Package 'DAISIE'

data frame to add the column to

location in data frame where to insert the column. Position can also be a name of a column

the elements of the column to insert. If the column has a name, this name will be copied into the data frame. Id is does not have a name, it will get the name "nc".

Numeric defining maximum area.

A numeric with the current island area at present (i.e., at the end of the simulation).

Numeric value from 0 to 1 indicating where in the island's history the peak area is achieved.

Numeric defining total island age.

Numeric defining amplitude of area fluctuation from sea level.

Numeric defining frequency of sine wave of area change from sea level.

Numeric defining the angle in degrees specifying the slope of the island.

the CS model to run, options are 1 for single rate DAISIE model, 2 for multi-rate DAISIE, or 0 for IW test model

the parameter to relax (integrate over). Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis"

standard deviation of the parameter to relax

upper bound of the parameter to relax

Numeric defining the scaling parameter for exponent for calculating cladogenesis rate.

Numeric defining the exponent for calculating extinction rate.

Numeric rate of cladogenesis

Numeric rate of extinction

Numeric carrying capacity

Numeric rate of immigration

Numeric rate of anagenesis

A numeric with the per capita transition rate with state1

A numeric with the per capita immigration rate with state2

A numeric with the per capita extinction rate with state2

A numeric with the per capita anagenesis rate with state2

A numeric with the per capita cladogenesis rate with state2

A numeric with the per capita transition rate with state2

A numeric with the number of species with trait state 2 on mainland

A numeric with the per capita transition rate with state1

A numeric with the per capita immigration rate with state2

A numeric with the per capita extinction rate with state2

A numeric with the per capita anagenesis rate with state2

A numeric with the per capita cladogenesis rate with state2

A numeric with the per capita transition rate with state2

A numeric with the number of species with trait state 2 on mainland

A numeric with the carrying capacity for state 2

sets step-size to factor * (t1 - t0).

Probability distribution in matrix format as output by DAISIE_probdist().

Island datalist or simulated data in DAISIE datalist format. Can be a single island (empirical data) generated with DAISIE_dataprep or DAISIEprep. Can also be simulated data generated with DAISIE_sim function.

Default sort_clade_sizes = T outputs clade sizes sorted in ascending order of number of species. sort_clade_sizes=F outputs clade sizes in the same order as they appear in the input datalist.

List showing the total number of species in each island clade (including missing species). Each item [[i]] on the list gives the sizes of all clades for a single island. If option sort_clade_sizes = T, the clade sizes for are sorted by increasing number of species. If option sort_clade_sizes = F the clade sizes are given in the same order as in the input datalist.

The total number of species in the largest island clade for each island.

Mean clade size (average of all island clades)

The total number of colonisations (clades) on each island.

The total number of species on each island. These are the extant species at present, including missing species; in case of simulations, this is the number of species present on the island at the end of the simulation.

max_steps: sets max. iterations to max_steps.

Data frame (table) with user-specified data. See file Galapagos_datatable.Rdata for a template of an input table. Each row on the table represents and independent colonisation event. Table has the following four columns.

$Clade_name - name of independent colonization event
$Status - One of the following categories:
* "Non_endemic": applies to non-endemic species when an approximate colonisation time is known
* "Non_endemic_MaxAge": applies to non-endemic species for cases where colonisation time is unknown
* "Endemic": applies to endemic species or endemic clades when an approximate colonisation time is known
* "Endemic_MaxAge": applies to endemic species or endemic clades for cases where the colonisation time is unknown, or when the user wants to specify an upper bound for colonisation. This could for example apply to endemic species that have recently gone extinct because of anthropogenic causes, and which are not included in the phylogeny ("NA" should be given in the branching times column). It could also apply to insular radiations with long stem branches, for which the time of the first cladogenetic event is known, but the precise time of colonisation is not.
* "Endemic_MaxAge_MinAge": same as Endemic_MaxAge but also includes a minimum age for colonisation.
* "Non_endemic_MaxAge_MinAge": same as Non_endemic_MaxAge but also includes a minimum age for colonisation.#'
* "Endemic&Non_Endemic": when endemic clade is present and its mainland ancestor has re-colonized
$Missing_species - Number of island species that were not sampled for particular clade (only applicable for "Endemic" clades). If NA is given in branching times column, this should be equal to the number of species in the clade minus 1
$Branching_times - Stem age of the population/species in the case of "Non_endemic", "Non_endemic_MaxAge" and "Endemic" species with no extant close relatives on the island. Set "NA" if colonisation time unknown and no upper bound is known. For "Endemic" cladogenetic species these should be branching times of the radiation, including the stem age of the radiation (colonisation time estimate).

