# chronopl

##### Molecular Dating With Penalized Likelihood

This function estimates the node ages of a tree using semi-parametric method based on penalized likelihood (Sanderson 2002). The branch lengths of the input tree are interpreted as (mean) numbers of substitutions.

- Keywords
- models

##### Usage

`chronopl(phy, lambda, node.age = 1, node = "root", CV = FALSE)`

##### Arguments

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

. - lambda
- value of the smoothng parameter.
- node.age
- numeric values specifying the fixed node ages.
- node
- the numbers of the nodes whose ages are given by
`node.age`

;`"root"`

is a short-cut the number of the node. - CV
- whether to perform cross-validation.

##### 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
`node.age`

, 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.

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.

##### Value

- an object of class
`"phylo"`

with branch lengths as estimated by the function. There are two or three further attributes: ploglik the maximum penalized log-likelihood. rates the estimated rates for each branch. 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 2.1-1, License: GPL (>= 2)*