likPOUMMGivenTreeVTips {POUMM}

Density of observed tip-values given a tree, assuming Ornstein-Uhlenbeck process for the genetic contributions along the tree and normally distributed environmental deviations.

Description

Calculates the (log-)probability density of trait values at the tip-nodes given the tree and assuming that the trait value at the tips is the sum of a genetic contribution, g, that evolved on the tree according to an OU process with parameters alpha, theta, sigma and an environmental deviation, e, that is distributed normally and independently between the tips of the tree. Note: Without additional assumptions for the distribution of the value at the root of the tree, the likelihood is not defined at alpha=0, although this corresponds to the limiting Brownian motion process with mean value theta and unit time variance sigma^2. Considering the observed data and tree as a fixed parameter and the POUMM parameters as variables, this function is interpreted as the POUMM likelihood.

Usage

likPOUMMGivenTreeVTips(
  z,
  tree,
  alpha,
  theta,
  sigma,
  sigmae = 0,
  g0 = NA,
  g0Prior = NULL,
  log = TRUE,
  pruneInfo = pruneTree(tree, z),
  usempfr = 0,
  maxmpfr = 2,
  precbits = 128,
  debug = FALSE
)

Arguments

z

A numeric vector of size length(tree$tip.label) representing the trait values at the tip-nodes.

tree

an object of class phylo

alpha

the strength of the selection

theta

long term mean value of the OU process

sigma

the unit-time standard deviation of the random component in the OU process.

sigmae

the standard deviation of the environmental deviation added to the genetic contribution at each tip, by default 0, meaning no environmental deviation.

g0

Numeric, NA or NaN, either a fixed genotypic value at the root of tree or NA or NaN. A NA "Not Available" will cause to analytically calculate the value of g0 that would maximize the conditional likelihood of the data given g0. A NaN "Not a Number" will cause integration over g0 taking values in (-Inf,+Inf) assuming that g0 is normally distributed with mean g0Prior$mean and variance g0Prior$var (see parameter g0Prior).

g0Prior

Either NULL or a list with named numeric or character members "mean" and "var". Specifies a prior normal distribution for the parameter g0. If characters, the members mean and var are evaluated as R-expressions.

log

Logical indicating whether log-likelihood should be returned instead of likelihood, default is TRUE.

pruneInfo

list returned by pruneTree(tree) to be passed in explicit calls to dVGivenTreeOU.

usempfr

integer indicating if and how mpfr should be used for small parameter values (any(c(alpha, sigma, sigmae) < 0.01)). Using the mpfr package can be forced by specifying an integer greater or equal to 2. Setting usempfr=0 (default) causes high precision likelihood calculation to be done on each encounter of parameters with at least 1 bigger log-likelihood value than any of the currently found maximum log-likelihood or the previously calculated log-likelihood value Requires the Rmpfr package. Note that using mpfr may increase the time for one likelihood calculation more than 100-fold. Set usempfr to -1 or less to completely disable Rmpfr functionality.

maxmpfr

integer (not used)

precbits

integer specifying precision bits for mpfr. Default is 512.

debug

logical, if set to TRUE some debugging information is printed during likelihood calculation

Value

A numeric with attributes "g0" and "g0LogPrior".