Maximization of the loglikelihood under the DAISIE model with clade-specific diversity-dependence

This function computes the maximum likelihood estimates of the parameters of the DAISIE model with clade-specific diversity-dependence and a shift in parameters for data from lineages colonizing an island. It also outputs the corresponding loglikelihood that can be used in model comparisons.

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.

Usage

DAISIE_SR_ML_CS(
  datalist,
  initparsopt,
  idparsopt,
  parsfix,
  idparsfix,
  idparsnoshift = 6:10,
  res = 100,
  ddmodel = 0,
  cond = 0,
  island_ontogeny = NA,
  tol = c(1e-04, 1e-05, 1e-07),
  maxiter = 1000 * round((1.25)^length(idparsopt)),
  methode = "odeint::runge_kutta_cash_karp54",
  optimmethod = "simplex",
  CS_version = list(model = 1, function_to_optimize = "DAISIE"),
  verbose = 0,
  tolint = c(1e-16, 1e-10),
  jitter = 0,
  num_cycles = 1
)

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

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
- Endemic_Singleton_MaxAge: 5
- Endemic_Clade_MaxAge: 6
- Endemic&Non_Endemic_Clade_MaxAge: 7
- Non_endemic_MaxAge_MinAge: 8
- Endemic_Singleton_MaxAge_MinAge: 9
$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)

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) after the shift
id = 7 corresponds to mu (extinction rate) after the shift
id = 8 corresponds to K (clade-level carrying capacity) after the shift
id = 9 corresponds to gamma (immigration rate) after the shift
id = 10 corresponds to lambda^a (anagenesis rate) after the shift
id = 11 corresponds to the time of shift

parsfix

The values of the parameters that should not be optimized

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.

idparsnoshift

The ids of the parameters that should not be different before and after the shift.

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

island_ontogeny

type of island ontonogeny. If NA, then constant ontogeny is assumed.

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"

optimmethod

Method used in likelihood optimization. Default is "subplex" (see subplex package). Alternative is 'simplex' which was the method in previous versions.

CS_version

a numeric or list. Default is CS_version = list(model = 1, function_to_optimize = 'DAISIE'), but for a relaxed-rate model the list can contain more elements:

model: the CS model to run, options are 1 for single rate DAISIE model, 2 for multi-rate DAISIE, or 0 for IW test model
function_to_optimize: the DAISIE loglikelihood function that will be optimized. Options are: "DAISIE", default, the full DAISIE loglikelihood "DAISIE_approx", an approximate loglikelihood "DAISIE_DE", an exact loglikelkhood for K = Inf based on the D-E approach
integration_method: the method used to do integraion in the relaxed rate model. Options are: 'standard' the default numerical integration 'MC' Monte Carlo integration 'stratified' using quantiles of the gamma distribution
relaxed_par: the parameter to relax (integrate over) in the relaxed rate model. Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis"
par_sd: standard deviation of the parameter to relax
par_upper_bound upper bound of the parameter to relax
seed: seed of the random number generator in case of 'MC'
sample_size: size of sample in case of 'MC' or 'stratified'
parallel: use parallel computing or not in case of 'MC' or 'stratified'
n_cores: number of cores to use when run in parallel

verbose

sets whether parameters and likelihood should be printed (1) or not (0).

tolint

Vector of two elements containing the absolute and relative tolerance of the integration.

jitter

Numeric for optimizer(). Jitters the parameters being optimized by the specified amount which should be very small, e.g. 1e-5. Jitter when link[subplex]{subplex}() produces incorrect output due to parameter transformation.

num_cycles

The number of cycles the optimizer will go through. Default is 1.

Value

The output is a dataframe containing estimated parameters and maximum loglikelihood.

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

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. <DOI:10.1111/ele.12461>.

