This function estimates the node ages of a tree using a semi-parametric method based on penalized likelihood (Sanderson 2002). The branch lengths of the input tree are interpreted as mean numbers of substitutions (i.e., per site).
chronopl(phy, lambda, age.min = 1, age.max = NULL,
node = "root", S = 1, tol = 1e-8,
CV = FALSE, eval.max = 500, iter.max = 500, ...)an object of class "phylo".
value of the smoothing parameter.
numeric values specifying the fixed node ages (if
age.max = NULL) or the youngest bound of the nodes known to
be within an interval.
numeric values specifying the oldest bound of the nodes known to be within an interval.
the numbers of the nodes whose ages are given by
age.min; "root" is a short-cut for the root.
the number of sites in the sequences; leave the default if branch lengths are in mean number of substitutions.
the value below which branch lengths are considered effectively zero.
whether to perform cross-validation.
the maximal number of evaluations of the penalized likelihood function.
the maximal number of iterations of the optimization algorithm.
further arguments passed to control nlminb.
an object of class "phylo" with branch lengths as estimated by
the function. There are three or four further attributes:
the maximum penalized log-likelihood.
the estimated rates for each branch.
the message returned by nlminb indicating
whether the optimisation converged.
the influence of each observation on overall date
estimates (if CV = TRUE).
The idea of this method is to use a trade-off between a parametric formulation where each branch has its own rate, and a nonparametric term where changes in rates are minimized between contiguous branches. A smoothing parameter (lambda) controls this trade-off. If lambda = 0, then the parametric component dominates and rates vary as much as possible among branches, whereas for increasing values of lambda, the variation are smoother to tend to a clock-like model (same rate for all branches).
lambda must be given. The known ages are given in
age.min, and the correponding node numbers in node.
These two arguments must obviously be of the same length. By default,
an age of 1 is assumed for the root, and the ages of the other nodes
are estimated.
If age.max = NULL (the default), it is assumed that
age.min gives exactly known ages. Otherwise, age.max and
age.min must be of the same length and give the intervals for
each node. Some node may be known exactly while the others are
known within some bounds: the values will be identical in both
arguments for the former (e.g., age.min = c(10, 5), age.max =
c(10, 6), node = c(15, 18) means that the age of node 15 is 10
units of time, and the age of node 18 is between 5 and 6).
If two nodes are linked (i.e., one is the ancestor of the other) and
have the same values of age.min and age.max (say, 10 and
15) this will result in an error because the medians of these values
are used as initial times (here 12.5) giving initial branch length(s)
equal to zero. The easiest way to solve this is to change slightly the
given values, for instance use age.max = 14.9 for the youngest
node, or age.max = 15.1 for the oldest one (or similarly for
age.min).
The input tree may have multichotomies. If some internal branches are of zero-length, they are collapsed (with a warning), and the returned tree will have less nodes than the input one. The presence of zero-lengthed terminal branches of results in an error since it makes little sense to have zero-rate branches.
The cross-validation used here is different from the one proposed by Sanderson (2002). Here, each tip is dropped successively and the analysis is repeated with the reduced tree: the estimated dates for the remaining nodes are compared with the estimates from the full data. For the \(i\)th tip the following is calculated:
$$\sum_{j=1}^{n-2}{\frac{(t_j - t_j^{-i})^2}{t_j}}$$,
where \(t_j\) is the estimated date for the \(j\)th node with the full phylogeny, \(t_j^{-i}\) is the estimated date for the \(j\)th node after removing tip \(i\) from the tree, and \(n\) is the number of tips.
The present version uses the nlminb to optimise
the penalized likelihood function: see its help page for details on
parameters controlling the optimisation procedure.
Sanderson, M. J. (2002) Estimating absolute rates of molecular evolution and divergence times: a penalized likelihood approach. Molecular Biology and Evolution, 19, 101--109.