Maximization of the loglikelihood under the DAISIE model with island-wide diversity-dependence

This function computes the maximum likelihood estimates of the parameters of the DAISIE model with island-wide diversity-dependence for data from lineages colonizing an island. It also outputs the corresponding loglikelihood that can be used in model comparisons.

Usage

DAISIE_ML_IW(
  datalist,
  initparsopt,
  idparsopt,
  parsfix,
  idparsfix,
  res = 100,
  ddmodel = 11,
  cond = 0,
  tol = c(1e-04, 1e-05, 1e-07),
  maxiter = 1000 * round((1.25)^length(idparsopt)),
  methode = "ode45",
  optimmethod = "subplex",
  verbose = 0,
  tolint = c(1e-16, 1e-14),
  jitter = 0,
  num_cycles = 1
)

Arguments

datalist: Data object containing information on colonisation and branching times. This object can be generated using the DAISIE_dataprep function, which converts a user-specified data table into a data object, but the object can of course also be entered directly. It is an R list object with the following elements.
The first element of the list has two or three components:

$island_age - the island age
Then, depending on whether a distinction between types is made, we have:
$not_present - the number of mainland lineages that are not present on the island
or:
$not_present_type1 - the number of mainland lineages of type 1 that are not present on the island
$not_present_type2 - the number of mainland lineages of type 2 that are not present on the island

The remaining elements of the list each contains information on a single colonist lineage on the island and has 5 components:

$colonist_name - the name of the species or clade that colonized the island
$branching_times - island age followed by stem age of the population/species in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close relatives on the island. For endemic clades with more than one species on the island (cladogenetic clades/ radiations) these should be island age followed by the branching times of the island clade including the stem age of the clade
$stac - the status of the colonist

* Non_endemic_MaxAge: 1
* Endemic: 2
* Endemic&Non_Endemic: 3
* Non_Endemic: 4
* Endemic_Singleton_MaxAge: 5
* Endemic_Clade_MaxAge: 6
* Endemic&Non_Endemic_Clade_MaxAge: 7

$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)
$type1or2 - whether the colonist belongs to type 1 or type 2
initparsopt: The initial values of the parameters that must be optimized, they are all positive.
idparsopt: The ids of the parameters that must be optimized. The ids are defined as follows:

id = 1 corresponds to lambda^c (cladogenesis rate)
id = 2 corresponds to mu (extinction rate)
id = 3 corresponds to K (clade-level carrying capacity)
id = 4 corresponds to gamma (immigration rate)
id = 5 corresponds to lambda^a (anagenesis rate)
id = 6 corresponds to lambda^c (cladogenesis rate) for an optional subset of the species
id = 7 corresponds to mu (extinction rate) for an optional subset of the species
id = 8 corresponds to K (clade-level carrying capacity) for an optional subset of the species
id = 9 corresponds to gamma (immigration rate) for an optional subset of the species
id = 10 corresponds to lambda^a (anagenesis rate) for an optional subset of the species
id = 11 corresponds to p_f (fraction of mainland species that belongs to the second subset of species.
parsfix: The values of the parameters that should not be optimized.
idparsfix: The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.
res: Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade.
ddmodel: Sets the model of diversity-dependence:

ddmodel = 0 : no diversity dependence
ddmodel = 1 : linear dependence in speciation rate
ddmodel = 11: linear dependence in speciation rate and in immigration rate
ddmodel = 2 : exponential dependence in speciation rate
ddmodel = 21: exponential dependence in speciation rate and in immigration rate
cond: cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model
tol: Sets the tolerances in the optimization. Consists of:
reltolx = relative tolerance of parameter values in optimization
reltolf = relative tolerance of function value in optimization
abstolx = absolute tolerance of parameter values in optimization.
maxiter: Sets the maximum number of iterations in the optimization.
methode: Method of the ODE-solver. Supported Boost ODEINT solvers (steppers) are: "odeint::runge_kutta_cash_karp54" "odeint::runge_kutta_fehlberg78" "odeint::runge_kutta_dopri5" "odeint::bulirsch_stoer" without odeint::-prefix, deSolve{ode} method is assumed. The default method overall is "lsodes" for DAISIE_ML_CS() and "ode45" from ode() for DAISIE_ML_IW().
optimmethod: Method used in likelihood optimization. Default is `subplex` (see `subplex()` for full details). Alternative is "simplex" which was the method in previous versions.
verbose: A numeric vector of length 1, which in simulations and `DAISIEdataprep()` can be `1` or `0`, where `1` gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: `0` does not print, `1` prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), `2` prints the same as `1 and also the intermediate output of the parameters and loglikelihood, while `3` the same as `2` and prints intermediate progress during likelihood computation.
tolint: Vector of two elements containing the absolute and relative tolerance of the integration.
jitter: Numeric for optimizer(). Jitters the parameters being optimized by the specified amount which should be very small, e.g. 1e-5. Jitter when link{subplex}{subplex}() produces incorrect output due to parameter transformation.
num_cycles: The number of cycles the optimizer will go through. Default is 1.

Value

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

lambda_c: gives the maximum likelihood estimate of lambda^c, the rate of cladogenesis
mu: gives the maximum likelihood estimate of mu, the extinction rate
K: gives the maximum likelihood estimate of K, the carrying-capacity
gamma: gives the maximum likelihood estimate of gamma, the immigration rate
lambda_a: gives the maximum likelihood estimate of lambda^a, the rate of anagenesis
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 result of sort(c(idparsopt, idparsfix)) should be identical to c(1:5). If not, an error is reported that the input is incoherent. The same happens when the length of initparsopt is different from the length of idparsopt, and the length of parsfix is different from the length of idparsfix.

References

Valente, L.M., A.B. Phillimore and R.S. Etienne (2015). Equilibrium and non-equilibrium dynamics simultaneously operate in the Galapagos islands. Ecology Letters 18: 844-852. <DOI:10.1111/ele.12461>.

Author

Rampal S. Etienne