Author

Rampal S. Etienne

Examples


# \donttest{
## In all following DAISIE_ML calls very high tolerances and low system size
## are used  for fast computation for this example. Use default or better
## tol, tolint an res values in actual analyses.
##################
### When all species have the same rates, and we want to optimize all 5
### parameters, we use:
utils::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,
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
)
#> 1 2.5 2.7 20 0.009 1.01 -84.5959050148538 initial 
#> 2 2.57394366197183 2.45663824604141 20.5887850467288 0.00926995184208962 1.03999852231307 -81.8657661030481 expand 
#> 3 2.57394366197183 2.45663824604141 20.5887850467288 0.00926995184208962 1.03999852231307 -81.8657661030481 reflect 
#> 4 2.57394366197183 2.45663824604141 20.5887850467288 0.00926995184208962 1.03999852231307 -81.8657661030481 reflect 
#> 5 2.74284618561567 2.41708167570535 21.9640528073801 0.00867696756642243 1.03199226061908 -80.3388594174952 expand 
#> 6 2.74284618561567 2.41708167570535 21.9640528073801 0.00867696756642243 1.03199226061908 -80.3388594174952 reflect 
#> 7 2.70637938367915 2.12114736980287 23.0309393662987 0.00953589839799602 1.05994022098098 -79.7462715978321 expand 
#> 8 2.70637938367915 2.12114736980287 23.0309393662987 0.00953589839799602 1.05994022098098 -79.7462715978321 reflect 
#> 9 2.70637938367915 2.12114736980287 23.0309393662987 0.00953589839799602 1.05994022098098 -79.7462715978321 reflect 
#> 10 2.70637938367915 2.12114736980287 23.0309393662987 0.00953589839799602 1.05994022098098 -79.7462715978321 reflect 
#> 11 2.84334710792816 1.97039300575139 25.0829855784988 0.00886824459772644 1.06740685343025 -79.6775250850769 reflect 
#> 12 2.78183185437412 2.24229745702683 22.577390672626 0.00888840113935901 1.0446236231185 -79.6306459405685 contract inside 
#> 13 2.78183185437412 2.24229745702683 22.577390672626 0.00888840113935901 1.0446236231185 -79.6306459405685 contract inside 
#> 14 2.82641052532241 2.0127798365611 24.4312752737618 0.00894272385417175 1.11063474977204 -79.5829880091709 reflect 
#> 15 2.78316111473384 2.05701580189927 26.5509972005936 0.0092381323039169 1.02220752078419 -79.1627377008177 expand 
#> 16 2.78316111473384 2.05701580189927 26.5509972005936 0.0092381323039169 1.02220752078419 -79.1627377008177 reflect 
#> 17 2.78316111473384 2.05701580189927 26.5509972005936 0.0092381323039169 1.02220752078419 -79.1627377008177 reflect 
#> 18 2.75429507249273 2.14303048649572 27.4342707282386 0.00862926193376708 1.06086239546257 -78.5245798083218 expand 
#> 19 2.75429507249273 2.14303048649572 27.4342707282386 0.00862926193376708 1.06086239546257 -78.5245798083218 reflect 
#> 20 2.86204413593059 2.19359023891543 31.6669800169811 0.00855205369812969 0.946382965840598 -78.0661758333716 expand 
