yule.time: Fits the Time-Dependent Yule Model

Description

This function fits by maximum likelihood the time-dependent Yule model. The time is measured from the past (root.time) to the present.

Usage

yule.time(phy, birth, BIRTH = NULL, root.time = 0, opti = "nlm", start = 0.01)

Arguments

phy

an object of class "phylo".

birth

a (vectorized) function specifying how the birth (speciation) probability changes through time (see details).

BIRTH

a (vectorized) function giving the primitive of birth.

root.time

a numeric value giving the time of the root node (time is measured from the past towards the present).

opti

a character string giving the function used for optimisation of the likelihood function. Three choices are possible: "nlm", "nlminb", or "optim", or any unambiguous abbreviation of these.

start

the initial values used in the optimisation.

Value

An object of class "yule" (see yule).

Details

The model fitted is a straightforward extension of the Yule model with covariates (see yule.cov). Rather than having heterogeneity among lineages, the speciation probability is the same for all lineages at a given time, but can change through time.

The function birth must meet these two requirements: (i) the parameters to be estimated are the formal arguments; (ii) time is named t in the body of the function. However, this is the opposite for the primitive BIRTH: t is the formal argument, and the parameters are used in its body. See the examples.

It is recommended to use BIRTH if possible, and required if speciation probability is constant on some time interval. If this primitive cannot be provided, a numerical integration is done with integrate.

The standard-errors of the parameters are computed with the Hessian of the log-likelihood function.

Examples

Run this code

### define two models...
birth.logis <- function(a, b) 1/(1 + exp(-a*t - b)) # logistic
birth.step <- function(l1, l2, Tcl) { # 2 rates with one break-point
    ans <- rep(l1, length(t))
    ans[t > Tcl] <- l2
    ans
}
### ... and their primitives:
BIRTH.logis <- function(t) log(exp(-a*t) + exp(b))/a + t
BIRTH.step <- function(t)
{
    out <- numeric(length(t))
    sel <- t <= Tcl
    if (any(sel)) out[sel] <- t[sel] * l1
    if (any(!sel)) out[!sel] <- Tcl * l1 + (t[!sel] - Tcl) * l2
    out
}
data(bird.families)
### fit both models:
yule.time(bird.families, birth.logis)
yule.time(bird.families, birth.logis, BIRTH.logis) # same but faster
yule.time(bird.families, birth.step)  # fails
yule.time(bird.families, birth.step, BIRTH.step,
          opti = "nlminb", start = c(.01, .01, 100))

Run the code above in your browser using DataLab

Last chance! 50% off unlimited learning