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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.

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.

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))

ape

Analyses of Phylogenetics and Evolution

v5.5

GPL-2 | GPL-3

Authors

Emmanuel Paradis [aut, cre, cph] (<https://orcid.org/0000-0003-3092-2199>), Simon Blomberg [aut, cph] (<https://orcid.org/0000-0003-1062-0839>), Ben Bolker [aut, cph] (<https://orcid.org/0000-0002-2127-0443>), Joseph Brown [aut, cph] (<https://orcid.org/0000-0002-3835-8062>), Santiago Claramunt [aut, cph] (<https://orcid.org/0000-0002-8926-5974>), Julien Claude [aut, cph] (<https://orcid.org/0000-0002-9267-1228>), Hoa Sien Cuong [aut, cph], Richard Desper [aut, cph], Gilles Didier [aut, cph] (<https://orcid.org/0000-0003-0596-9112>), Benoit Durand [aut, cph], Julien Dutheil [aut, cph] (<https://orcid.org/0000-0001-7753-4121>), RJ Ewing [aut, cph], Olivier Gascuel [aut, cph], Thomas Guillerme [aut, cph] (<https://orcid.org/0000-0003-4325-1275>), Christoph Heibl [aut, cph] (<https://orcid.org/0000-0002-7655-3299>), Anthony Ives [aut, cph] (<https://orcid.org/0000-0001-9375-9523>), Bradley Jones [aut, cph] (<https://orcid.org/0000-0003-4498-1069>), Franz Krah [aut, cph] (<https://orcid.org/0000-0001-7866-7508>), Daniel Lawson [aut, cph] (<https://orcid.org/0000-0002-5311-6213>), Vincent Lefort [aut, cph], Pierre Legendre [aut, cph] (<https://orcid.org/0000-0002-3838-3305>), Jim Lemon [aut, cph], Guillaume Louvel [aut, cph] (<https://orcid.org/0000-0002-7745-0785>), Eric Marcon [aut, cph] (<https://orcid.org/0000-0002-5249-321X>), Rosemary McCloskey [aut, cph] (<https://orcid.org/0000-0002-9772-8553>), Johan Nylander [aut, cph], Rainer Opgen-Rhein [aut, cph], Andrei-Alin Popescu [aut, cph], Manuela Royer-Carenzi [aut, cph], Klaus Schliep [aut, cph] (<https://orcid.org/0000-0003-2941-0161>), Korbinian Strimmer [aut, cph] (<https://orcid.org/0000-0001-7917-2056>), Damien de Vienne [aut, cph] (<https://orcid.org/0000-0001-9532-5251>)

Initial release

2021-04-24