DDD (version 1.9)

dd_SR_ML: Maximization of the loglikelihood under a diversity-dependent diversification model with a shift in the parameters

Description

This function computes the maximum likelihood estimates of the parameters of a diversity-dependent diversification model with shifting parameters at time t = tshift for a given set of phylogenetic branching times. It also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

dd_SR_ML(brts, initparsopt = c(0.5, 0.1, 2 * (1 + length(brts) + missnumspec),
   2 * (1 + length(brts) + missnumspec), max(brts)/2), parsfix = NULL, idparsopt
   = c(1:3, 6:7), idparsfix = NULL, idparsnoshift = (1:7)[c(-idparsopt,
   (-1)^(length(idparsfix) != 0) * idparsfix)], res = 10 * (1 + length(brts) +
   missnumspec), ddmodel = 1, missnumspec = 0, cond = TRUE, btorph = 1,
   allbp = FALSE, tol = c(1E-3,1E-4,1E-6), maxiter = 1000 * round((1.25)^
   length(idparsopt)))

Arguments

brts

A set of branching times of a phylogeny, all positive

initparsopt

The initial values of the parameters that must be optimized

parsfix

The values of the parameters that should not be optimized

idparsopt

The ids of the parameters that must be optimized, e.g. 1:7 for all parameters. The ids are defined as follows: id == 1 corresponds to lambda (speciation rate) before the shift id == 2 corresponds to mu (extinction rate) before the shift id == 3 cor

idparsfix

The ids of the parameters that should not be optimized, e.g. c(1,3,4,6) if lambda and K should not be optimized, but only mu. In that case idparsopt must be c(2,5,7). The default is to fix all parameters not specified in idparsopt.

idparsnoshift

The ids of the parameters that should not shift; This can only apply to ids 4, 5 and 6, e.g. idparsnoshift = c(4,5) means that lambda and mu have the same values before and after tshift

res

sets the maximum number of species for which a probability must be computed, must be larger than 1 + length(brts)

ddmodel

sets the model of diversity-dependence: ddmodel == 1 : linear dependence in speciation rate ddmodel == 2 : exponential dependence in speciation rate ddmodel == 3 : linear dependence in extinction rate ddmodel == 4 : exponential dependence in extinctio

missnumspec

The number of species that are in the clade but missing in the phylogeny

cond

Conditioning on non-extinction of the phylogeny (TRUE or FALSE)

btorph

Sets whether the likelihood is for the branching times (0) or the phylogeny (1)

allbp

Sets whether a search should be done with various initial conditions, with tshift at each of the branching points (TRUE/FALSE)

tol

Sets the tolerances in the optimization. Consists of: reltolx = relative tolerance of parameter values in optimization reltolf = relative tolerance of function value in optimization abstolx = absolute tolerance of parameter values in optimization

maxiter

Sets the maximum number of iterations in the optimization

Value

• lambda_1
  gives the maximum likelihood estimate of lambda before the shift
• mu_1
  gives the maximum likelihood estimate of mu before the shift
• K_1
  gives the maximum likelihood estimate of K before the shift
• lambda_2
  gives the maximum likelihood estimate of lambda after the shift
• mu_2
  gives the maximum likelihood estimate of mu after the shift
• K_2
  gives the maximum likelihood estimate of K after the shift
• t_shift
  gives the time of the shift
• loglik
  gives the maximum loglikelihood
• df
  gives the number of estimated parameters, i.e. degrees of feedom
• conv
  gives a message on convergence of optimization; conv = 0 means convergence

Details

The output is a dataframe containing estimated parameters and maximum loglikelihood. The computed loglikelihood contains the factor q! m!/(q + m)! where q is the number of species in the phylogeny and m is the number of missing species, as explained in the supplementary material to Etienne et al. 2012.

References

- Etienne et al. 2012, Proc. Roy. Soc. B 279: 1300-1309, doi: 10.1098/rspb.2011.1439 - Etienne & Haegeman 2012. Am. Nat. Am. Nat. 180: E75-E89, doi: 10.1086/667574

See Also

dd_SR_loglik, dd_ML, dd_KI_ML,

Examples

cat("Estimating parameters for a set of branching times brts with the default settings:")
brts = 1:20
dd_SR_ML(brts)
dd_SR_ML(1:4,initparsopt = c(2.23,0.0002,1.58,4.41,3.01),idparsopt = c(1:3,6,7),tol = c(0.01,0.01,0.01))