#> 21 2.86204413593059 2.19359023891543 31.6669800169811 0.00855205369812969 0.946382965840598 -78.0661758333716 reflect 
#> 22 2.86204413593059 2.19359023891543 31.6669800169811 0.00855205369812969 0.946382965840598 -78.0661758333716 reflect 
#> 23 2.64925115410287 2.23034773420279 38.7962397448645 0.00870553013143953 0.893635283226929 -77.3830595239629 expand 
#> 24 2.64925115410287 2.23034773420279 38.7962397448645 0.00870553013143953 0.893635283226929 -77.3830595239629 reflect 
#> 25 2.60310626652623 2.1789263548788 63.1948537688694 0.00855363831751474 0.905831373380445 -77.0023187204308 expand 
#> 26 2.60310626652623 2.1789263548788 63.1948537688694 0.00855363831751474 0.905831373380445 -77.0023187204308 reflect 
#> 27 2.63242686267853 2.43433005754289 533.077309297241 0.00794038281584965 0.680849200627572 -76.5552088156323 expand 
#> 28 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 reflect 
#> 29 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 contract inside 
#> 30 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 reflect 
#> 31 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 contract inside 
#> 32 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 reflect 
#> 33 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 contract inside 
#> 34 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 contract inside 
#> 35 2.49286775938259 2.3734734143204 164.775513239887 0.00800244492266152 0.77842499078473 -76.1839971067622 contract inside 
#> 36 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 reflect 
#> 37 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 contract inside 
#> 38 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 contract inside 
#> 39 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 contract inside 
#> 40 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 reflect 
#> 41 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 reflect 
#> 42 2.46596328388119 2.54179282979495 832.277455262044 0.0082051054591192 0.671095261096637 -76.0624890503913 contract inside 
#> 43 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 reflect 
#> 44 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 45 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 46 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 47 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 48 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 49 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 reflect 
#> 50 2.40848268090857 2.46891079511793 1507.86316593413 0.00828414704598906 0.714668525250214 -76.0600208232112 contract inside 
#> 51 2.40337584039381 2.50701677707043 840.364038599141 0.00839104037209457 0.697077868938166 -76.0590367052956 reflect 
#> Optimization has terminated successfully. 
#>   lambda_c       mu       K      gamma  lambda_a    loglik df conv
#> 1 2.403376 2.507017 840.364 0.00839104 0.6970779 -76.05904  5    0

