tess.likelihood {TESS}

tess.likelihood: Probability density of a tree under a tree-wide time-dependent birth-death process

Description

tess.likelihood computes the probability of a reconstructed phylogenetic tree under time-dependent diversification rates. The rates may be any positive function of time or a constant. Additionally, mass-extinction event can be provided and a uniform taxon sampling probability. You have several options for the start of the process (origin vs MRCA) and the condition of the process (time, survival or taxa; note that survival and taxa implicitly condition on the time too!). See equation (5) in Hoehna (2013) for more information. Note that constant rates lead to much faster computations. The likelihood can be computed for incompletely sampled trees if you give a sampling probability != 1.0. You have two options for the sampling strategy: uniform|diversified. The detailed description of these can be found in the references. More information can be obtained in the vignette about how to apply this likelihood function.

Usage

tess.likelihood(times,
                lambda,
                mu,
                massExtinctionTimes=c(),
                massExtinctionSurvivalProbabilities=c(),
                missingSpecies = c(),
                timesMissingSpecies = c(),
                samplingProbability=1.0,
                samplingStrategy="uniform",
                MRCA=TRUE,
                CONDITION="survival",
                log=TRUE)

Arguments

times

The branching times of the phylogeny.

lambda

The speciation rate function or constant.

mu

The extinction rate function or constant.

massExtinctionTimes

The set of mass-extinction times after the start of the process.

massExtinctionSurvivalProbabilities

The set of survival probabilities for each speciation event. The set must have the same length as the set of mass-extinction times.

missingSpecies

The number of species missed which originated in a given time interval (empirical taxon sampling).

timesMissingSpecies

The times intervals of the missing species (empirical taxon sampling).

samplingProbability

The probability for a species to be included in the sample.

samplingStrategy

The strategy how samples were obtained. Options are: uniform|diversified|age.

MRCA

Does the process start with the most recent common ancestor? If not, the tree must have a root edge!

CONDITION

do we condition the process on time|survival|taxa?

log

Should we log-transform the likelihood?

Value

Returns the (log) probability of the tree, i.e. the likelihood of the parameters given the tree.

Author(s)

Sebastian Hoehna

References

S. Hoehna: Fast simulation of reconstructed phylogenies under global, time-dependent birth-death processes. 2013, Bioinformatics, 29:1367-1374

S. Hoehna: Likelihood Inference of Non-Constant Diversification Rates with Incomplete Taxon Sampling. 2014, PLoS one, Public Library of Science, 9, e84184.

S. Hoehna: The time-dependent reconstructed evolutionary process with a key-role for mass-extinction events. 2015, Journal of Theoretical Biology, 380, 321-331.

Examples

# load a test data set
data(cettiidae)

# convert the phylogeny into the branching times
times <- as.numeric( branching.times(cettiidae) )

# construct speciation and extinction rate function that resemble the rate-shift
# any other function could be used too
l <- Vectorize(function(x) { if (x > 0.5 || x < 0.3) { return (1) } else { return (2) } })
e <- Vectorize(function(x) { if (x > 0.5 || x < 0.3) { return (0.95) } else { return (0.5) } })

# now compute the likelihood for the tree
tess.likelihood(times,l,e,MRCA=TRUE,log=TRUE)

# a second approach is the specific episodic birth-death process likelihood function
# we need to give the rates for each episode and the end time of the episodes
# you should see that both are equivalent in this setting
# the function approach is more general but also slower.
tess.likelihood.rateshift(times,
				lambda=c(2,1,2),
				mu=c(0.95,0.5,0.95),
				rateChangeTimesLambda=c(0.3,0.5),
				rateChangeTimesMu=c(0.3,0.5),
				MRCA=TRUE,
				log=TRUE)