Simulate (non-)oceanic islands with given parameters under a time-dependent regime

This function simulates islands with given cladogenesis, extinction, Kprime, immigration and anagenesis parameters, all of which modelled as time-dependent parameters.

Time dependency aims to capture the effect of area changes islands undego from their emergence until subsidence. Thus, oceanic, volcanic island ontogeny scenarios can be modelled (by a beta function), as well as the effect of sea level fluctuations (modelled through a sine function). See paramter entry area_pars for details. Both island ontogeny and sea level fluctuations are allowed to operate simultaneuosly.

This function also 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_time_dep(
  time,
  M,
  pars,
  replicates,
  area_pars,
  hyper_pars,
  divdepmodel = "CS",
  nonoceanic_pars = c(0, 0),
  num_guilds = NULL,
  sample_freq = 25,
  plot_sims = TRUE,
  island_ontogeny = "const",
  sea_level = "const",
  extcutoff = 1000,
  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.

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

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

divdepmodel

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.

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

num_guilds

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

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.

island_ontogeny

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.

sea_level

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.

extcutoff

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

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: A numeric with the number of mainland lineages that are not present on the island.
$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)
$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

References

Valente, L.M., A.B. Phillimore and R.S. Etienne (2015). Equilibrium and non-equilibrium dynamics simultaneously operate in the Galapagos islands. Ecology Letters 18: 844-852.

Valente, L.M., Etienne, R.S. and Phillimore, A.B. (2014). The effects of island ontogeny on species diversity and phylogeny. Proceedings of the Royal Society B: Biological Sciences 281(1784), p.20133227.

Author

Luis Valente and Albert Phillimore