Maximization of the loglikelihood under the DAMOCLES model

This function computes the maximum likelihood estimates of the parameters of the DAMOCLES model for a given phylogeny and presence-absence data. It also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

DAMOCLES_ML(
  phy,
  pa,
  initparsopt,
  idparsopt = 1:length(initparsopt),
  parsfix = NULL,
  idparsfix = NULL,
  idparsequal = NULL,
  pars2 = c(0.001, 1e-04, 1e-05, 1000),
  optimmethod = "simplex",
  pchoice = 0,
  edgeTList = NULL,
  methode = "analytical",
  model = 0,
  num_cycles = 1,
  verbose = FALSE,
  cond = 0
)

Arguments

phy: phylogeny in phylo format
pa: presence-absence table.
The first column contains the labels of the species (corresponding to the tip labels in the phylogeny.
The second column contains the presence (1) or absence (0) of species in the local community.
initparsopt: The initial values of the parameters that must be optimized
idparsopt: The ids of the parameters that must be optimized, e.g. 1:2 for extinction rate, and offset of immigration rate The ids are defined as follows:
id == 1 corresponds to mu (extinction rate)
id == 2 corresponds to gamma_0 (offset of immigration rate)
id == 3 corresponds to gamma_1 (parameter controlling decline in immigration rate with time)
parsfix: The values of the parameters that should not be optimized. See idparsfix.
idparsfix: The ids of the parameters that should not be optimized, e.g. c(1,3) if mu and gamma_1 should not be optimized, but only gamma_0. In that case idparsopt must be c(2). The default is to fix all parameters not specified in idparsopt.
idparsequal: The ids of the parameters that should be set equal to the first parameter of the same type.
pars2: Vector of settings:
pars2[1] sets the relative tolerance in the parameters

pars2[2] sets the relative tolerance in the function

pars2[3] sets the absolute tolerance in the parameters

pars2[4] sets the maximum number of iterations
optimmethod: Method used in optimization of the likelihood. Current default is 'subplex'. Alternative is 'simplex' (default of previous version)
pchoice: sets the p-value to optimize:
pchoice == 0 corresponds to the sum of p_0f + p_1f
pchoice == 1 corresponds to p_0f
pchoice == 2 corresponds to p_1f
edgeTList: list of edge lengths that need to be succesively pruned; if not specified, it will computed using compute_edgeTList
methode: method used to solve the ODE. Either 'analytical' for the analytical solution, 'Matrix' for matrix exponentiation using package Matrix or 'expm' using package 'expm' or any of the numerical solvers, used in deSolve.
model: model used. Default is 0 (standard null model). Other options are 1 (binary traits) 2 (trinary environmental trait) or 3 (diversity-dependent colonization - beta version)
num_cycles: the number of cycles of opimization. If set at Inf, it will do as many cycles as needed to meet the tolerance set for the target function.
verbose: Whether intermediate output should be printed. Default is FALSE.
cond: Whether likelihood should be conditioned on non-empty community. Default is no conditioning.

Value

mu: gives the maximum likelihood estimate of mu
gamma_0: gives the maximum likelihood estimate of gamma_0
gamma_1: gives the maximum likelihood estimate of gamma_1
loglik: gives the maximum loglikelihood
df: gives the number of estimated parameters, i.e. degrees of feedom
conv: gives a message on convergence of optimization; conv = 0 means convergence

Details

The output is a dataframe containing estimated parameters and maximum loglikelihood.

References

Pigot, A.L. & R.S. Etienne (2015). A new dynamic null model for phylogenetic community structure. Ecology Letters 18: 153-163.

Author

Rampal S. Etienne