3 \title{Molecular Dating With Penalized Likelihood}
5 chronopl(phy, lambda, node.age = 1, node = "root", CV = FALSE)
8 \item{phy}{an object of class \code{"phylo"}.}
9 \item{lambda}{value of the smoothng parameter.}
10 \item{node.age}{numeric values specifying the fixed node ages.}
11 \item{node}{the numbers of the nodes whose ages are given by
12 \code{node.age}; \code{"root"} is a short-cut the number of the
14 \item{CV}{whether to perform cross-validation.}
17 This function estimates the node ages of a tree using semi-parametric
18 method based on penalized likelihood (Sanderson 2002). The branch
19 lengths of the input tree are interpreted as (mean) numbers of
23 The idea of this method is to use a trade-off between a parametric
24 formulation where each branch has its own rate, and a nonparametric
25 term where changes in rates are minimized between contiguous
26 branches. A smoothing parameter (lambda) controls this trade-off. If
27 lambda = 0, then the parametric component dominates and rates vary as
28 much as possible among branches, whereas for increasing values of
29 lambda, the variation are smoother to tend to a clock-like model (same
30 rate for all branches).
32 \code{lambda} must be given. The known ages are given in
33 \code{node.age}, and the correponding node numbers in \code{node}.
34 These two arguments must obviously be of the same length. By default,
35 an age of 1 is assumed for the root, and the ages of the other nodes
38 The cross-validation used here is different from the one proposed by
39 Sanderson (2002). Here, each tip is dropped successively and the
40 analysis is repeated with the reduced tree: the estimated dates for
41 the remaining nodes are compared with the estimates from the full
42 data. For the \eqn{i}{i}th tip the following is calculated:
44 \deqn{\sum_{j=1}^{n-2}{\frac{(t_j - t_j^{-i})^2}{t_j}}}{SUM[j = 1, ..., n-2] (tj - tj[-i])^2/tj},
46 where \eqn{t_j}{tj} is the estimated date for the \eqn{j}{j}th node
47 with the full phylogeny, \eqn{t_j^{-i}}{tj[-i]} is the estimated date
48 for the \eqn{j}{j}th node after removing tip \eqn{i}{i} from the tree,
49 and \eqn{n}{n} is the number of tips.
52 an object of class \code{"phylo"} with branch lengths as estimated by
53 the function. There are two or three further attributes:
55 \item{ploglik}{the maximum penalized log-likelihood.}
56 \item{rates}{the estimated rates for each branch.}
57 \item{D2}{the influence of each observation on overall date
58 estimates (if \code{CV = TRUE}).}
61 Sanderson, M. J. (2002) Estimating absolute rates of molecular
62 evolution and divergence times: a penalized likelihood
63 approach. \emph{Molecular Biology and Evolution}, \bold{19},
66 \author{Emmanuel Paradis \email{Emmanuel.Paradis@mpl.ird.fr}}
68 \code{\link{chronogram}}, \code{\link{ratogram}},
69 \code{\link{NPRS.criterion}}, \code{\link{chronoMPL}}