DAISIE_margprobdist: The marginal distribution of endemics and non-endemics under...
In DAISIE: Dynamical Assembly of Islands by Speciation, Immigration and Extinction

Description Usage Arguments Value Author(s) References Examples

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

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

`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; either this or initprobs must be NULL
`initprobs`	The initial probability distribution for the number of endemics and non-endemics; either this or initEI must be NULL
`pb`	Rather than computing the joint distribution from given parameter values, one can also specify a precomputed probability distribution in the matrix format of DAISIE_probdist.

out

A list of three vectors:

pE The probability distribution of the number of endemic species
pI The probability distribution of the number of non-endemic species
pN The probability distribution of the sum of the number of endemics and non-endemics

Rampal S. Etienne

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.

### Compute the marginal probability distributions 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

DAISIE_margprobdist(
   pars1 = c(0.3,0.35,Inf,0.75,0.012),
   pars2 = c(100,250),
   tvec = c(4,8),
   initEI = c(5,1),
   initprobs = NULL
   )