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

utils::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,
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
   )
#> 1 2.5 2.7 0.009 1.01 -76.0462971262433 initial 
#> 2 2.54585152838428 2.63600256245996 0.00916870297550856 1.02864472677177 -76.0052230632261 contract outside 
#> Optimization has terminated successfully. 
#>   lambda_c       mu   K       gamma lambda_a    loglik df conv
#> 1 2.545852 2.636003 Inf 0.009168703 1.028645 -76.00522  4    0

### 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:

utils::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),
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
   )
#> 1 0.38 0.55 0.004 1.1 2.28 -72.3280499887132 initial 
#> 2 0.38753773178094 0.560884136610278 0.00380007964954201 1.12165963431786 2.32466849838729 -72.3108979349047 reflect 
#> Optimization has terminated successfully. 
#>    lambda_c        mu   K      gamma lambda_a lambda_c2       mu2  K2
#> 1 0.3875377 0.5608841 Inf 0.00380008  1.12166  2.324668 0.5608841 Inf
#>       gamma2 lambda_a2 prop_type2   loglik df conv
#> 1 0.00380008   1.12166      0.163 -72.3109  5    0

### 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:

utils::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),
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
   )
#> 1 0.19 0.09 0.002 0.87 20 8.9 15 -71.4013080907571 initial 
#> 2 0.19 0.09 0.002 0.87 20 8.9 15.75 -69.8668523696926 reflect 
#> 3 0.19 0.09 0.002 0.87 20 8.9 15.75 -69.8668523696926 reflect 
#> 4 0.19 0.09 0.002 0.87 20 8.9 15.75 -69.8668523696926 reflect 
#> 5 0.198647116716674 0.0884399643419118 0.00209108623683683 0.867083135661897 20.9070208353907 8.60722130907681 15.6803105517608 -68.8796294264893 expand 
#> 6 0.198647116716674 0.0884399643419118 0.00209108623683683 0.867083135661897 20.9070208353907 8.60722130907681 15.6803105517608 -68.8796294264893 reflect 
#> 7 0.196571554822603 0.0871380557214326 0.00192445883176214 0.864649477339252 21.7284214417376 8.37522882078276 16.2956457857271 -67.399281978692 expand 
#> 8 0.196571554822603 0.0871380557214326 0.00192445883176214 0.864649477339252 21.7284214417376 8.37522882078276 16.2956457857271 -67.399281978692 reflect 
#> 9 0.196571554822603 0.0871380557214326 0.00192445883176214 0.864649477339252 21.7284214417376 8.37522882078276 16.2956457857271 -67.399281978692 reflect 
#> 10 0.196571554822603 0.0871380557214326 0.00192445883176214 0.864649477339252 21.7284214417376 8.37522882078276 16.2956457857271 -67.399281978692 reflect 
#> 11 0.194600287825488 0.0841862620030736 0.00203374911014966 0.838939984711527 21.9179996903289 8.56960916249118 17.9337386175874 -65.9883382687776 expand 
#> 12 0.194600287825488 0.0841862620030736 0.00203374911014966 0.838939984711527 21.9179996903289 8.56960916249118 17.9337386175874 -65.9883382687776 reflect 
#> 13 0.194600287825488 0.0841862620030736 0.00203374911014966 0.838939984711527 21.9179996903289 8.56960916249118 17.9337386175874 -65.9883382687776 reflect 
#> 14 0.192743342208585 0.0856990355230438 0.00186800497141212 0.845708765343543 22.369519914392 7.82899332026389 19.3747045961653 -64.6586070063567 expand 
#> 15 0.192743342208585 0.0856990355230438 0.00186800497141212 0.845708765343543 22.369519914392 7.82899332026389 19.3747045961653 -64.6586070063567 reflect 
#> 16 0.192743342208585 0.0856990355230438 0.00186800497141212 0.845708765343543 22.369519914392 7.82899332026389 19.3747045961653 -64.6586070063567 reflect 
#> 17 0.208204301714696 0.0783777985833893 0.00184040111915886 0.776948488557296 25.6853960543531 7.81381722834349 21.490671833278 -64.1416047238092 expand 
#> 18 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 19 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 20 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 21 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 22 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 23 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 24 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 25 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 26 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract outside 
#> 27 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 28 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 29 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 reflect 
#> 30 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 31 0.201863787594532 0.0815168094743516 0.00196743381430806 0.81945851988081 24.0756581386455 7.79915899233233 21.3841787717698 -64.0864682001683 contract inside 
#> 32 0.202738038477864 0.0782137121807482 0.00202059513014824 0.798656174821273 26.6417087649857 7.54584960705099 20.4951320279636 -63.9440392457202 expand 
#> Optimization has terminated successfully. 
#>   lambda_c         mu   K       gamma  lambda_a lambda_c2     mu2       K2
#> 1 0.202738 0.07821371 Inf 0.002020595 0.7986562  26.64171 7.54585 20.49513
#>        gamma2 lambda_a2 prop_type2    loglik df conv
#> 1 0.002020595 0.7986562      0.163 -63.94404  7    0