Age of island in appropriate units

The size of the mainland pool, i.e the number of species that can potentially colonize the island

Number of clade types. Default: number_clade_types = 1 all species are considered to belong to same macroevolutionary process. If number_clade_types = 2, there are two types of clades with distinct macroevolutionary processes.

If number_clade_types = 2, list_type2_clades specifies the names of the clades that have a distinct macroevolutionary process. The names must match those in the $Clade_name column of the source data table (e.g. list_type2_clades = "Finches"). If number_clade_types = 1, then list_type2_clades = NA should be specified (default)

Specifies the fraction of potential mainland colonists that have a distinct macroevolutionary process. Applies only if number_clade_types = 2. Default "proportional" sets the fraction to be proportional to the number of clades of distinct macroevolutionary process that have colonised the island. Alternatively, the user can specify a value between 0 and 1 (e.g. if mainland pool size is 1000 and prop_type2_pool = 0.02 then number of type2 species is 20).

Default= 1E-5 should be appropriate in most cases. This value is used to set the maximum age of colonisation of "Non_endemic_MaxAge" and "Endemic_MaxAge" species to an age that is slightly younger than the island for cases when the age provided for that species is older than the island. The new maximum age is then used as an upper bound to integrate over all possible colonisation times.

Boolean. States if intermediate results should be printed to console. Defaults to TRUE.

R list object containing data:
The first element of the list has two or three components:
$island_age - the island age
Then, depending on whether a distinction between species 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 following 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 "Endemic" cladogenetic species these are 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_MaxAge: 5 (if only colonisation time was given)
* Endemic_MaxAge: 6 (if colonisation time and cladogenesis times were given)
$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)
$type_1or2 - whether the colonist belongs to type 1 or type 2

The time at which the expectations need to be computed.

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.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

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

List output from DAISIE_sim_core_cr(), DAISIE_sim_core_time_dep(), DAISIE_sim_core_cr_shift() or DAISIE_sim_min_type2() functions. Minimally, this must be a list that has as many elements as replicates. Each element must be a list with the elements island_age, not_present and stt_all. stt_all must be a data frame with the column names Time, nI, nA, nC and present.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

A named list containing diversification rates considering two trait states created by create_trait_pars:

• [1]:A numeric with the per capita transition rate with state1

• [2]:A numeric with the per capita immigration rate with state2

• [3]:A numeric with the per capita extinction rate with state2

• [4]:A numeric with the per capita anagenesis rate with state2

• [5]:A numeric with the per capita cladogenesis rate with state2

• [6]:A numeric with the per capita transition rate with state2

• [7]:A numeric with the number of species with trait state 2 on mainland

List output from DAISIE_sim_core_cr(), DAISIE_sim_core_time_dep(), DAISIE_sim_core_cr_shift() or DAISIE_sim_min_type2() functions. Minimally, this must be a list that has as many elements as replicates. Each element must be a list with the elements island_age, not_present and stt_all. stt_all must be a data frame with the column names Time, nI, nA, nC and present.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

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 or 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 followed by stem age of the population/species in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close relatives on the island. For endemic clades with more than one species on the island (cladogenetic clades/ radiations) these should be island age followed by the branching times of the island clade including the stem age of the clade
$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

$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

The initial values of the parameters that must be optimized, they are all positive.

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.

The values of the parameters that should not be optimized.

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.

Numeric for how many simulations should run.

Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

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

num_threads < 0 or omitted: retrieves number of threads.
num_threads = 0: sets the number of threads to the number of available cores.
num_threads = 1: single-threaded execution.
num_threads > 1: sets the number of threads to num_threads.

Contains the 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)
pars1[6] is optional; it may contain M, the total number of species on the mainland

Contains the model settings

pars2[1] corresponds to lx = length of ODE variable x
pars2[2] corresponds to ddmodel = diversity-dependent model, model of diversity-dependence, which can be one of

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
Only ddmodel = 11 is currently implemented

pars2[3] corresponds to cond = setting of conditioning

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota

pars2[4] Specifies whether intermediate output should be provided, because computation may take long. Default is 0, no output. A value of 1 means the parameters and loglikelihood are printed. A value of 2 means also intermediate progress during loglikelihood computation is shown.

