Loglikelihood for macro-evolutionary succession under diversity-dependent diversification with the key innovation at time t = t_d

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

Usage

dd_MS_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_M (speciation rate) of the subclade
pars1[5] corresponds to mu_S (extinction rate) of the subclade
pars1[6] corresponds to t_d (the time of the key innovation)
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[4] sets the time of splitting of the branch that will undergo the key innovation leading to different parameters

pars2[5] sets the verbosity: 0 = no output, 1 = trace of the optimization only (no output from this function), 2 = parameters and loglikelihood shown on screen, 3 = as 2 plus messages about invalid parameter values and numerical problems

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 new corrected version 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

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


pars1 = c(0.2,0.1,40,1.0,0.1,9.8)
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_MS_loglik(pars1,pars2,brtsM,brtsS,missnumspec)
#> [1] -Inf