diversitree (version 0.10-1)

make.bd.t: Time-varing Birth-Death Models

Description

Create a likelihood function for the birth-death model, where birth and/or death rates are arbitrary functions of time.

Usage

make.bd.t(tree, functions, sampling.f=NULL, unresolved=NULL,
          control=list(), truncate=FALSE, spline.data=NULL)

Arguments

tree

An ultrametric bifurcating phylogenetic tree, in ape “phylo” format.

functions

A named list of functions of time. See details.

sampling.f

Probability of an extant species being included in the phylogeny (sampling fraction). By default, all extant species are assumed to be included.

unresolved

Not yet included: present in the argument list for future compatibility with make.bd.

control

List of control parameters for the ODE solver. See details in make.bisse.

truncate

Logical, indicating if functions should be truncated to zero when negative (rather than causing an error). May be scalar (applying to all functions) or a vector (of length 2).

spline.data

List of data for spline-based time functions. See details

.

Author

Richard G. FitzJohn

Examples

## First, show equivalence to the plain Birth-death model.  This is not
## a very interesting use of the functions, but it serves as a useful
## check.

## Here is a simulated 25 species tree for testing.
set.seed(1)
pars <- c(.1, .03)
phy <- trees(pars, "bd", max.taxa=25)[[1]]

## Next, make three different likelihood functions: a "normal" one that
## uses the direct birth-death calculation, an "ode" based one (that
## uses numerical integration to compute the likelihood, and is
## therefore not exact), and one that is time-varying, but that the
## time-dependent functions are constant.t().
lik.direct <- make.bd(phy)
lik.ode <- make.bd(phy, control=list(method="ode"))
lik.t <- make.bd.t(phy, c("constant.t", "constant.t"))

lik.direct(pars) # -22.50267

## ODE-based likelihood calculations are correct to about 1e-6.
lik.direct(pars) - lik.ode(pars)

## The ODE calculation agrees exactly with the time-varying (but
## constant) calculation.
lik.ode(pars) - lik.t(pars)

## Next, make a real case, where speciation is a linear function of
## time.
lik.t2 <- make.bd.t(phy, c("linear.t", "constant.t"))

## Confirm that this agrees with the previous calculations when the
## slope is zero
pars2 <- c(pars[1], 0, pars[2])
lik.t2(pars2) - lik.t(pars)

## The time penalty comes from moving to the ODE-based solution, not
## from the time dependence.
system.time(lik.direct(pars)) # ~ 0.000
system.time(lik.ode(pars))    # ~ 0.003
system.time(lik.t(pars))      # ~ 0.003
system.time(lik.t2(pars2))    # ~ 0.003

if (FALSE) {
fit <- find.mle(lik.direct, pars)
fit.t2 <- find.mle(lik.t2, pars2)

## No significant improvement in model fit:
anova(fit, time.varying=fit.t2)
}