bd_ML {DDD}

Maximization of the loglikelihood under the diversity-independent, possibly time-dependent diversification model

Description

This function computes the maximum likelihood estimates of the parameters of a diversity-independent diversification model for a given set of phylogenetic branching times. It also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

bd_ML(
  brts,
  initparsopt = c(0.1, 0.05 * (tdmodel <= 1) + 10 * (length(brts) + missnumspec) *
    (tdmodel > 1)),
  idparsopt = c(1, 2 + (tdmodel > 1)),
  idparsfix = (1:4)[-idparsopt],
  parsfix = rep(0, 4)[idparsfix],
  missnumspec = 0,
  tdmodel = 0,
  cond = 1,
  btorph = 1,
  soc = 2,
  tol = c(0.001, 1e-04, 1e-06),
  maxiter = 1000 * round((1.25)^length(idparsopt)),
  changeloglikifnoconv = FALSE,
  optimmethod = "subplex",
  num_cycles = 1,
  methode = "odeint::runge_kutta_cash_karp54",
  verbose = FALSE
)

Arguments

brts

A set of branching times of a phylogeny, all positive

initparsopt

The initial values of the parameters that must be optimized

idparsopt

The ids of the parameters that must be optimized, e.g. 1:3 for intrinsic speciation rate, extinction rate and carrying capacity. The ids are defined as follows:
id == 1 corresponds to lambda0 (speciation rate)
id == 2 corresponds to mu0 (extinction rate)
id == 3 corresponds to lamda1 (parameter controlling decline in speciation rate with time)
id == 4 corresponds to mu1 (parameter controlling decline in extinction rate with time)

idparsfix

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda0 and lambda1 should not be optimized, but only mu0 and mu1. In that case idparsopt must be c(2,4). The default is to fix all parameters not specified in idparsopt.

parsfix

The values of the parameters that should not be optimized

missnumspec

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

tdmodel

Sets the model of time-dependence:
tdmodel == 0 : constant speciation and extinction rates
tdmodel == 1 : speciation and/or extinction rate is exponentially declining with time
tdmodel == 2 : stepwise decline in speciation rate as in diversity-dependence without extinction
tdmodel == 3 : decline in speciation rate following deterministic logistic equation for ddmodel = 1
tdmodel == 4 : decline in speciation rate such that the expected number of species matches with that of ddmodel = 1 with the same mu

cond

Conditioning:
cond == 0 : conditioning on stem or crown age
cond == 1 : conditioning on stem or crown age and non-extinction of the phylogeny
cond == 2 : conditioning on stem or crown age and on the total number of extant taxa (including missing species)
cond == 3 : conditioning on the total number of extant taxa (including missing species)

btorph

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

soc

Sets whether stem or crown age should be used (1 or 2)

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

changeloglikifnoconv

if TRUE the loglik will be set to -Inf if ML does not converge

optimmethod

Method used in optimization of the likelihood. Current default is 'subplex'. Alternative is 'simplex' (default of previous versions)

num_cycles

the number of cycles of opimization. If set at Inf, it will do as many cycles as needed to meet the tolerance set for the target function.

methode

The method used to solve the master equation under tdmodel = 4, default is 'odeint::runge_kutta_cash_karp54'.

verbose

Show the parameters and loglikelihood for every call to the loglik function

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.

Value

A dataframe with the following elements:

lambda0

gives the maximum likelihood estimate of lambda0

mu0

gives the maximum likelihood estimate of mu0

lambda1

gives the maximum likelihood estimate of lambda1

mu1

gives the maximum likelihood estimate of mu1

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

Author(s)

Rampal S. Etienne & Bart Haegeman

References

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

See Also

bd_loglik

Examples

cat("Estimating parameters for a set of branching times brts with the default settings:")
brts = 1:20
bd_ML(brts = brts, cond = 1)