### 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:

utils::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),
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
   )
#> 1 2.48 2.7 0.009 1.01 2.25 0.163 -75.7158713607349 initial 
#> 2 2.48 2.7 0.009 1.01 2.25 0.163 -75.7158713607349 contract inside 
#> 3 2.48 2.7 0.009 1.01 2.25 0.163 -75.7158713607349 contract inside 
#> 4 2.48 2.7 0.009 1.01 2.25 0.163 -75.7158713607349 contract inside 
#> 5 2.48 2.7 0.009 1.01 2.25 0.163 -75.7158713607349 contract inside 
#> 6 2.51874708809887 2.72094014248618 0.00929801284883615 1.04316733408277 2.29081286315155 0.148315171825522 -75.6741036671472 expand 
#> 7 2.51874708809887 2.72094014248618 0.00929801284883615 1.04316733408277 2.29081286315155 0.148315171825522 -75.6741036671472 contract outside 
#> 8 2.51874708809887 2.72094014248618 0.00929801284883615 1.04316733408277 2.29081286315155 0.148315171825522 -75.6741036671472 reflect 
#> 9 2.51874708809887 2.72094014248618 0.00929801284883615 1.04316733408277 2.29081286315155 0.148315171825522 -75.6741036671472 reflect 
#> 10 2.51874708809887 2.72094014248618 0.00929801284883615 1.04316733408277 2.29081286315155 0.148315171825522 -75.6741036671472 reflect 
#> 11 2.49664301817893 2.72343553773099 0.00952760936241741 1.00210198211517 2.26953127536223 0.140412720939446 -75.645463308938 expand 
#> 12 2.49664301817893 2.72343553773099 0.00952760936241741 1.00210198211517 2.26953127536223 0.140412720939446 -75.645463308938 reflect 
#> 13 2.49664301817893 2.72343553773099 0.00952760936241741 1.00210198211517 2.26953127536223 0.140412720939446 -75.645463308938 reflect 
#> 14 2.49664301817893 2.72343553773099 0.00952760936241741 1.00210198211517 2.26953127536223 0.140412720939446 -75.645463308938 reflect 
#> 15 2.56492941825021 2.78513524392111 0.00936477446497385 1.05074544815357 2.32980085811406 0.119724254346001 -75.5878907455841 expand 
#> 16 2.56492941825021 2.78513524392111 0.00936477446497385 1.05074544815357 2.32980085811406 0.119724254346001 -75.5878907455841 reflect 
#> 17 2.53776162129591 2.75898560369769 0.0100043169111592 1.04381319428314 2.28464475007781 0.10192700058471 -75.5291817144172 expand 
#> 18 2.53776162129591 2.75898560369769 0.0100043169111592 1.04381319428314 2.28464475007781 0.10192700058471 -75.5291817144172 reflect 
#> 19 2.53776162129591 2.75898560369769 0.0100043169111592 1.04381319428314 2.28464475007781 0.10192700058471 -75.5291817144172 reflect 
#> 20 2.59195771925564 2.86532962137574 0.0104183523557991 0.961950195093442 2.32746572332359 0.0843638313744798 -75.4498157430252 expand 
#> 21 2.59195771925564 2.86532962137574 0.0104183523557991 0.961950195093442 2.32746572332359 0.0843638313744798 -75.4498157430252 reflect 
#> 22 2.603459033558 2.90460992644193 0.00997219864374222 1.00327502251763 2.38673327486163 0.0587628138176481 -75.3911723784466 expand 
#> 23 2.603459033558 2.90460992644193 0.00997219864374222 1.00327502251763 2.38673327486163 0.0587628138176481 -75.3911723784466 reflect 
#> 24 2.70019600200814 2.97023958067162 0.010983807871058 0.959915503697238 2.34977362082495 0.0187620792993542 -75.1510916604556 expand 
#> 25 2.70019600200814 2.97023958067162 0.010983807871058 0.959915503697238 2.34977362082495 0.0187620792993542 -75.1510916604556 reflect 
#> 26 2.70019600200814 2.97023958067162 0.010983807871058 0.959915503697238 2.34977362082495 0.0187620792993542 -75.1510916604556 reflect 
#> 27 2.65767074803726 3.02588031368108 0.0111380132637994 0.911533436460283 2.35486052868374 0.0123090350501884 -75.1301455998755 reflect 
#> 28 2.65767074803726 3.02588031368108 0.0111380132637994 0.911533436460283 2.35486052868374 0.0123090350501884 -75.1301455998755 contract inside 
#> 29 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 reflect 
#> 30 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 31 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 32 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 33 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 34 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 reflect 
#> 35 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 36 2.7296333524322 3.0960410585842 0.0108669611642466 0.948708457787273 2.38034226611695 0.00238921928808448 -75.0638455628087 contract inside 
#> 37 2.72614639675389 3.06871411492363 0.0111311862370589 0.916297363084071 2.38895390433604 0.00176916100242538 -75.0608849286769 reflect 
