dd_MS_ML: Maximization of the loglikelihood under a diversity-dependent...

In DDD: Diversity-Dependent Diversification

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

Description

This function computes the maximum likelihood estimates of the parameters of a diversity-dependent diversification model where the diversity-dependent dynamics of an innovative subclade have different parameters from the dynamics of the main clade from time t_d, but both are governed by the same carrying capacity and experience each other's diversity. Required isa given set of phylogenetic branching times of main clade and subclade and the time of splitting of the lineage that will form the subclade. The function also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

dd_MS_ML(
  brtsM,
  brtsS,
  tsplit,
  initparsopt = c(0.5, 0.1, 2 * (1 + length(brtsM) + length(brtsS) + sum(missnumspec)),
    (tsplit + max(brtsS))/2),
  parsfix = NULL,
  idparsopt = c(1:3, 6),
  idparsfix = NULL,
  idparsnoshift = (1:6)[c(-idparsopt, (-1)^(length(idparsfix) != 0) * idparsfix)],
  res = 10 * (1 + length(c(brtsM, brtsS)) + sum(missnumspec)),
  ddmodel = 1.3,
  missnumspec = 0,
  cond = 0,
  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 = "ode45",
  correction = FALSE,
  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 t_d (the time of the key innovation)
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 in the ode solver. This can be either 'analytical' for explicit matrix exponentation or any of the solvers in the deSolve package.
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

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_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
t_d	gives the time of the key innovation 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

Note

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

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_MS_loglik, dd_ML, dd_KI_ML, dd_SR_ML,

Examples

cat("This will estimate parameters for two sets of branching times brtsM, brtsS\n")
cat("without conditioning.\n")
cat("The tolerance of the optimization is set high so runtime is fast in this example.\n")
cat("In real applications, use the default or more stringent settins for tol.\n")
brtsM = 4:10
brtsS = seq(0.1,3.5,0.7)
tsplit = 5
dd_MS_ML(brtsM = brtsM, brtsS = brtsS, tsplit = tsplit, idparsopt = c(1:3,6),
          initparsopt = c(0.885, 2e-14, 10, 4.001), idparsfix = NULL, parsfix = NULL,
          idparsnoshift = c(4,5), cond = 0, tol = c(3E-1,3E-1,3E-1))

DDD documentation built on July 26, 2023, 5:25 p.m.