# chronopl

From ape v2.1-1
0th

Percentile

##### 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:
• ploglikthe maximum penalized log-likelihood.
• ratesthe estimated rates for each branch.
• D2the 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.

chronogram, ratogram, NPRS.criterion, chronoMPL