dd_SR_ML {DDD}

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 = 1,
  btorph = 1,
  soc = 2,
  allbp = FALSE,
  tol = c(0.001, 1e-04, 1e-06),
  maxiter = 1000 * round((1.25)^length(idparsopt)),
  changeloglikifnoconv = FALSE,
  optimmethod = "subplex",
  num_cycles = 1,
  methode = "analytical",
  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

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 corresponds to K (clade-level carrying capacity) before the shift
id == 4 corresponds to lambda (speciation rate) after the shift
id == 5 corresponds to mu (extinction rate) after the shift
id == 6 corresponds to K (clade-level carrying capacity) after the shift
id == 7 corresponds to tshift (the time of shift)

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 == 2.1 : variant of exponential dependence in speciation rate with offset at infinity
ddmodel == 2.2 : 1/n dependence in speciation rate
ddmodel == 3 : linear dependence in extinction rate
ddmodel == 4 : exponential dependence in extinction rate
ddmodel == 4.1 : variant of exponential dependence in extinction rate with offset at infinity
ddmodel == 4.2 : 1/n dependence in extinction rate with offset at infinity

missnumspec

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

cond

Conditioning:
cond == 0 : no conditioning
cond == 1 : conditioning on non-extinction of the phylogeny
cond == 2 : conditioning on non-extinction of the phylogeny and on the total number of extant taxa (including missing species)
cond == 3 : conditioning on the total number of extant taxa (including missing species)

Note: cond == 3 assumes a uniform prior on stem age, as is the standard in constant-rate birth-death models, see e.g. D. Aldous & L. Popovic 2004. Adv. Appl. Prob. 37: 1094-1115 and T. Stadler 2009. J. Theor. Biol. 261: 58-66.

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)

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

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, default is 'analytical' which uses matrix exponentiation; alternatively numerical ODE solvers can be used, such as 'odeint::runge_kutta_cash_karp54'. These were used in the package before version 3.1.

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

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

Note

The optimization may get trapped in local optima. Try different starting values to search for the global optimum.

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

dd_SR_loglik, dd_ML, dd_KI_ML,

Examples

cat("This will estimate parameters for a sets of branching times brts without conditioning.\n")
cat("The tolerance of the optimization is set ridiculously high to make runtime fast.\n")
cat("In real applications, use the default or more stringent settings for tol.\n")
brts = 1:10
dd_SR_ML(brts = brts, initparsopt = c(0.4581, 1E-6, 17.69, 11.09, 8.9999), idparsopt = c(1:3,6,7),
         idparsfix = NULL, parsfix = NULL, idparsnoshift = c(4,5), cond = 0,
         tol = c(1E-1,1E-1,1E-1),optimmethod = 'simplex'
)