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 or 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_MaxAge: 5

$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)

Method of the ODE-solver. Supported Boost ODEINT solvers (steppers) are: 'odeint::runge_kutta_cash_karp54' 'odeint::runge_kutta_fehlberg78' [default] 'odeint::runge_kutta_dopri5' 'odeint::bulirsch_stoer' 'odeint::adams_bashforth_[1|2|3|4|5|6|7|8]} \code{'odeint::adams_bashforth_moulton_[1|2|3|4|5|6|7|8] without odeint::-prefix, ode method is assumed.

Absolute tolerance of the integration

Relative tolerance of the integration

Logical controling if progress is printed to console.

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).

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.

The times at which the probabilities need to be computed.

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.

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

Probability distribution in matrix format as output by DAISIE_probdist().

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

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 or 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 followed by stem age of the population/species in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close relatives on the island. For endemic clades with more than one species on the island (cladogenetic clades/ radiations) these should be island age followed by the branching times of the island clade including the stem age of the clade
$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

$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

Sets the type of data: 'single' for a single island or archipelago treated as one, and 'multiple' for multiple archipelagoes potentially sharing the same parameters.

The initial values of the parameters that must be optimized, they are all positive.

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.

The values of the parameters that should not be optimized.

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.

For datatype = 'single' only: 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.

For datatype = 'multiple' only: Matrix containing the ids of the parameters, linking them to initparsopt and parsfix. Per island system we use the following order:

* lac = (initial) cladogenesis rate
* mu = extinction rate
* K = maximum number of species possible in the clade
* gam = (initial) immigration rate
* laa = (initial) anagenesis rate
Example: idparsmat = rbind(c(1, 2, 3, 4, 5), c(1, 2, 3, 6, 7)) has different rates of immigration and anagenesis for the two islands.

Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade.

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 = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

Sets the equilibrium constraint that can be used during the likelihood optimization. Only available for datatype = 'single'.

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.

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.

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

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.

Sets the maximum number of iterations in the optimization.

Method of the ODE-solver. Supported Boost ODEINT solvers (steppers) are: "odeint::runge_kutta_cash_karp54" "odeint::runge_kutta_fehlberg78" "odeint::runge_kutta_dopri5" "odeint::bulirsch_stoer" without odeint::-prefix, deSolve{ode} method is assumed. The default method overall is "lsodes" for DAISIE_ML_CS() and "ode45" from ode() for DAISIE_ML_IW().

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

a numeric or list. Default is 1 for the standard DAISIE model, for a relaxed-rate model a list with the following 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.

• relaxed_par: the parameter to relax (integrate over). Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis".

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

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

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.

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

gives the maximum likelihood estimate of lambda^c, the rate of cladogenesis

gives the maximum likelihood estimate of mu, the extinction rate

gives the maximum likelihood estimate of K, the carrying-capacity

gives the maximum likelihood estimate of gamma, the immigration rate

gives the maximum likelihood estimate of lambda^a, the rate of anagenesis

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

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

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

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

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

gives the maximum loglikelihood

gives the number of estimated parameters, i.e. degrees of feedom

gives a message on convergence of optimization; conv = 0 means convergence

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 or 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 followed by stem age of the population/species in the case of Non-endemic, Non-endemic_MaxAge species and Endemic species with no close relatives on the island. For endemic clades with more than one species on the island (cladogenetic clades/ radiations) these should be island age followed by the branching times of the island clade including the stem age of the clade
$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

$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

The initial values of the parameters that must be optimized, they are all positive.

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.

The values of the parameters that should not be optimized.

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.

Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade.

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 = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

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.

Sets the maximum number of iterations in the optimization.

Method of the ODE-solver. Supported Boost ODEINT solvers (steppers) are: "odeint::runge_kutta_cash_karp54" "odeint::runge_kutta_fehlberg78" "odeint::runge_kutta_dopri5" "odeint::bulirsch_stoer" without odeint::-prefix, deSolve{ode} method is assumed. The default method overall is "lsodes" for DAISIE_ML_CS() and "ode45" from ode() for DAISIE_ML_IW().

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

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

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

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.

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

gives the maximum likelihood estimate of lambda^c, the rate of cladogenesis

gives the maximum likelihood estimate of mu, the extinction rate

gives the maximum likelihood estimate of K, the carrying-capacity

gives the maximum likelihood estimate of gamma, the immigration rate

gives the maximum likelihood estimate of lambda^a, the rate of anagenesis

gives the maximum loglikelihood

gives the number of estimated parameters, i.e. degrees of feedom

gives a message on convergence of optimization; conv = 0 means convergence

Data object containing information on colonisation and branching times of species for several islands or archipelagos, as well as the area, isolation and age of each of the islands/archipelagos. See data(archipelagos41) for an example.

