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DDD (version 3.2)

dd_ML: 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 = if(ddmodel < 5) {c(0.2,0.1,2*(length(brts) + missnumspec))} else {c(0.2,0.1,2*(length(brts) + missnumspec),0.01)}, idparsopt = 1:length(initparsopt), idparsfix = (1:(3 + (ddmodel == 5)))[-idparsopt], parsfix = (ddmodel < 5) * c(0.2,0.1, 2 * (length(brts) + missnumspec))[-idparsopt] + (ddmodel == 5) * c(0.2, 0.1, 2 * (length(brts) + missnumspec), 0)[-idparsopt], res = 10 * (1 + length(brts) + missnumspec), ddmodel = 1, missnumspec = 0, cond = 1, btorph = 1, soc = 2, tol = c(1E-3,1E-4,1E-6), maxiter = 1000 * round((1.25)^length(idparsopt)), changeloglikifnoconv = FALSE, optimmethod = 'subplex', methode = 'analytical' )

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 == 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. This conditioning turns out, for the diversity-dependent model, to provide the least-biased parameter estimates when extinction is low, but may still contain considerable bias if extinction is high. The default value has therefore been changed from 1 to 3 starting with DDD version 2.2.
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)
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 'lsoda' or 'ode45'. These were used in the package before version 3.1.

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

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

See Also

dd_loglik, dd_SR_ML, dd_KI_ML,

Examples

Run this code
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')

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