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

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

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

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, 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

Author

Rampal S. Etienne & Bart Haegeman

Examples


cat("Estimating parameters for a set of branching times brts with the default settings:")
#> Estimating parameters for a set of branching times brts with the default settings:
brts = 1:20
bd_ML(brts = brts, cond = 1)
#> You are optimizing lambda0 mu0 
#> You are fixing lambda1 mu1 
#> Optimizing the likelihood - this may take a while. 
#> The loglikelihood for the initial parameter values is -67.8956450330451.
#> 
#> Maximum likelihood parameter estimates: lambda0: 0.082413, mu0: 0.000012, lambda1: 0.000000, mu1: 0.000000: 
#> Maximum loglikelihood: -66.379536
#>      lambda0          mu0 lambda1 mu1    loglik df conv
#> 1 0.08241342 1.162588e-05       0   0 -66.37954  2    0