The initial values of the parameters that must be optimized; they are all positive

The ids of the parameters that must be optimized. The ids are defined as follows (see Valente et al 2020 Supplementary Tables 1 and 2 a better explanation of the models and parameters):

id = 1 corresponds to lambda^c0 (cladogenesis rate for unit area)
id = 2 corresponds to y (exponent of area for cladogenesis rate)
id = 3 corresponds to mu0 (extinction rate for unit area)
id = 4 corresponds to x (exponent of 1/area for extinction rate)
id = 5 corresponds to K0 (clade-level carrying capacity for unit area)
id = 6 corresponds to z (exponent of area for clade-level carrying capacity)
id = 7 corresponds to gamma0 (immigration rate for unit distance)
id = 8 corresponds to alpha (exponent of 1/distance for immigration rate)
id = 9 corresponds to lambda^a0 (anagenesis rate for unit distance)
id = 10 corresponds to beta (exponent of 1/distance for anagenesis rate)
id = 11 corresponds to d0 in models M15 to M19, and models with distance_dep = 'sigmoidal_col', 'sigmoidal_ana' or 'sigmoidal_clado'; or d0 for colonisation (when specifying distance_dep = 'sigmoidal_col_ana'
id = 12 corresponds to d0 for anagenesis when specifying distance_dep = 'sigmoidal_col_ana'

The values of the parameters that should not be optimized

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.

Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade

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 = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota

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

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

Sets the maximum number of iterations in the optimization

Method of the ODE-solver. See package deSolve for details. Default is "lsodes"

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

a numeric or list. Default is 1 for the standard DAISIE model, for a relaxed-rate model a list with the following 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.

• relaxed_par: the parameter to relax (integrate over). Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis".

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

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

Use 'continent' if the distance to the continent should be used, use 'nearest_big' if the distance to the nearest big landmass should be used, and use 'biologically_realistic' if the distance should take into account some biologically realism, e.g. an average of the previous two if both are thought to contribute.

Sets what type of distance dependence should be used. Default is a power law, denoted as 'power' (models M1-14 in Valente et al 2020). Alternatives are additive or interactive contributions of distance and area to the rate of cladogenesis ("area_additive_clado"; "area_interactive_clado", "area_interactive_clado1" and "area_interactive_clado2"). Other alternatives are exponential relationship denoted by 'exp'; or sigmoids, either 'sigmoidal_col' for a sigmoid in the colonization, 'sigmoidal_ana' for sigmoidal anagenesis, 'sigmoidal_clado' for sigmoidal cladogenesis, and 'sigmoidal_col_ana' for sigmoids in both colonization and anagenesis.
A key for the different options of distance_dep that should be specified to run the models from Valente et al 2020 (Supplementary Data Table 1 and 2) is given below:
* M1 to M14 - 'power'
* M15 -'area_additive_clado'
* M16 and M19 -'area_interactive_clado'
* M17 -'area_interactive_clado1'
* M18 - 'area_interactive_clado2'
* M20 and M24 - sigmoidal_col'
* M21, M25 and M28 - sigmoidal_ana'
* M22 and M26 - 'sigmoidal_clado'
* M23 and M27 - 'sigmoidal_col_ana'

Sets whether parallel computation should be used. Use 'no' if no parallel computing should be used, 'cluster' for parallel computing on a unix/linux cluster, and 'local' for parallel computation on a local machine.

Number of cpus used in parallel computing. Default is 3. Will not have an effect if parallel = 'no'.

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

gives the maximum likelihood estimate of lambda^c, the rate of cladogenesis for unit area

gives the maximum likelihood estimate of y, the exponent of area for the rate of cladogenesis

gives the maximum likelihood estimate of mu0, the extinction rate

gives the maximum likelihood estimate of x, the exponent of 1/area for the extinction rate

gives the maximum likelihood estimate of K0, the carrying-capacity for unit area

gives the maximum likelihood estimate of z, the exponent of area for the carrying capacity

gives the maximum likelihood estimate of gamma0, the immigration rate for unit distance

gives the maximum likelihood estimate of alpha, the exponent of 1/distance for the rate of colonization

gives the maximum likelihood estimate of lambda^a0, the rate of anagenesis for unit distance

gives the maximum likelihood estimate of beta, the exponent of 1/distance for the rate of anagenesis

gives the maximum loglikelihood

gives the number of estimated parameters, i.e. degrees of feedom

gives a message on convergence of optimization; conv = 0 means convergence

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).

