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

Description

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

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dd_MS_loglik(pars1, pars2, brtsM, brtsS, missnumspec, methode = 'analytical')

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 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)

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 'lsoda' or 'ode45'. 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_MS_ML, dd_loglik, dd_KI_loglik, dd_SR_loglik

Examples

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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,methode = 'ode45')

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