dd_LR: Bootstrap likelihood ratio test of diversity-dependent diversification model

Description

This function computes the maximum likelihood and the associated estimates of the parameters of a diversity-dependent diversification model for a given set of phylogenetic branching times. It then performs a bootstrap likelihood ratio test of the diversity-dependent (DD) model against the constant-rates (CR) birth-death model. Finally, it computes the power of this test.

Usage

dd_LR(
   brts,
   initparsoptDD,
   initparsoptCR,
   missnumspec,
   outputfilename = NULL,
   seed = 42,
   endmc = 1000,
   alpha = 0.05,
   plotit = TRUE,
   res = 10 * (1 + length(brts) + missnumspec),
   ddmodel = 1,
   cond = 1,
   btorph = 1,
   soc = 2,
   tol = c(1E-3,1E-4,1E-6),
   maxiter = 2000,
   changeloglikifnoconv = FALSE,
   optimmethod = 'subplex',
   methode = 'analytical'    
   )

Arguments

brts

A set of branching times of a phylogeny, all positive

initparsoptDD

The initial values of the parameters that must be optimized for the diversity-dependent (DD) model: lambda_0, mu and K

initparsoptCR

The initial values of the parameters that must be optimized for the constant-rates (CR) model: lambda and mu

missnumspec

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

outputfilename

The name (and location) of the file where the output will be saved. Default is no save.

seed

The seed for the pseudo random number generator for simulating the bootstrap data

endmc

The number of bootstraps

alpha

The significance level of the test

plotit

Boolean to plot results or not

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

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)

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

treeCR

a list of trees generated under the constant-rates model using the ML parameters under the CR model

treeDD

a list of trees generated under the diversity-dependent model using the ML parameters under the diversity-dependent model

out

a dataframe with the parameter estimates and maximum likelihoods for diversity-dependent and constant-rates models $model - the model used to generate the data. 0 = unknown (for real data), 1 = CR, 2 = DD $mc - the simulation number for each model $lambda_CR - speciation rate estimated under CR $mu_CR - extinction rate estimated under CR $LL_CR - maximum likelihood estimated under CR $conv_CR - convergence code for likelihood optimization; conv = 0 means convergence $lambda_DD1 - initial speciation rate estimated under DD for first set of initial values $mu_DD1 - extinction rate estimated under DD for first set of initial values $K_DD1 - clade-wide carrying-capacity estimated under DD for first set of initial values $LL_DD1 - maximum likelihood estimated under DD for first set of initial values $conv_DD1 - convergence code for likelihood optimization for first set of initial values; conv = 0 means convergence $lambda_DD2 - initial speciation rate estimated under DD for second set of initial values $mu_DD2 - extinction rate estimated under DD for second set of initial values $K_DD2 - clade-wide carrying-capacity estimated under DD for second set of initial values $LL_DD2 - maximum likelihood estimated under DD for second set of initial values $conv_DD2 - convergence code for likelihood optimization for second set of initial values; conv = 0 means convergence $LR - likelihood ratio between DD and CR

pvalue

p-value of the test

LRalpha

Likelihood ratio at the signifiance level alpha

poweroftest

power of the test for significance level alpha

Details

The output is a list with 3 elements:

References