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.

The times at which the probabilities need to be computed.

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.

A list of three vectors:

expC The expectation of the number of colonizations/lineages at the given times
pC The probability distribution of the number of colonizations (lineages) at the given times

Island data object. Can be in DAISIE list format (see Galapagos_datalist and DAISIE_data_prep for examples) or in table format (see Galapagos_datatable for an example).

Title of the plot

Age of island in appropriate units. In DAISIE_plot_age_diversity() and DAISIE_plot_island() if island input is in table format, the age of the island must be specified. If island input is in DAISIE list format, this option will override the island age specified in the island list.

A list of trees, in phylo format, named after their respective clades

The age of the island, on the same scale as the branch lengths of the trees. If unspecified, the depth of the deepest stem across trees.

A vector of colonization times, with one value per clade. Order must be the same as in 'trees'. If unspecified, all clades are assigned the age of the island as colonization time.

Optional data frame with clade-level metadata. One column must be named "clade".

Optional aesthetic mapping to apply to the trees, as returned by the 'ggplot2::aes' function. Mapped variables can be anything in the columns of the 'data' node-wise data frame associated to the 'ggtree' plot being created (e.g. node, label, clade, mrca) or anything in the columns of the clade-wise 'metadata', if provided (in this case the aesthetics is mapped to all nodes within each clade).

Length of the extra tips grafted to each tree at the island age. These are a hack for scaling the plot. Keep this value small.

Optional arguments to be passed to 'geom_point' when plotting points at colonization events (e.g. size, shape...).

Optional background color of the figure. This is because we use rectangles as a hack to hide tree branches prior to island colonization. Default to white background.

Island data object. Can be in DAISIE list format (see Galapagos_datalist and DAISIE_data_prep for examples) or in table format (see Galapagos_datatable for an example).

Age of island in appropriate units. In DAISIE_plot_age_diversity() and DAISIE_plot_island() if island input is in table format, the age of the island must be specified. If island input is in DAISIE list format, this option will override the island age specified in the island list.

List output from DAISIE_sim_core_cr(), DAISIE_sim_core_time_dep(), DAISIE_sim_core_cr_shift() or DAISIE_sim_min_type2() functions. Minimally, this must be a list that has as many elements as replicates. Each element must be a list with the elements island_age, not_present and stt_all. stt_all must be a data frame with the column names Time, nI, nA, nC and present.

Boolean to indicate to plot all values plus one. Set to TRUE for default behavior. Set to FALSE to plot all values without adding one. Only works when there is one type of species.

String to indicate if stt of all species or all possible stt should be plotted. Default is "all_species", "type1_species" or "type2_species" should be plotted.

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

A named list containing diversification rates considering two trait states created by create_trait_pars:

• [1]:A numeric with the per capita transition rate with state1

• [2]:A numeric with the per capita immigration rate with state2

• [3]:A numeric with the per capita extinction rate with state2

• [4]:A numeric with the per capita anagenesis rate with state2

• [5]:A numeric with the per capita cladogenesis rate with state2

• [6]:A numeric with the per capita transition rate with state2

• [7]:A numeric with the number of species with trait state 2 on mainland

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).

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.

The times at which the probabilities need to be computed.

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.

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

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

Option divdepmodel = 'CS' runs a model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist. Option divdepmodel = 'IW' runs a model with island-wide carrying capacity, where diversity-dependence operates within and among clades. Option divdepmodel = 'GW' runs a model with diversity-dependence operates within a guild.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

The number of guilds on the mainland. The number of mainland species is divided by the number of guilds when divdepmodel = "GW"

Fraction of mainland species that belongs to the second subset of species (type 2). Applies only when two types of species are simulated (length(pars) = 10). For DAISIE_dataprep() applies only if number_clade_types = 2. In DAISIE_dataprep() the default "proportional" sets the fraction to be proportional to the number of clades of distinct macroevolutionary process that have colonised the island.

Applies only when two types of species are being simulated. Default replicates_apply_type2 = TRUE runs simulations until the number of islands where a type 2 species has colonised is equal to the specified number of replicates. This is recommended if prop_type2_pool is small or if the rate of immigration of type two species (pars[9]) is low, meaning that more replicates are needed to achieved an adequate sample size of islands with type 2 species. Setting replicates_apply_type2 = FALSE simulates islands up to the specified number of replicates regardless of whether type 2 species have colonised or not.

