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.
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(0.001, 1e-04, 1e-06),
maxiter = 2000,
changeloglikifnoconv = FALSE,
optimmethod = "subplex",
methode = "analytical"
)a list of trees generated under the constant-rates model using the ML parameters under the CR model
a list of trees generated under the diversity-dependent model using the ML parameters under the diversity-dependent model
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
p-value of the test
Likelihood ratio at the signifiance level alpha
power of the test for significance level alpha
A set of branching times of a phylogeny, all positive
The initial values of the parameters that must be optimized for the diversity-dependent (DD) model: lambda_0, mu and K
The initial values of the parameters that must be optimized for the constant-rates (CR) model: lambda and mu
The number of species that are in the clade but missing in the phylogeny
The name (and location) of the file where the output will be saved. Default is no save.
The seed for the pseudo random number generator for simulating the bootstrap data
The number of bootstraps
The significance level of the test
Boolean to plot results or not
Sets the maximum number of species for which a probability must be computed, must be larger than 1 + length(brts)
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
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.
Sets whether the likelihood is for the branching times (0) or the phylogeny (1)
Sets whether stem or crown age should be used (1 or 2)
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
Sets the maximum number of iterations in the optimization
if TRUE the loglik will be set to -Inf if ML does not converge
Method used in optimization of the likelihood. Current default is 'subplex'. Alternative is 'simplex' (default of previous versions)
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.
Rampal S. Etienne & Bart Haegeman
The output is a list with 3 elements:
- Etienne, R.S. et al. 2016. Meth. Ecol. Evol. 7: 1092-1099,
doi: 10.1111/2041-210X.12565
- 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
dd_loglik, dd_ML