chronopl: Molecular Dating With Penalized Likelihood

Description

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.

Usage

chronopl(phy, lambda, node.age = NULL, nodes = NULL, CV = FALSE)

Arguments

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).

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 `nodes'. These two arguments must obviously be of the same length. If they are left NULL, then the age at the root is fixed at one.

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.

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.