#> 38 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 expand 
#> 39 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 40 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 41 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 42 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 43 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 44 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 reflect 
#> 45 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 46 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 reflect 
#> 47 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 contract inside 
#> 48 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 reflect 
#> 49 2.68832727923785 3.0257355876853 0.0107743517214694 0.927149572781689 2.26025342420151 0.0058184598839985 -74.9952297228629 reflect 
#> 50 2.68295779358785 2.99682474232905 0.0103810517203084 0.980504452065124 2.1609045062705 0.00906451201024566 -74.9662814997851 expand 
#> 51 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 expand 
#> 52 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 reflect 
#> 53 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 reflect 
#> 54 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 reflect 
#> 55 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 reflect 
#> 56 2.6966088249286 3.01491339938815 0.0104994816393992 0.966982621053112 2.14419473223335 0.00102400236426943 -74.9000245553884 reflect 
#> 57 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 reflect 
#> 58 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 reflect 
#> 59 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 reflect 
#> 60 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 contract inside 
#> 61 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 reflect 
#> 62 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 contract inside 
#> 63 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 contract inside 
#> 64 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 contract outside 
#> 65 2.64804591523941 2.96585990335029 0.0102859194289707 0.973297176932631 2.00847553480825 0.0024493079383061 -74.8596932883144 reflect 
#> 66 2.64683342152589 2.94136047626618 0.009935493001708 0.980938562451797 1.91938872508038 0.0011838246615075 -74.8505311519972 reflect 
#> 67 2.64683342152589 2.94136047626618 0.009935493001708 0.980938562451797 1.91938872508038 0.0011838246615075 -74.8505311519972 reflect 
#> 68 2.64683342152589 2.94136047626618 0.009935493001708 0.980938562451797 1.91938872508038 0.0011838246615075 -74.8505311519972 contract inside 
#> 69 2.64683342152589 2.94136047626618 0.009935493001708 0.980938562451797 1.91938872508038 0.0011838246615075 -74.8505311519972 reflect 
#> 70 2.63903125598561 2.94740770703226 0.0100372318074471 1.00274835481682 1.91958072463951 0.00111047598534693 -74.8418281805701 reflect 
#> 71 2.63030298828697 2.93830541335918 0.0101639895713657 0.969588194571472 1.92960287289089 0.0010211445092613 -74.8335744094726 reflect 
#> 72 2.63030298828697 2.93830541335918 0.0101639895713657 0.969588194571472 1.92960287289089 0.0010211445092613 -74.8335744094726 reflect 
#> 73 2.63030298828697 2.93830541335918 0.0101639895713657 0.969588194571472 1.92960287289089 0.0010211445092613 -74.8335744094726 reflect 
#> 74 2.63030298828697 2.93830541335918 0.0101639895713657 0.969588194571472 1.92960287289089 0.0010211445092613 -74.8335744094726 contract inside 
#> 75 2.63030298828697 2.93830541335918 0.0101639895713657 0.969588194571472 1.92960287289089 0.0010211445092613 -74.8335744094726 reflect 
#> 76 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 expand 
#> 77 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 contract inside 
#> 78 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 reflect 
#> 79 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 reflect 
#> 80 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 contract inside 
#> 81 2.58760227974038 2.90350978364879 0.0103819627901399 0.99730152780014 1.86510414833794 0.00228770759700229 -74.811985779196 reflect 
#> 82 2.55463512489623 2.88317802733378 0.0102287237583974 1.01600041770707 1.78180506413061 0.00195940213901571 -74.800374980665 expand 
#> 83 2.51928038530493 2.82334702924103 0.0103626432951557 1.01820395588645 1.70058420260719 0.00314288975060286 -74.7938958042882 expand 
#> 84 2.51928038530493 2.82334702924103 0.0103626432951557 1.01820395588645 1.70058420260719 0.00314288975060286 -74.7938958042882 reflect 
