2 \alias{compar.cheverud}
3 \title{Cheverud's Comparative Method}
5 This function computes the phylogenetic variance component and the
6 residual deviation for continous characters, taking into account the
7 phylogenetic relationships among species, following the comparative
8 method described in Cheverud et al. (1985). The correction proposed by
12 compar.cheverud(y, W, tolerance = 1e-06, gold.tol = 1e-04)
15 \item{y}{A vector containing the data to analyse.}
16 \item{W}{The phylogenetic connectivity matrix. All diagonal elements
18 \item{tolerance}{Minimum difference allowed to consider eigenvalues as
20 \item{gold.tol}{Precision to use in golden section search alogrithm.}
23 Model: \deqn{y = \rho W y + e}{y = rho.W.y + e}
25 where \eqn{e}{e} is the error term, assumed to be normally distributed.
26 \eqn{\rho}{rho} is estimated by the maximum likelihood procedure given
27 in Rohlf (2001), using a golden section search algorithm. The code of
28 this function is indeed adapted from a MatLab code given in appendix
29 in Rohlf's article, to correct a mistake in Cheverud's original paper.
32 A list with the following components:
34 \item{rhohat}{The maximum likelihood estimate of \eqn{\rho}{rho}}
35 \item{Wnorm}{The normalized version of \code{W}}
36 \item{residuals}{Error terms (\eqn{e}{e})}
39 Cheverud, J. M., Dow, M. M. and Leutenegger, W. (1985) The quantitative
40 assessment of phylogenetic constraints in comparative analyses: sexual
41 dimorphism in body weight among primates. \emph{Evolution},
42 \bold{39}, 1335--1351.
44 Rohlf, F. J. (2001) Comparative methods for the analysis of continuous
45 variables: geometric interpretations. \emph{Evolution}, \bold{55},
48 Harvey, P. H. and Pagel, M. D. (1991) \emph{The comparative method in
49 evolutionary biology}. Oxford University Press.
51 \author{Julien Dutheil \email{julien.dutheil@univ-montp2.fr}}
52 \seealso{\code{\link{compar.lynch}}}
54 ### Example from Harvey and Pagel's book:
57 W <- matrix(c(1,1/6,1/6,1/6,1/6,1,1/2,1/2,1/6,1/2,1,1,1/6,1/2,1,1), 4)
60 ### Example from Rohlf's 2001 article:
73 y<-c(-0.12,0.36,-0.1,0.04,-0.15,0.29,-0.11,-0.06)