DAISIE_probdist {DAISIE}

The joint distribution of endemics and non-endemics under the DAISIE model

Description

This function calculates the joint distribution of the number of endemics and non-endemics for a given set of parameter values, a given mainland species pool size and a given set of times

Usage

DAISIE_probdist(pars1, pars2, tvec, initEI = c(0, 0), initprobs = NULL)

Arguments

pars1

Vector of model parameters:

pars1[1] corresponds to lambda^c (cladogenesis rate)
pars1[2] corresponds to mu (extinction rate)
pars1[3] corresponds to K (clade-level carrying capacity)
pars1[4] corresponds to gamma (immigration rate)
pars1[5] corresponds to lambda^a (anagenesis rate).

pars2

Vector of settings:

pars2[1] corresponds to res, the maximum number of endemics or non-endemics for which the ODE system is solved; this must be much larger than the actual number for which the probability needs to be calculated.)
pars2[2] corresponds to M, size of the mainland pool, i.e the number of species that can potentially colonize the island.

tvec

The times at which the probabilities need to be computed.

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.

initprobs

The initial probability distribution for the number of endemics and non-endemics; either this or initEI must be NULL.

Details

To obtain a matrix of probabilities with endemics in rows and non-endemics in columns for a certain time, one can run DAISIE_convertprobdist

Value

A matrix of dimensions 1 + length(tvec) and pars[2]^2 + 1] where the first column contains the times at which the probabilities are evaluated and the other columns contain the joint probabilities.

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 probability distribution at t = 4 and t = 8, for a mainland pool
# size of 250 potential colonists and a vector of 5 parameters (cladogenesis,
# extinction, clade-level carrying capacity, immigration, anagenesis) starting
# from an empty island

prob_dists <- DAISIE_probdist(
   pars1 = c(0.3,0.35,Inf,0.75,0.012),
   pars2 = c(100,250),
   tvec = c(4,8),
   initEI = c(0,0),
   initprobs = NULL
   )