3 \title{Molecular Dating With Penalized Likelihood}
5 chronopl(phy, lambda, age.min = 1, age.max = NULL,
6 node = "root", S = 1, tol = 1e-8,
7 CV = FALSE, eval.max = 500, iter.max = 500, ...)
10 \item{phy}{an object of class \code{"phylo"}.}
11 \item{lambda}{value of the smoothing parameter.}
12 \item{age.min}{numeric values specifying the fixed node ages (if
13 \code{age.max = NULL}) or the youngest bound of the nodes known to
14 be within an interval.}
15 \item{age.max}{numeric values specifying the oldest bound of the nodes
16 known to be within an interval.}
17 \item{node}{the numbers of the nodes whose ages are given by
18 \code{age.min}; \code{"root"} is a short-cut for the root.}
19 \item{S}{the number of sites in the sequences; leave the default if
20 branch lengths are in mean number of substitutions.}
21 \item{tol}{the value below which branch lengths are considered
23 \item{CV}{whether to perform cross-validation.}
24 \item{eval.max}{the maximal number of evaluations of the penalized
26 \item{iter.max}{the maximal number of iterations of the optimization
28 \item{\dots}{further arguments passed to control \code{nlminb}.}
31 This function estimates the node ages of a tree using a
32 semi-parametric method based on penalized likelihood (Sanderson
33 2002). The branch lengths of the input tree are interpreted as mean
34 numbers of substitutions (i.e., per site).
37 The idea of this method is to use a trade-off between a parametric
38 formulation where each branch has its own rate, and a nonparametric
39 term where changes in rates are minimized between contiguous
40 branches. A smoothing parameter (lambda) controls this trade-off. If
41 lambda = 0, then the parametric component dominates and rates vary as
42 much as possible among branches, whereas for increasing values of
43 lambda, the variation are smoother to tend to a clock-like model (same
44 rate for all branches).
46 \code{lambda} must be given. The known ages are given in
47 \code{age.min}, and the correponding node numbers in \code{node}.
48 These two arguments must obviously be of the same length. By default,
49 an age of 1 is assumed for the root, and the ages of the other nodes
52 If \code{age.max = NULL} (the default), it is assumed that
53 \code{age.min} gives exactly known ages. Otherwise, \code{age.max} and
54 \code{age.min} must be of the same length and give the intervals for
55 each node. Some node may be known exactly while the others are
56 known within some bounds: the values will be identical in both
57 arguments for the former (e.g., \code{age.min = c(10, 5), age.max =
58 c(10, 6), node = c(15, 18)} means that the age of node 15 is 10
59 units of time, and the age of node 18 is between 5 and 6).
61 The input tree may have multichotomies. If some internal branches are
62 of zero-length, they are collapsed (with a warning), and the returned
63 tree will have less nodes than the input one. The presence of
64 zero-lengthed terminal branches of results in an error since it makes
65 little sense to have zero-rate branches.
67 The cross-validation used here is different from the one proposed by
68 Sanderson (2002). Here, each tip is dropped successively and the
69 analysis is repeated with the reduced tree: the estimated dates for
70 the remaining nodes are compared with the estimates from the full
71 data. For the \eqn{i}{i}th tip the following is calculated:
73 \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},
75 where \eqn{t_j}{tj} is the estimated date for the \eqn{j}{j}th node
76 with the full phylogeny, \eqn{t_j^{-i}}{tj[-i]} is the estimated date
77 for the \eqn{j}{j}th node after removing tip \eqn{i}{i} from the tree,
78 and \eqn{n}{n} is the number of tips.
80 The present version uses the \code{\link[stats]{nlminb}} to optimise
81 the penalized likelihood function: see its help page for details on
82 parameters controlling the optimisation procedure.
85 an object of class \code{"phylo"} with branch lengths as estimated by
86 the function. There are three or four further attributes:
88 \item{ploglik}{the maximum penalized log-likelihood.}
89 \item{rates}{the estimated rates for each branch.}
90 \item{message}{the message returned by \code{nlminb} indicating
91 whether the optimisation converged.}
92 \item{D2}{the influence of each observation on overall date
93 estimates (if \code{CV = TRUE}).}
96 Sanderson, M. J. (2002) Estimating absolute rates of molecular
97 evolution and divergence times: a penalized likelihood
98 approach. \emph{Molecular Biology and Evolution}, \bold{19},
101 \author{Emmanuel Paradis \email{Emmanuel.Paradis@mpl.ird.fr}}
103 \code{\link{chronogram}}, \code{\link{ratogram}},
104 \code{\link{NPRS.criterion}}, \code{\link{chronoMPL}}