#> 85 2.50997371253308 2.84125512881648 0.0104742429590286 1.04696716242467 1.70300905915644 0.00187578021046235 -74.7759936210548 expand 
#> 86 2.50997371253308 2.84125512881648 0.0104742429590286 1.04696716242467 1.70300905915644 0.00187578021046235 -74.7759936210548 reflect 
#> 87 2.50997371253308 2.84125512881648 0.0104742429590286 1.04696716242467 1.70300905915644 0.00187578021046235 -74.7759936210548 reflect 
#> 88 2.44792980518697 2.78089849933532 0.0105125216744423 1.06208202392478 1.58822703354283 0.00319477062837254 -74.7739593939673 reflect 
#> 89 2.44792980518697 2.78089849933532 0.0105125216744423 1.06208202392478 1.58822703354283 0.00319477062837254 -74.7739593939673 reflect 
#> 90 2.44792980518697 2.78089849933532 0.0105125216744423 1.06208202392478 1.58822703354283 0.00319477062837254 -74.7739593939673 reflect 
#> 91 2.41570112130133 2.77485636478573 0.0107563277723347 1.11359026895604 1.55926468544312 0.00340074856121198 -74.7705287820466 reflect 
#> 92 2.41570112130133 2.77485636478573 0.0107563277723347 1.11359026895604 1.55926468544312 0.00340074856121198 -74.7705287820466 reflect 
#> 93 2.41570112130133 2.77485636478573 0.0107563277723347 1.11359026895604 1.55926468544312 0.00340074856121198 -74.7705287820466 reflect 
#> 94 2.41570112130133 2.77485636478573 0.0107563277723347 1.11359026895604 1.55926468544312 0.00340074856121198 -74.7705287820466 reflect 
#> 95 2.46940745913186 2.81429643773155 0.0105545697932961 1.0594263824651 1.63712656116076 0.00151293911871725 -74.7666492992176 reflect 
#> 96 2.46940745913186 2.81429643773155 0.0105545697932961 1.0594263824651 1.63712656116076 0.00151293911871725 -74.7666492992176 reflect 
#> 97 2.46940745913186 2.81429643773155 0.0105545697932961 1.0594263824651 1.63712656116076 0.00151293911871725 -74.7666492992176 reflect 
#> 98 2.46940745913186 2.81429643773155 0.0105545697932961 1.0594263824651 1.63712656116076 0.00151293911871725 -74.7666492992176 reflect 
#> 99 2.46940745913186 2.81429643773155 0.0105545697932961 1.0594263824651 1.63712656116076 0.00151293911871725 -74.7666492992176 reflect 
#> 100 2.44445399663609 2.80807963443812 0.0105948317176711 1.09856547623253 1.60364135745409 0.00228432429356676 -74.7656356032692 reflect 
#> 101 2.48848876325422 2.83386532450039 0.0105594201841479 1.07870007752174 1.66889884674085 0.00145804879262552 -74.7618251463201 reflect 
#> 102 2.40630617228411 2.77469777649672 0.0108912028425772 1.11689035220103 1.55453406813276 0.00224680836966302 -74.7603861645145 reflect 
#> 103 2.3976325215724 2.75692978996009 0.0107708029656868 1.1262454646859 1.51645684508383 0.00243035694488876 -74.7588965342065 shrink 
#> 104 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 105 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 106 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 107 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 108 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 109 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 110 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 111 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 contract outside 
#> 112 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 contract outside 
#> 113 2.43092678345642 2.79456661235003 0.0107100098557127 1.10716385136969 1.5787957884049 0.00139844256395703 -74.7512704710398 reflect 
#> 114 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 115 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 shrink 
#> 116 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 117 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 118 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 119 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 120 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 reflect 
#> 121 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 contract outside 
#> 122 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 contract inside 
#> 123 2.42672923545847 2.78603953324378 0.0107974062080357 1.09008530109826 1.57925966017767 0.00133511595738737 -74.7484373669663 contract inside 
#> Optimization has terminated successfully. 
#>   lambda_c      mu   K      gamma lambda_a lambda_c2     mu2  K2     gamma2
#> 1 2.426729 2.78604 Inf 0.01079741 1.090085  2.426729 1.57926 Inf 0.01079741
#>   lambda_a2  prop_type2    loglik df conv
#> 1  1.090085 0.001335116 -74.74844  6    0

