3 \title{Lynch's Comparative Method}
5 compar.lynch(x, G, eps = 1e-4)
8 \item{x}{eiher a matrix, a vector, or a data.frame containing the data
9 with species as rows and variables as columns.}
10 \item{G}{a matrix that can be interpreted as an among-species correlation
12 \item{eps}{a numeric value to detect convergence of the EM algorithm.}
15 This function computes the heritable additive value and the residual
16 deviation for continous characters, taking into account the
17 phylogenetic relationships among species, following the comparative
18 method described in Lynch (1991).
21 The parameter estimates are computed following the EM
22 (expectation-maximization) algorithm. This algorithm usually leads to
23 convergence but may lead to local optima of the likelihood
24 function. It is recommended to run several times the function in order
25 to detect these potential local optima. The `optimal' value for
26 \code{eps} depends actually on the range of the data and may be
27 changed by the user in order to check the stability of the parameter
28 estimates. Convergence occurs when the differences between two
29 successive iterations of the EM algorithm leads to differences between
30 both residual and additive values less than or equal to \code{eps}.
33 The present function does not perform the estimation of ancestral
34 phentoypes as proposed by Lynch (1991). This will be implemented in
38 A list with the following components:
39 \item{vare}{estimated residual variance-covariance matrix.}
40 \item{vara}{estimated additive effect variance covariance matrix.}
41 \item{u}{estimates of the phylogeny-wide means.}
42 \item{A}{addtitive value estimates.}
43 \item{E}{residual values estimates.}
44 \item{lik}{logarithm of the likelihood for the entire set of observed
48 Lynch, M. (1991) Methods for the analysis of comparative data in
49 evolutionary biology. \emph{Evolution}, \bold{45}, 1065--1080.
51 \author{Julien Claude \email{claude@isem.univ-montp2.fr}}
53 \code{\link{pic}}, \code{\link{compar.gee}}
56 ### The example in Lynch (1991)
57 cat("((((Homo:0.21,Pongo:0.21):0.28,",
58 "Macaca:0.49):0.13,Ateles:0.62):0.38,Galago:1.00);",
59 file = "ex.tre", sep = "\n")
60 tree.primates <- read.tree("ex.tre")
62 X <- c(4.09434, 3.61092, 2.37024, 2.02815, -1.46968)
63 Y <- c(4.74493, 3.33220, 3.36730, 2.89037, 2.30259)
64 compar.lynch(cbind(X, Y),
65 G = vcv.phylo(tree.primates, cor = TRUE))