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Any arguments to pass on to plotting functions.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

Fraction of mainland species that belongs to the second subset of species (type 2). Applies only when two types of species are simulated (length(pars) = 10). For DAISIE_dataprep() applies only if number_clade_types = 2. In DAISIE_dataprep() the default "proportional" sets the fraction to be proportional to the number of clades of distinct macroevolutionary process that have colonised the island.

Applies only when two types of species are being simulated. Default replicates_apply_type2 = TRUE runs simulations until the number of islands where a type 2 species has colonised is equal to the specified number of replicates. This is recommended if prop_type2_pool is small or if the rate of immigration of type two species (pars[9]) is low, meaning that more replicates are needed to achieved an adequate sample size of islands with type 2 species. Setting replicates_apply_type2 = FALSE simulates islands up to the specified number of replicates regardless of whether type 2 species have colonised or not.

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

The number of guilds on the mainland. The number of mainland species is divided by the number of guilds when divdepmodel = "GW"

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

a numeric vector specifying when the rate shifts occur before the present.

Option divdepmodel = 'CS' runs a model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist. Option divdepmodel = 'IW' runs a model with island-wide carrying capacity, where diversity-dependence operates within and among clades. Option divdepmodel = 'GW' runs a model with diversity-dependence operates within a guild.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

The number of guilds on the mainland. The number of mainland species is divided by the number of guilds when divdepmodel = "GW"

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Any arguments to pass on to plotting functions.

Object (data.frame) containing a table with columns with the following names: Archipelago: names of the archipelagos or islands to be simulated; Area - the area of the archipelago/island; Age: Age of the oldest island in the archipelago, or age of the island if single island. Distance - distance to the mainland (or other applicable isolation metric). As an example, the dataset from Valente et al 2020 for 41 archipelagos is provided in data(archipelago_data).

The size of the mainland pool, i.e the number of species that can potentially colonize the island(s).

Contains the model hyperparameters:

pars[1] corresponds to lambda^c0 (initial cladogenesis rate)
pars[2] corresponds to y (dependency of cladogenesis on area) 0 - no dependency, positive value - cladogenesis increases with area, negative value - cladogenesis decreases with area
pars[3] corresponds to mu_0 (initial extinction rate)
pars[4] corresponds to x (dependency of extinction on area) 0 - no dependency, positive value - extinction increases with area, negative value - extinction decreases with area.
pars[5] corresponds to K_0 (initial carrying capacity). Set K=Inf for non-diversity dependence.
pars[6] corresponds to z (dependency of K on area). 0 - no dependency, positive value - K increases with area, negative value - K decreases with area.
pars[7] corresponds to gamma_0 (initial immigration rate)
pars[8] corresponds to alpha (dependency of immigration on island isolation). 0 - no dependency, positive value - immigration increases with distance, negative value - immigration decreases with distance
pars[9] corresponds to lambda^a_0 (initial anagenesis rate)
pars[10] corresponds to beta (dependency of anagenesis on island isolation). 0 - no dependency,positive value - anagenesis increases with distance, negative value - anagenesis decreases with distance.
pars[11] corresponds to d0, parameter that describes interactive/additive effect of isolation and area on cladogenesis (power models); or that describes the shape of the sigmoidal relationship between isolation and a parameter (sigmoidal models).

Number of island replicates to be simulated per island in the table archipelago_data. If there are 5 islands in archipelago_data, and number of replicates is set to 10, 50 islands will be simulated.

Option divdepmodel = 'CS' runs model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist.
Option divdepmodel = 'IW' runs model with island-wide carrying capacity, where diversity-dependence operates within and among clades.

Shape of dependency of parameter with distance. Can be of type
'power' or type
'sigmoidal'.

