Maximization of the loglikelihood under a diversity-dependent diversification model with decoupling of a subclade's diversication dynamics from the main clade's dynamics

This function computes the maximum likelihood estimates of the parameters of a diversity-dependent diversification model with decoupling of the diversification dynamics of a subclade from the dynamics of the main clade for a given set of phylogenetic branching times of main clade and subclade and the time of splitting of the lineage that will form the subclade. It also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

dd_KI_ML(
  brtsM,
  brtsS,
  tsplit,
  initparsopt = c(0.5, 0.1, 2 * (1 + length(brtsM) + missnumspec[1]), 2 * (1 +
    length(brtsS) + missnumspec[length(missnumspec)]), (tsplit + max(brtsS))/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(c(brtsM, brtsS)) + sum(missnumspec)),
  ddmodel = 1,
  missnumspec = 0,
  cond = 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",
  correction = TRUE,
  verbose = FALSE
)

Arguments

brtsM: A set of branching times of the main clade in a phylogeny, all positive
brtsS: A set of branching times of the subclade in a phylogeny, all positive
tsplit: The branching time at which the lineage forming the subclade branches off, 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_M (speciation rate) of the main clade
id == 2 corresponds to mu_M (extinction rate) of the main clade
id == 3 corresponds to K_M (clade-level carrying capacity) of the main clade
id == 4 corresponds to lambda_S (speciation rate) of the subclade
id == 5 corresponds to mu_S (extinction rate) of the subclade
id == 6 corresponds to K_S (clade-level carrying capacity) of the subclade
id == 7 corresponds to t_d (the time of decoupling)
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 + max(length(brtsM),length(brtsS))
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
missnumspec: The number of species that are in the clade but missing in the phylogeny. One can specify the sum of the missing species in main clade and subclade or a vector c(missnumspec_M,missnumspec_S) with missing species in main clade and subclade respectively.
cond: Conditioning:
cond == 0 : no conditioning
cond == 1 : conditioning on non-extinction of the phylogeny
soc: Sets whether stem or crown age should be used (1 or 2); stem age only works when cond = 0
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.
correction: Sets whether the correction should be applied (TRUE) or not (FALSE)
verbose: Show the parameters and loglikelihood for every call to the loglik function

Value

lambda_M: gives the maximum likelihood estimate of lambda of the main clade
mu_M: gives the maximum likelihood estimate of mu of the main clade
K_M: gives the maximum likelihood estimate of K of the main clade
lambda_2: gives the maximum likelihood estimate of lambda of the subclade
mu_S: gives the maximum likelihood estimate of mu of the subclade
K_S: gives the maximum likelihood estimate of K of the subclade
t_d: gives the time of the decoupling event
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.

Note

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

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

Author

Rampal S. Etienne & Bart Haegeman

Examples


cat("This will estimate parameters for two sets of branching times brtsM, brtsS\n")
#> This will estimate parameters for two sets of branching times brtsM, brtsS
cat("without conditioning.\n")
#> without conditioning.
cat("The tolerance of the optimization is set high so runtime is fast in this example.\n")
#> The tolerance of the optimization is set high so runtime is fast in this example.
cat("In real applications, use the default or more stringent settins for tol.\n")
#> In real applications, use the default or more stringent settins for tol.
brtsM = 4:10
brtsS = seq(0.1,3.5,0.7)
tsplit = 5
dd_KI_ML(brtsM = brtsM, brtsS = brtsS, tsplit = tsplit, idparsopt = c(1:3,6,7),
  initparsopt = c(0.885, 2e-14, 6.999, 6.848, 4.001), idparsfix = NULL,
  parsfix = NULL,idparsnoshift = c(4,5), cond = 0, tol = c(3E-1,3E-1,3E-1),
  optimmethod = 'simplex')
#> You are optimizing la_M mu_M K_M K_S t_d 
#> You are fixing nothing 
#> You are not shifting la_S mu_S 
#> Optimizing the likelihood - this may take a while. 
#> The loglikelihood for the initial parameter values is -24.45333 
#> 1 0.885 2e-14 6.999 6.848 4.001 -24.4533303187317 initial 
#> Optimization has terminated successfully. 
#> 
#> Maximum likelihood parameter estimates: 0.885000 0.000000 6.999000 0.885000 0.000000 6.848000 4.001000
#> Maximum loglikelihood: -24.453330