DAISIE_ExpEIN {DAISIE}

The expected number of endemics and non-endemics under the DAISIE model

Description

This function calculates the expected 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

Usage

DAISIE_ExpEIN(t, pars, M, initEI = c(0, 0))

Arguments

t

The time at which the expectations 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

The initial values for the number of endemics and non-endemics. In DAISIE_probdist() or DAISIE_margprobdist() either this or initprobs must be NULL. In DAISIE_numcol() when it is NULL, it is assumed that the island is empty.

Value

out

The output is a list with three elements:

ExpE The number of endemic species
ExpI The number of non-endemic species
ExpN The sum of the number of endemics and non-endemics

Author(s)

Rampal S. Etienne

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.

Examples

### Compute the expected values at t = 4, for a mainland pool size of 1000 potential
# colonists and a vector of 5 parameters (cladogenesis, extinction, clade-level carrying
# capacity, immigration, anagenesis)

DAISIE_ExpEIN(
   t = 4,
   pars = c(0.5,0.1,Inf,0.01,0.4),
   M = 1000
   )