R: Fits the Time-Dependent Yule Model

yule.time {ape} | R Documentation

## 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.

### 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.

### Value

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

### Author(s)

Emmanuel Paradis

### References

Hubert, N., Paradis, E., Bruggemann, H. and Planes, S. (2011) Community assembly and diversification in Indo-Pacific coral reef fishes. Ecology and Evolution, 1, 229–277.

### See Also

`branching.times`, `ltt.plot`, `birthdeath`, `yule`, `yule.cov`, `bd.time`

### Examples

    ### 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
    ## Not run: yule.time(bird.families, birth.step)  # fails
    yule.time(bird.families, birth.step, BIRTH.step,
              opti = "nlminb", start = c(.01, .01, 100))

[Package ape version 5.1 Index]