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Simulate (non-)oceanic islands with given parameters under a relaxed-rate model

Source: R/DAISIE_sim_relaxed_rate.R
DAISIE_sim_relaxed_rate.Rd

This function simulates islands with given cladogenesis, extinction, Kprime, immigration and anagenesis parameters, all of which can be modelled as time-constant parameters with variation between clades in one or multiple parameters. Further, it allows for the simulation of non-oceanic islands, generating islands for which the starting condition includes potential endemic and non-endemic species.

Usage

DAISIE_sim_relaxed_rate(
  time,
  M,
  pars,
  replicates,
  relaxed_par,
  nonoceanic_pars = c(0, 0),
  sample_freq = 25,
  plot_sims = TRUE,
  hyper_pars = create_hyper_pars(d = 0, x = 0),
  area_pars = create_area_pars(max_area = 1, current_area = 1, proportional_peak_t = 0,
    total_island_age = 0, sea_level_amplitude = 0, sea_level_frequency = 0,
    island_gradient_angle = 0),
  cond = 0,
  verbose = TRUE,
  ...
)

Arguments

time

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.

M

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

pars

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.

replicates

Integer specifying number of island replicates to be simulated.

relaxed_par

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

nonoceanic_pars

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

sample_freq

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.

plot_sims

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.

hyper_pars

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

area_pars

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

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

verbose

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.

Value

A list. The highest level of the least corresponds to each individual replciate. The first element of each replicate is composed of island information containing:

  • $island_age: A numeric with the island age.

  • $not_present: the number of mainland lineages that are not present on the island. It is only present if only 1 type of species is simulated. Becomes $not_present_type1: the number of mainland lineages of type 1 that are not present on the island and $not_present_type2: the number of mainland lineages of type 2 that are not present on the island, if two types are simulated.

  • $stt_all: STT table for all species on the island (nI - number of non-endemic species; nA - number of anagenetic species, nC - number of cladogenetic species, present - number of independent colonisations present)

  • $stt_stt_type1: STT table for type 1 species on the island - only if 2 types of species were simulated (nI - number of non-endemic species; nA - number of anagenetic species, nC - number of cladogenetic species, present - number of independent colonisations present).

  • $stt_stt_type2: STT table for type 2 species on the island - only if 2 types of species were simulated (nI - number of non-endemic species; nA - number of anagenetic species, nC - number of cladogenetic species, present - number of independent colonisations present ).

  • $brts_table: Only for simulations under "IW". Table containing information on order of events in the data, for use in maximum likelihood optimization.).

The subsequent elements of the list pertaining to each replcate contain information on a single colonist lineage on the island and have 4 components:

  • $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: An integer ranging from 1 to 4 indicating the status of the colonist:

    1. Non_endemic_MaxAge

    2. Endemic

    3. Endemic&Non_Endemic

    4. Non_endemic_MaxAge

  • $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

See also

DAISIE_plot_sims() for plotting STT of simulation outputs.

Other simulation models: DAISIE_sim_cr_shift(), DAISIE_sim_time_dep(), DAISIE_sim()

Author

Luis Valente, Albert Phillimore, Joshua Lambert, Shu Xie, Pedro Neves, Richèl J. C. Bilderbeek, Rampal Etienne

Examples

## Simulate an island for 1 million years, with a relaxed the rate of
## cladogenesis between clades. Pool size 500.

clado_rate <- 0.5
ext_rate <- 0.2
carr_cap <- Inf
immig_rate <- 0.005
ana_rate <- 1
par_sd <- 1
sim_pars <- c(clado_rate, ext_rate, carr_cap, immig_rate, ana_rate, par_sd)
set.seed(1)
island_replicates <- DAISIE_sim_relaxed_rate(
  time = 1,
  M = 500,
  pars = sim_pars,
  replicates = 2,
  relaxed_par = "cladogenesis",
  plot_sims = FALSE,
  verbose = FALSE
)