DAISIE (version 4.6.0)

DAISIE_margprobdist2: The probability distribution of the number of endemics and non-endemics under the DAISIE model

Description

This function calculates the probability distribution of the number of endemics, non-endemics and the sum of these for a given set of parameter values, a given mainland species pool size and a given time, where there can be diversity-dependence

Usage

DAISIE_margprobdist2(
  tvec,
  pars,
  M,
  initEI_mat = NULL,
  res = 1000,
  ddmodel = 11,
  methode = "ode45",
  reltolint = 1e-16,
  abstolint = 1e-16
)

Value

probsEIN

The output is a list with three elements:

probsE The number of endemic species at the times in tvec
probsI The number of non-endemic species at the times in tvec
probsN The sum of the number of endemics and non-endemics at the times in tvec

Arguments

tvec

The times at which the probabilities need to be computed.

pars

A numeric vector containing the model parameters:

• pars[1]: lambda^c (cladogenesis rate)

• pars[2]: mu (extinction rate)

• pars[3]: K (carrying capacity), set K=Inf for diversity independence.

• pars[4]: gamma (immigration rate)

• pars[5]: lambda^a (anagenesis rate)

• pars[6]: lambda^c (cladogenesis rate) for either type 2 species or rate set 2 in rate shift model

• pars[7]: mu (extinction rate) for either type 2 species or rate set 2 in rate shift model

• pars[8]: K (carrying capacity) for either type 2 species or rate set 2 in rate shift model, set K=Inf for diversity independence.

• pars[9]: gamma (immigration rate) for either type 2 species or rate set 2 in rate shift model

• pars[10]: lambda^a (anagenesis rate) for either type 2 species or rate set 2 in rate shift model

Elements 6:10 are required only when type 2 species are included or in the rate shift model. For DAISIE_sim_relaxed_rate() pars[6] is the standard deviation of the gamma distribution for the relaxed parameter and the parameter chosen by the relaxed_par argument is the mean of the gamma distribution for the relaxed parameter.

M

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

initEI_mat

matrix where each row represents the initial number of endemic and non-endemic species per colonizing lineage.

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

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, ode method is assumed. The default method overall is "lsodes" for DAISIE_ML_CS() and "ode45" from ode() for DAISIE_ML_IW().

reltolint

Numeric relative tolerance of the integration

abstolint

Numeric absolute tolerance of the integration

Author

Rampal S. Etienne

Examples

DAISIE_margprobdist2(tvec = c(0.000001,0.5,0.75,1),
                               pars = c(0.3,0.1,10,1,0.1),
                               M = 1000,
                               initEI_mat = rbind(c(1,0),c(2,0),c(0,1)))