Loglikelihood for diversity-dependent diversification models with a shift in the parameters at time t = tshift

This function computes loglikelihood of a diversity-dependent diversification model for a given set of branching times and parameter values where the parameters are allowed to shift at time t = tshift

Usage

dd_SR_loglik(pars1, pars2, brts, missnumspec, methode = "analytical")

Arguments

pars1: Vector of parameters:

pars1[1] corresponds to lambda (speciation rate) before the shift
pars1[2] corresponds to mu (extinction rate) before the shift
pars1[3] corresponds to K (clade-level carrying capacity) before the shift
pars1[4] corresponds to lambda (speciation rate) after the shift
pars1[5] corresponds to mu (extinction rate) after the shift
pars1[6] corresponds to K (clade-level carrying capacity) after the shift
pars1[7] corresponds to tshift (the time of shift)
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
- pars2[3] == 1 conditioning on non-extinction of the phylogeny
- pars2[3] == 2 conditioning on non-extinction of the phylogeny and on the total number of extant taxa (including missing species)

pars2[4] sets whether the likelihood is for the branching times (0) or the phylogeny (1)

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)
brts: A set of branching times of a phylogeny, all positive
missnumspec: The number of species that are in the clade but missing in the phylogeny
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

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

dd_SR_loglik(pars1 = c(0.2,0.1,50,0.2,0.1,70,5), pars2 = c(100,1,1,1,0,2),
   brts = 1:10, missnumspec = 0) 
#> [1] -27.37304