When distance_dep = 'power' is specified, cladogenesis_dep specifies the type of effect of area and isolation on cladogenesis. The possible options are:
'NULL' (no additive or interactive effect of area on isolation, same as models M1-M14 in Valente et al 2020)
'additive' (additive effect of area and isolation on cladogenesis, same as model M15 in Valente et al 2020)
'interactive' (interactive effect of area and isolation on cladogenesis, same as models M16 and M19 in Valente et al 2020)
'interactive1' (interactive effect of area and isolation on cladogenesis, same as model M17 in Valente et al 2020)
'interactive2' (interactive effect of area and isolation on cladogenesis, same as model M18 in Valente et al 2020)

When distance_dep = 'sigmoidal', sigmoidal_par specifies to which parameter the sigmoidal relationship with distance is applied. Options:
'cladogenesis'
'anagenesis'
'colonisation'.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A string determining which parameter is relaxed in a relaxed rate model.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Any arguments to pass on to plotting functions.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

Option divdepmodel = 'CS' runs a model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist. Option divdepmodel = 'IW' runs a model with island-wide carrying capacity, where diversity-dependence operates within and among clades. Option divdepmodel = 'GW' runs a model with diversity-dependence operates within a guild.

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

The number of guilds on the mainland. The number of mainland species is divided by the number of guilds when divdepmodel = "GW"

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Any arguments to pass on to plotting functions.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A numeric value specifying the peakiness (or shaprness) of the ontogeny curve. Higher values imply peakier ontogeny. This value is internally calculated by calc_peak() given the area at the present and the area_pars.

A numeric value for maximum island area during the simulation.

A numeric value for minimum island area during the simulation.

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

The number of guilds on the mainland. The number of mainland species is divided by the number of guilds when divdepmodel = "GW"

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A numeric value specifying the peakiness (or shaprness) of the ontogeny curve. Higher values imply peakier ontogeny. This value is internally calculated by calc_peak() given the area at the present and the area_pars.

A numeric value for maximum island area during the simulation.

A numeric value for minimum island area during the simulation.

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A vector of length two with:

• [1]: the probability of sampling a species from the mainland

• [2]: the probability of the species sampled from the mainland being nonendemic

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A numeric value specifying the peakiness (or shaprness) of the ontogeny curve. Higher values imply peakier ontogeny. This value is internally calculated by calc_peak() given the area at the present and the area_pars.

A numeric value for maximum island area during the simulation.

A numeric value for minimum island area during the simulation.

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

Option divdepmodel = 'CS' runs a model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist. Option divdepmodel = 'IW' runs a model with island-wide carrying capacity, where diversity-dependence operates within and among clades. Option divdepmodel = 'GW' runs a model with diversity-dependence operates within a guild.

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

A named list containing diversification rates considering two trait states created by create_trait_pars:

• [1]:A numeric with the per capita transition rate with state1

• [2]:A numeric with the per capita immigration rate with state2

• [3]:A numeric with the per capita extinction rate with state2

• [4]:A numeric with the per capita anagenesis rate with state2

• [5]:A numeric with the per capita cladogenesis rate with state2

• [6]:A numeric with the per capita transition rate with state2

• [7]:A numeric with the number of species with trait state 2 on mainland

Any arguments to pass on to plotting functions.

Numeric defining the length of the simulation in time units. For example, if an island is known to be 4 million years old, setting time = 4 will simulate the entire life span of the island; setting time = 2 will stop the simulation at the mid-life of the island.

Numeric defining the size of mainland pool, i.e. the number of species that can potentially colonize the island.

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.

Integer specifying number of island replicates to be simulated.

Option divdepmodel = 'CS' runs a model with clade-specific carrying capacity, where diversity-dependence operates only within single clades, i.e. only among species originating from the same mainland colonist. Option divdepmodel = 'IW' runs a model with island-wide carrying capacity, where diversity-dependence operates within and among clades. Option divdepmodel = 'GW' runs a model with diversity-dependence operates within a guild.

Numeric specifing the number of units times should be divided by for plotting purposes. Larger values will lead to plots with higher resolution, but will also run slower.

Default = TRUE plots species-through-time (STT) plots. It detects how many types of species are present. If only one type of species is present, STT is plotted for all species. If two types are present, three plots are produced: STT for all, STT for type 1 and STT for type 2.

In DAISIE_sim_time_dep(), DAISIE_ML_CS and plotting a string describing the type of island ontogeny. Can be "const", "beta" for a beta function describing area through time.
In all other functions a numeric describing the type of island ontogeny. Can be 0 for constant, 1 for a beta function describing area through time. In ML functions island_ontogeny = NA assumes constant ontogeny. Time dependent estimation is not yet available as development is still ongoing. Will return an error if called in that case.

In DAISIE_sim_time_dep() and plotting a string describing the type of sea level. Can be "const" or "sine" for a sine function describing area through time.
In all other functions a numeric describing the type of sea level. Can be 0 for constant, 1 for a sine function describing area through time.