### When we have two islands with the same rates except for immigration and anagenesis rate,
# and we want to optimize all parameters, we use:

utils::data(Galapagos_datalist)
DAISIE_ML(
   datalist = list(Galapagos_datalist,Galapagos_datalist),
   datatype = 'multiple',
   initparsopt = c(2.5,2.7,20,0.009,1.01,0.009,1.01),
   idparsmat = rbind(1:5,c(1:3,6,7)),
   idparsopt = 1:7,
   parsfix = NULL,
   idparsfix = NULL,
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
)
#> 1 2.5 2.7 20 0.009 1.01 0.009 1.01 -152.092594252487 initial 
#> 2 2.52605459057072 2.63600256245996 20.2065573770492 0.00909639479298986 1.02061194263909 0.00909639479298986 1.02061194263909 -151.992287429145 contract outside 
#> Optimization has terminated successfully. 
#>   lambda_c       mu        K       gamma lambda_a    loglik df conv
#> 1 2.526055 2.636003 20.20656 0.009096395 1.020612 -151.9923  7    0
#> 2 2.526055 2.636003 20.20656 0.009096395 1.020612 -151.9923  7    0

### When we consider the four Macaronesia archipelagoes and set all parameters the same
# except for rates of cladogenesis, extinction and immigration for Canary Islands,
# rate of cladogenesis is fixed to 0 for the other archipelagoes,
# diversity-dependence is assumed to be absent
# and we want to optimize all parameters, we use:

utils::data(Macaronesia_datalist)
DAISIE_ML(
   datalist = Macaronesia_datalist,
   datatype = 'multiple',
   initparsopt = c(1.053151832,0.052148979,0.512939011,0.133766934,0.152763179),
   idparsmat = rbind(1:5,c(6,2,3,7,5),1:5,1:5),
   idparsopt = c(2,4,5,6,7),
   parsfix = c(0,Inf),
   idparsfix = c(1,3),
   tol = c(0.1, 0.02, 0.01),
   tolint = c(1e-4, 1e-2),
   res = 50
)
#> 1 1.053151832 0.052148979 0.512939011 0.133766934 0.152763179 -450.17407499527 initial 
#> 2 1.053151832 0.052148979 0.512939011 0.133766934 0.16040133795 -450.058250935912 contract outside 
#> 3 1.03786426282794 0.0541816809380983 0.4683911241782 0.13897708254106 0.158712270927341 -450.013754616694 expand 
#> 4 1.03786426282794 0.0541816809380983 0.4683911241782 0.13897708254106 0.158712270927341 -450.013754616694 reflect 
#> 5 1.03786426282794 0.0541816809380983 0.4683911241782 0.13897708254106 0.158712270927341 -450.013754616694 reflect 
#> 6 1.03786426282794 0.0541816809380983 0.4683911241782 0.13897708254106 0.158712270927341 -450.013754616694 reflect 
#> 7 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 reflect 
#> 8 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 reflect 
#> 9 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 reflect 
#> 10 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 reflect 
#> 11 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 reflect 
#> 12 1.04404958741138 0.0545029604424431 0.46204367138012 0.133643327000722 0.167074968672945 -449.959060732459 contract inside 
#> 13 1.05962183449368 0.0537300873444435 0.448263719007431 0.130651302345391 0.167589576448827 -449.927841049739 reflect 
#> 14 1.05962183449368 0.0537300873444435 0.448263719007431 0.130651302345391 0.167589576448827 -449.927841049739 contract outside 
#> 15 1.05962183449368 0.0537300873444435 0.448263719007431 0.130651302345391 0.167589576448827 -449.927841049739 reflect 
#> 16 1.06020464341123 0.0551998785283674 0.458543874664053 0.130509117335218 0.167791123996767 -449.922987212235 reflect 
#> 17 1.06020464341123 0.0551998785283674 0.458543874664053 0.130509117335218 0.167791123996767 -449.922987212235 reflect 
#> 18 1.06020464341123 0.0551998785283674 0.458543874664053 0.130509117335218 0.167791123996767 -449.922987212235 reflect 
#> 19 1.06020464341123 0.0551998785283674 0.458543874664053 0.130509117335218 0.167791123996767 -449.922987212235 contract inside 
#> Optimization has terminated successfully. 
#>    lambda_c       mu   K      gamma  lambda_a   loglik df conv
#> 1 0.0000000 1.060205 Inf 0.05519988 0.4585439 -449.923  5    0
#> 2 0.1305091 1.060205 Inf 0.16779112 0.4585439 -449.923  5    0
#> 3 0.0000000 1.060205 Inf 0.05519988 0.4585439 -449.923  5    0
#> 4 0.0000000 1.060205 Inf 0.05519988 0.4585439 -449.923  5    0

# }