dd_ML {DDD}

Maximization of the loglikelihood under a diversity-dependent diversification model

Description

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

Usage

dd_ML(
  brts,
  initparsopt = initparsoptdefault(ddmodel, brts, missnumspec),
  idparsopt = 1:length(initparsopt),
  idparsfix = (1:(3 + (ddmodel == 5)))[-idparsopt],
  parsfix = parsfixdefault(ddmodel, brts, missnumspec, idparsopt),
  res = 10 * (1 + length(brts) + missnumspec),
  ddmodel = 1,
  missnumspec = 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 = "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

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 lambda (speciation rate)
id == 2 corresponds to mu (extinction rate)
id == 3 corresponds to K (clade-level carrying capacity)
id == 4 corresponds to r (r = b/a where mu = mu_0 + b * N and lambda = lambda_0 - a * N) (This is only available when ddmodel = 5)

idparsfix

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

parsfix

The values of the parameters that should not be optimized

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 with parameter K (= diversity where speciation = extinction)
ddmodel == 1.3 : linear dependence in speciation rate with parameter K' (= diversity where speciation = 0)
ddmodel == 1.4 : positive diversity-dependence in speciation rate with parameter K' (= diversity where speciation rate reaches half its maximum); lambda = lambda0 * S/(S + K') where S is species richness
ddmodel == 1.5 : positive and negative dependence in speciation rate with parameter K' (= diversity where speciation = 0); lambda = lambda0 * S/K' * (1 - S/K') where S is species richness
ddmodel == 2 : exponential dependence in speciation rate with parameter K (= diversity where speciation = extinction)
ddmodel == 2.1 : variant of exponential dependence in speciation rate with offset at infinity
ddmodel == 2.2 : 1/n dependence in speciation rate
ddmodel == 2.3 : exponential dependence in speciation rate with parameter x (= exponent)
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
ddmodel == 5 : linear dependence in speciation and extinction rate

missnumspec

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

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)
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)

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

gives the maximum likelihood estimate of lambda

mu

gives the maximum likelihood estimate of mu

K

gives the maximum likelihood estimate of K

r

(only if ddmodel == 5) gives the ratio of linear dependencies in speciation and extinction rates

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

dd_loglik, dd_SR_ML, dd_KI_ML,

Examples

cat("Estimating the intrinsic speciation rate lambda and the carrying capacity K")
cat("for a fixed extinction rate of 0.1, conditioning on clade survival and two missing species:")
brts = 1:5
dd_ML(brts = brts,initparsopt = c(1.3078,7.4188), idparsopt = c(1,3), parsfix = 0.1,
      cond = 1, missnumspec = 2, tol = c(1E-3,1E-3,1E-4), optimmethod = 'simplex')