of variance for a sequence of scores.
- ratio: depends of the parameter posinega. If posinega > 0, the statistic ratio exists and equals \(\sum_{i=1}^{posinega}R^{2}_i\). It compares the part of variance explained by internal nodes to the one explained by end nodes when we can define how many vectors correspond to internal nodes.

References

Ollier, S., Chessel, D. and Couteron, P. (2005) Orthonormal Transform to Decompose the Variance of a Life-History Trait across a Phylogenetic Tree. Biometrics, 62, 471--477.

See Also

orthobasis.phylo

Examples

if(require(ape) && require(phylobase)){

## a phylogenetic example
data(ungulates)
tre <- read.tree(text=ungulates$tre)
plot(tre)

## look at two traits
afbw <- log(ungulates$tab[,1])
neonatw <- log((ungulates$tab[,2]+ungulates$tab[,3])/2)
names(afbw) <- tre$tip.label
names(neonatw) <- tre$tip.label
plot(afbw, neonatw) # relationship between traits
lm1 <- lm(neonatw~afbw)
resid <- residuals(lm1)
abline(lm1)

## plot the two traits and the residuals of lm1
x <- phylo4d(tre, cbind.data.frame(afbw, neonatw, residuals=resid))
table.phylo4d(x) # residuals are surely not independant

## default orthogram for residuals of lm1
orthogram(resid, tre)

## using another orthonormal basis (derived from Abouheif's proximity)
myOrthoBasis <- orthobasis.phylo(tre, method="oriAbouheif") # Abouheif's proximities
orthogram(resid, ortho=myOrthoBasis) # significant phylog. signal

## Abouheif's test
W <- proxTips(tre, method="oriAbouheif") # proximity matrix
abouheif.moran(resid, W)
}