Loglikelihood for diversity-dependent diversification models

This function computes loglikelihood of a diversity-dependent diversification model for a given set of branching times and parameter values.

Usage

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

Arguments

pars1: Vector of parameters:

pars1[1] corresponds to lambda (speciation rate)
pars1[2] corresponds to mu (extinction rate)
pars1[3] corresponds to K (clade-level carrying capacity)
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] == 1.4 : positive diversity-dependence in speciation rate with parameter K' (= diversity where speciation rate reaches half its maximum); lambda = lambda0 * S/(S + K') where S is species richness
- pars2[2] == 1.5 : positive and negative diversity-dependence in speciation rate with parameter K' (= diversity where speciation = 0); lambda = lambda0 * S/K' * (1 - S/K') where S is species richness
- 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[2] == 5 linear dependence in speciation and extinction rate

pars2[3] sets the conditioning:
- pars2[3] == 0 conditioning on stem or crown age
- pars2[3] == 1 conditioning on stem or crown age and non-extinction of the phylogeny
- pars2[3] == 2 conditioning on stem or crown age and on the total number of extant taxa (including missing species)
- pars2[3] == 3 conditioning 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. Before version 3.1 these were solvers from the deSolve package such as 'lsoda' and 'ode45'. Currently solvers from odeint are used, such as 'odeint::runge_kutta_cash_karp54', 'odeint::runge_kutta_fehlberg78', 'odeint::runge_kutta_dopri5', or odeint::bulirsch_stoer'. The first two are recommended in most cases.

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_loglik(pars1 = c(0.5,0.1,100), pars2 = c(100,1,1,1,0,2), brts = 1:10, missnumspec = 0) 
#> [1] -34.13958