dd_KI_loglik {DDD}

Loglikelihood for diversity-dependent diversification models with decoupling of a subclade from a main clade at time t = t_d

Description

This function computes loglikelihood of a diversity-dependent diversification model for a given set of branching times and parameter values where the diversity-dependent dynamics of a subclade decouple from the dynamics of the main clade at time t_d, potentially accompanied by a shift in parameters.

Usage

dd_KI_loglik(
  pars1,
  pars2,
  brtsM,
  brtsS,
  missnumspec,
  methode = "odeint::runge_kutta_cash_karp54"
)

Arguments

pars1

Vector of parameters:

pars1[1] corresponds to lambda_M (speciation rate) of the main clade
pars1[2] corresponds to mu_M (extinction rate) of the main clade
pars1[3] corresponds to K_M (clade-level carrying capacity) of the main clade
pars1[4] corresponds to lambda_S (speciation rate) of the subclade
pars1[5] corresponds to mu_S (extinction rate) of the subclade
pars1[6] corresponds to K_S (clade-level carrying capacity) of the subclade
pars1[7] corresponds to t_d (the time of decoupling)

pars2

Vector of model settings:

pars2[1] sets the maximum number of species for which a probability must be computed. This must be larger than 1 + missnumspec + length(brts).

pars2[2] sets the model of diversity-dependence:
- pars2[2] == 1 linear dependence in speciation rate with parameter K (= diversity where speciation = extinction)
- pars2[2] == 1.3 linear dependence in speciation rate with parameter K' (= diversity where speciation = 0)
- pars2[2] == 2 exponential dependence in speciation rate with parameter K (= diversity where speciation = extinction)
- pars2[2] == 2.1 variant of exponential dependence in speciation rate with offset at infinity
- pars2[2] == 2.2 1/n dependence in speciation rate
- pars2[2] == 2.3 exponential dependence in speciation rate with parameter x (= exponent)
- pars2[2] == 3 linear dependence in extinction rate
- pars2[2] == 4 exponential dependence in extinction rate
- pars2[2] == 4.1 variant of exponential dependence in extinction rate with offset at infinity
- pars2[2] == 4.2 1/n dependence in extinction rate

pars2[3] sets the conditioning:
- pars2[3] == 0 no conditioning (or just crown age)
- pars2[3] == 1 conditioning on non-extinction of the phylogeny
- pars2[3] == 2 conditioning on number of species and crown age; not yet implemented
- pars2[3] == 3 conditioning on number of species only; not yet implemented
- pars2[3] == 4 conditioning on survival of the subclade
- pars2[3] == 5 conditioning on survival of all subclades and of both crown lineages in the main clade. This assumes that subclades that have already shifted do not undergo another shift, i.e. shifts only occur in the main clade.

pars2[4] Obsolete.

pars2[5] sets whether the parameters and likelihood should be shown on screen (1) or not (0)

pars2[6] sets whether the first data point is stem age (1) or crown age (2)

pars2[7] sets whether the old (incorrect) likelihood should be used (0), or whether the new corrected likelihood should be used (1).

brtsM

A set of branching times of the main clade in the phylogeny, all positive

brtsS

A set of branching times of the subclade in the phylogeny, all positive

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.

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.

Value

The loglikelihood

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_KI_ML, dd_loglik dd_SR_loglik

Examples

pars1 = c(0.25,0.12,25.51,1.0,0.16,8.61,9.8)
pars2 = c(200,1,0,18.8,1,2)
missnumspec = 0
brtsM = c(25.2,24.6,24.0,22.5,21.7,20.4,19.9,19.7,18.8,17.1,15.8,11.8,9.7,8.9,5.7,5.2)
brtsS = c(9.6,8.6,7.4,4.9,2.5)
dd_KI_loglik(pars1,pars2,brtsM,brtsS,missnumspec)