DAISIE (version 1.0.2)

DAISIE_ML: Maximization of the loglikelihood under the DAISIE model

Description

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

Usage

DAISIE_ML( datalist, initparsopt, idparsopt, parsfix, idparsfix, idparsnoshift = 6:10, res = 100, ddmodel = 0, cond = 0, eqmodel = 0, x_E = 0.95, x_I = 0.98, tol = c(1e-04, 1e-05, 1e-07), maxiter = 1000 * round((1.25)^length(idparsopt)), methode = "lsodes" )

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 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 and stem age of the population/species in the case of Non-endemic, Non-endemic_MaxAge and Endemic anagenetic species. For cladogenetic species these should be island age and branching times of the radiation including the stem age of the radiation. $stac - the status of the colonist * Non_endemic_MaxAge: 1 * Endemic: 2 * Endemic&Non_Endemic: 3 * Non_endemic: 4 $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

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

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.

parsfix

The values of the parameters that should not be optimized

idparsnoshift

The ids of the parameters that should not be different between two groups of species; This can only apply to ids 6:10, e.g. idparsnoshift = c(6,7) means that lambda^c and mu have the same values for both groups

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

eqmodel

Sets the equilibrium constraint that can be used during the likelihood optimization. eqmodel = 0 : no equilibrium is assumed eqmodel = 13 : near-equilibrium is assumed on endemics using deterministic equation for endemics and immigrants. Endemics must be within x_E of the equilibrium value eqmodel = 15 : near-equilibrium is assumed on endemics and immigrants using deterministic equation for endemics and immigrants. Endemics must be within x_E of the equilibrium value, while non-endemics must be within x_I of the equilibrium value

x_E

Sets the fraction of the equlibrium endemic diversity above which the endemics are assumed to be in equilibrium; only active for eqmodel = 13 or 15

x_I

Sets the fraction of the equlibrium non-endemic diversity above which the system is assumed to be in equilibrium; only active for eqmodel = 15

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. See package deSolve for details. Default is "lsodes"

Value

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

lambda_c2

gives the maximum likelihood estimate of lambda^c2, the rate of cladogenesis for the optional second group of species

mu2

gives the maximum likelihood estimate of mu2, the extinction rate for the optional second group of species

K2

gives the maximum likelihood estimate of K2, the carrying-capacity for the optional second group of species

gamma2

gives the maximum likelihood estimate of gamma2, the immigration rate for the optional second group of species

lambda_a2

gives the maximum likelihood estimate of lambda^a2, the rate of anagenesis for the optional second group of species

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, idparsnoshift)) should be identical to c(1:10). 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. Including the 11th parameter (p_f) in either idparsopt or idparsfix (and therefore initparsopt or parsfix) is optional. If this parameter is not specified, then the information in the data is used, otherwise the information in the data is overruled.

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.

See Also

DAISIE_loglik_all, DAISIE_sim

Examples

cat("
### When all species have the same rates, and we want to optimize all 5 parameters,
# we use:

data(Galapagos_datalist)
DAISIE_ML(
   datalist = Galapagos_datalist,
   initparsopt = c(2.5,2.7,20,0.009,1.01),
   ddmodel = 11,
   idparsopt = 1:5,
   parsfix = NULL,
   idparsfix = NULL
)

### When all species have the same rates, and we want to optimize all parameters 
# except K (which we set equal to Inf), we use:

data(Galapagos_datalist)
DAISIE_ML(
   datalist = Galapagos_datalist,
   initparsopt = c(2.5,2.7,0.009,1.01),
   idparsopt = c(1,2,4,5),
   parsfix = Inf,
   idparsfix = 3
   )

### When all species have the same rates except that the finches have a different
# rate of cladogenesis, and we want to optimize all parameters except K (which we
# set equal to Inf), fixing the proportion of finch-type species at 0.163, we use:

data(Galapagos_datalist_2types)
DAISIE_ML(
   datalist = Galapagos_datalist_2types,
   initparsopt = c(0.38,0.55,0.004,1.1,2.28),
   idparsopt = c(1,2,4,5,6),
   parsfix = c(Inf,Inf,0.163),
   idparsfix = c(3,8,11),
   idparsnoshift = c(7,9,10)
   )

### When all species have the same rates except that the finches have a different
# rate of cladogenesis, extinction and a different K, and we want to optimize all
# parameters, fixing the proportion of finch-type species at 0.163, we use:

data(Galapagos_datalist_2types)
DAISIE_ML(
   datalist = Galapagos_datalist_2types,
   ddmodel = 11,   
   initparsopt = c(0.19,0.09,0.002,0.87,20,8.9,15),
   idparsopt = c(1,2,4,5,6,7,8),
   parsfix = c(Inf,0.163),
   idparsfix = c(3,11),
   idparsnoshift = c(9,10)
   )


### When all species have the same rates except that the finches have a different
# rate of extinction, and we want to optimize all parameters except K (which we 
# set equal to Inf), and we also# want to estimate the fraction of finch species
# in the mainland pool. we use:

data(Galapagos_datalist_2types)
DAISIE_ML(
   datalist = Galapagos_datalist_2types,
   initparsopt = c(2.48,2.7,0.009,1.01,2.25,0.163),
   idparsopt = c(1,2,4,5,7,11),
   parsfix = c(Inf,Inf),
   idparsfix = c(3,8),
   idparsnoshift = c(6,9,10)
   )
")