DDD (version 3.2)

dd_KI_ML: 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 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(1E-3,1E-4,1E-6), maxiter = 1000 * round((1.25)^length(idparsopt)), changeloglikifnoconv = FALSE, optimmethod = 'subplex', methode = 'analytical' )

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)

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_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.

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_KI_loglik, dd_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_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))