# chronopl

##### Molecular Dating With Penalized Likelihood

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).

- Keywords
- models

##### Usage

```
chronopl(phy, lambda, age.min = 1, age.max = NULL,
node = "root", S = 1, tol = 1e-8,
CV = FALSE, eval.max = 500, iter.max = 500, ...)
```

##### Arguments

- phy
- an object of class
`"phylo"`

. - lambda
- value of the smoothing parameter.
- age.min
- numeric values specifying the fixed node ages (if
`age.max = NULL`

) or the youngest bound of the nodes known to be within an interval. - age.max
- numeric values specifying the oldest bound of the nodes known to be within an interval.
- node
- the numbers of the nodes whose ages are given by
`age.min`

;`"root"`

is a short-cut for the root. - S
- the number of sites in the sequences; leave the default if branch lengths are in mean number of substitutions.
- tol
- the value below which branch lengths are considered effectively zero.
- CV
- whether to perform cross-validation.
- eval.max
- the maximal number of evaluations of the penalized likelihood function.
- iter.max
- the maximal number of iterations of the optimization algorithm.
- ...
- further arguments passed to control
`nlminb`

.

##### Details

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).

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.

##### Value

- an object of class
`"phylo"`

with branch lengths as estimated by the function. There are three or four further attributes: ploglik the maximum penalized log-likelihood. rates the estimated rates for each branch. message the message returned by `nlminb`

indicating whether the optimisation converged.D2 the influence of each observation on overall date estimates (if `CV = TRUE`

).

##### References

Sanderson, M. J. (2002) Estimating absolute rates of molecular
evolution and divergence times: a penalized likelihood
approach. *Molecular Biology and Evolution*, **19**,
101--109.

##### See Also

*Documentation reproduced from package ape, version 2.6-3, License: GPL (>= 2)*