likelihood_bdK: Likelihood birth-death k function

In sophia-lambert/UDivEvo: A package for Unknown Diversity Diversification Analysis in Evolution

Likelihood birth-death k function

Description

Computes the log likelihood of a rooted ultrametric phylogeny under a constant-time homogeneous birth-death model and k-sampling. The birth-death process is conditioned on the starting time of the process tottime and the survival of the process at present time as well as having k extant sampled tips at present. This function can computes the log likelihood on a stem or crown phylogeny. This function is specifically adapted for diversification analysis on phylogenies on which the sampling probability is unknown.

Usage

likelihood_bdK(
  tottime,
  nbtips,
  tj,
  root,
  dt = dt,
  rel.tol = rel.tol,
  tuned_dichotomy = tuned_dichotomy,
  brk = brk
)

Arguments

tottime	Numeric vector. The stem or crown age (also called MRCA) of the phylogeny depending on the conditioning of the process specified (see root argument) and the phylogeny used. The stem age of the phylogeny can be computed using max(TreeSim::getx(phylo))+phylo$root.edge (note that the phylo$root.edge needs to be known) and the crown age of the phylogeny can be computed using max(TreeSim::getx(phylo)).
nbtips	Integer. The number of extant sampled tips in the phylogeny typically noted k.
tj	List of numeric vector. A list of atomic numeric vector where the vector is specifying the node depths of the phylogeny. The list is of length 1. The node depths of a phylogeny can be computed using TreeSim::getx(phylo)[!TreeSim::getx(phylo)==tottime] in a list. This code works both for stem and crown phylogenies. Note that the tottime is not contained in node depths here since it is used for conditioning the process. Since there are k-1 internal nodes in a phylogeny and that the MRCA is not included in the node depths when conditioning in crown, the numeric vector is of length k-2 if the phylogeny is in crown and of length k-1 if it is in stem with k being the number of extant sampled tips in the phylogeny.
root	Integer. Specifying the conditioning of the birth-death process. root takes the value 0 if the phylogeny used is a stem phylogeny to condition the process on the stem age. It takes the value 1 if the phylogeny is a crown phylogeny to condition the process on the crown age.
dt	Numeric. If dt = 0, the integral on the sampling probability is computed using the R stats::integrate function. If dt≥0, the integral of the sampling probability is performed manually using a piece-wise constant approximation. dt represents the length of the interval on which the function integrated is assumed to be constant. For manual integral, advised value of dt are 1e-3 to 1e-5.
rel.tol	Numeric. This represents the relative accuracy requested when the integral is performed using stats::integrate function. Typically, .Machine$double.eps^0.25 is used but a value of 1e-10 has been tested and performs well.
tuned_dichotomy	Logical. If TRUE, when the log likelihood is equal to non finite value due to approximations, a dichotomy search is performed to find a tuning parameter that will be used for getting a finite value of the log likelihood. If TRUE, the log likelihood will take longer to calculate. Else if FALSE, no dichotomy search is performed; if the log likelihood is equal to non finite value due to approximations, the function will return this non finite value.
brk	Numeric. The number of steps used in the dichotomy search. Typically the value 200 is sufficient to avoid non finite values. In some case if the log likelihood is still equal to non finite value, the brk value 2000 will be required for more tuning but it will rarely take a larger value.

Details

This function is a closure, it takes all of the above as arguments and creates another function using the arguments described in the Value section. Note that when the phylogeny is in stem, the conditioning is done on the stem age and k number of extant tips while when the phylogeny is in crown, the conditioning is done on the crown age, k_1 and k_2 the number of extant tips of the sister clades diverging at the MRCA. This function is specifically intended to be used on phylogenies with unknown or highly uncertain global diversity estimates (the sampling probability is not known with accuracy). Note that the sampling probability is never estimated and that this function is not able to evaluate negative rates.

Value

Returns an object of class function. This function can take the following arguments (tun.init and seqphy.init) and will return another function. This last function will take the diversifications rate as arguments ((div and turn)) and will return the value of the log likelihood in a list together with the tuning parameter value used:

tun.init

Numeric The initial tuning parameter value. Typically, it will take the value log(1).

seqphy.init

Integer. Here seqphy.init = 1 since it is the likelihood of a single phylogeny that is computed.

div

Numeric. The net diversification rate also called r.

turn

Numeric. The turnover rate also called ε.

Note that this functioon can be used on a set of phylogenies. See likelihood_bdRho to check how to adapt the arguments for a set of phylogenies.

Author(s)

Sophia Lambert

See Also

fitMCMC_bdK and likelihood_bdRho

sophia-lambert/UDivEvo documentation built on Sept. 27, 2022, 11:05 p.m.