A named list of numeric hyperparameters for the rate calculations as returned by create_hyper_pars():

• [1]: is d the scaling parameter for exponent for calculating cladogenesis rate

• [2]: is x the exponent for calculating extinction rate

A named list containing area and sea level parameters as created by create_area_pars():

• [1]: maximum area

• [2]: current area

• [3]: value from 0 to 1 indicating where in the island's history the peak area is achieved

• [4]: total island age

• [5]: amplitude of area fluctuation from sea level

• [6]: frequency of sine wave of area change from sea level

• [7]: angle of the slope of the island

A numeric with the cutoff for the the maximum extinction rate preventing it from being too large and slowing down simulation.

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
. cond > 1 : conditioning on island age and having at least cond colonizations on the island. This last option is not yet available for the IW model

A numeric vector of length 1, which in simulations and 'DAISIEdataprep()' can be '1' or '0', where '1' gives intermediate output should be printed. For ML functions a numeric determining if intermediate output should be printed. The default: '0' does not print, '1' prints the initial likelihood and the settings that were selected (which parameters are to be optimised, fixed or shifted), '2' prints the same as '1 and also the intermediate output of the parameters and loglikelihood, while '3' the same as '2' and prints intermediate progress during likelihood computation.

A named list containing diversification rates considering two trait states created by create_trait_pars:

• [1]:A numeric with the per capita transition rate with state1

• [2]:A numeric with the per capita immigration rate with state2

• [3]:A numeric with the per capita extinction rate with state2

• [4]:A numeric with the per capita anagenesis rate with state2

• [5]:A numeric with the per capita cladogenesis rate with state2

• [6]:A numeric with the per capita transition rate with state2

• [7]:A numeric with the number of species with trait state 2 on mainland

Any arguments to pass on to plotting functions.

Contains the 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)
pars1[6] corresponds to lambda^c (cladogenesis rate) after the shift
pars1[7] corresponds to mu (extinction rate) after the shift
pars1[8] corresponds to K (clade-level carrying capacity) after the shift
pars1[9] corresponds to gamma (immigration rate) after the shift
pars1[10] corresponds to lambda^a (anagenesis rate) after the shift
pars1[11] corresponds to the time of shift

Contains the model settings

pars2[1] corresponds to lx = length of ODE variable x
pars2[2] corresponds to ddmodel = diversity-dependent model, model of diversity-dependence, which can be one of

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

pars2[3] corresponds to cond = setting of conditioning

cond = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota
cond > 1 : conditioning on island age and having at least cond colonizations on the island

pars2[4] sets whether parameters and likelihood should be printed (1) or not (0)

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 or 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_MaxAge: 5

$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)

Method of the ODE-solver. See package deSolve for details. Default is "lsodes"

a numeric or list. Default is 1 for the standard DAISIE model, for a relaxed-rate model a list with the following 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.

• relaxed_par: the parameter to relax (integrate over). Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis".

Absolute tolerance of the integration

Relative tolerance of the integration

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_MaxAge: 5

$missing_species - number of island species that were not sampled for particular clade (only applicable for endemic clades)

The initial values of the parameters that must be optimized

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

The values of the parameters that should not be optimized

The ids of the parameters that should not be optimized, e.g. c(1,3) if lambda^c and K should not be optimized.

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

Sets the maximum number of species for which a probability must be computed, must be larger than the size of the largest clade

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 = 0 : conditioning on island age
cond = 1 : conditioning on island age and non-extinction of the island biota

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

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.

Sets the maximum number of iterations in the optimization.

Method of the ODE-solver. See package deSolve for details. Default is "lsodes"

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

a numeric or list. Default is 1 for the standard DAISIE model, for a relaxed-rate model a list with the following 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.

• relaxed_par: the parameter to relax (integrate over). Options are "cladogenesis", "extinction", "carrying_capacity", "immigration", or "anagenesis".

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

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

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.

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

gives the maximum likelihood estimate of lambda^c, the rate of cladogenesis

gives the maximum likelihood estimate of mu, the extinction rate

gives the maximum likelihood estimate of K, the carrying-capacity

gives the maximum likelihood estimate of gamma, the immigration rate

gives the maximum likelihood estimate of lambda^a, the rate of anagenesis

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

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

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

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

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

gives the maximum loglikelihood

gives the number of estimated parameters, i.e. degrees of feedom

gives a message on convergence of optimization; conv = 0 means convergence