Runs a stage-based demographic population model simulation.

Simulates a stage-based demographic population model and returns simulation results across multiple replicate runs. Processes run at each simulation time-step include:

Density dependence calculations (ceiling, logistic, or user-defined)
Environmental stochasticity calculations
Stage transition (stochastic) calculations
Translocation calculations (user-defined)
Harvest calculations (user-defined)
Mortality calculations (user-defined)
Dispersal calculations (default or user-defined)
Results collection

Usage

population_simulator(inputs)

Arguments

inputs

Nested list/object with named elements:

random_seed

Number to seed the random number generation for stochasticity.

replicates

Number of replicate simulation runs (default is 1).

time_steps

Number of simulation time steps. Required input.

years_per_step

Number of years per time step (default is 1).

populations

Number of populations. Required input.

coordinates

Data frame (or matrix) of X-Y population coordinates.

stages

Number of life cycle stages.

region

A Region object defining the study region.

initial_abundance

Array (or matrix) of initial abundances (at each stage in rows) for each population (in columns). If there is only one stage and a region object is attached, then initial abundance may be provided in the form of a raster with the same specs as the region raster. A vector can be provided that will be forced to a matrix. Required input.

stage_matrix

Matrix of transition (fecundity & survival) rates between stages at each time step (Leslie/Lefkovitch matrix). Required input.

fecundity_mask

Matrix of 0-1 to indicate which (proportions) of transition rates refer to fecundity.

fecundity_max

Maximum transition fecundity rate (in Leslie/Lefkovitch matrix).

demographic_stochasticity

Boolean for choosing demographic stochasticity for transition, dispersal, harvest and/or other processes (default is TRUE).

standard_deviation

Standard deviation matrix (or single value) for applying environmental stochasticity to transition rates.

correlation

List containing either an environmental correlation matrix (correlation_matrix), a pre-calculated transposed (Cholesky) decomposition matrix (t_decomposition_matrix), or a compact transposed (Cholesky) decomposition matrix (t_decomposition_compact_matrix) and a corresponding map of population indices (t_decomposition_compact_map), as per SpatialCorrelation class attributes.

carrying_capacity

Array (matrix) of carrying capacity values at each population cell (populations rows by time_steps columns when across time). Required input.

density_dependence

Density dependence can be "ceiling" (default), "logistic" (Ricker), or a user-defined function (optionally nested in a list with additional attributes) for adjusting transition rates: function(params), where params is a list passed to the function containing:

transition_array: 3D array of transition rates: stages by stages by populations.
fecundity_mask: Matrix of 0-1 to indicate which (proportions) of transition rates refer to fecundity.
fecundity_max: Maximum transition fecundity rate (in Leslie/Lefkovitch matrix).
carrying_capacity: Array of carrying capacity values for each population.
stage_abundance: Matrix of abundances for each stage (rows) and population (columns).
population_abundance: Array of summed population abundances for all stages.
density_abundance: Array of summed population abundances for stages affected by density.
growth_rate_max: Maximum growth rate value or array for populations.
occupied_indices: Array of indices for populations occupied at (current) time step.
calculate_multipliers: Function (function(growth_rates)) for finding multipliers (when stages > 1) to apply to affected transitions that result in target growth rates (dominant eigenvalues).
apply_multipliers: Function (function(transition_array, multipliers) for applying multipliers (when stages > 1) to the affected transition rates within a transition array (returns multiplied array).
simulator: SimulatorReference object with dynamically accessible attached and results lists.
optional attributes: Additional numeric attributes when density dependence is optionally nested in a list.

returns a transformed transition 3D array

growth_rate_max

Maximum growth rate (utilized by density dependence processes).

density_affects

Matrix of booleans or numeric (0-1) indicating the transition vital rates affected by density (default is all).

density_stages

Array of booleans or numeric (0,1) for each stage to indicate which stages are affected by density (default is all).

density_precision

Numeric precision of the calculated multipliers (used when stages > 1) applied to affected transition rates (default is 3 decimal places).

translocation

An optional user-defined function (optionally nested in a list with additional attributes) for applying translocation or spatio-temporal management (to abundances): function(params), where params is a list passed to the function containing:

replicates: Number of replicate simulation runs.
time_steps: Number of simulation time steps.
years_per_step: Number of years per time step.
populations: Number of populations.
stages: Number of lifecycle stages.
demographic_stochasticity: Boolean for optionally choosing demographic stochasticity for the transformation.
density_stages: Array of booleans or numeric (0,1) for each stage to indicate which stages are affected by density.
r: Simulation replicate.
tm: Simulation time step.
carrying_capacity: Array of carrying capacity values for each population at time step.
stage_abundance: Matrix of (current) abundance for each stage (rows) and population (columns) at time step.
occupied_indices: Array of indices for populations occupied at (current) time step.
simulator: SimulatorReference object with dynamically accessible attached and results lists.
additional attributes: Additional attributes when the transformation is optionally nested in a list.

returns a transformed stage abundance matrix (or a list with stage abundance and carrying capacity)

harvest

An optional user-defined function (optionally nested in a list with additional attributes) for applying harvesting (to abundances): function(params) as per translocation.

mortality

An optional user-defined function (optionally nested in a list with additional attributes) for applying mortality (to abundances): function(params) as per translocation.

dispersal

Either a matrix of dispersal rates between populations (source columns to target rows) or a list of data frames of non-zero dispersal rates and indices for constructing a compact dispersal matrix, and optional changing rates over time (as per class DispersalGenerator dispersal_data attribute). Alternatively a user-defined function (optionally nested in a list with additional attributes) may be used: function(params), where params is a list passed to the function containing:

replicates: Number of replicate simulation runs.
time_steps: Number of simulation time steps.
years_per_step: Number of years per time step.
populations: Number of populations.
demographic_stochasticity: Boolean for optionally choosing demographic stochasticity for the transformation.
density_stages: Array of booleans or numeric (0,1) for each stage to indicate which stages are affected by density.
dispersal_stages: Array of relative dispersal (0-1) for each stage to indicate the degree to which each stage participates in dispersal.
r: Simulation replicate.
tm: Simulation time step.
carrying_capacity: Array of carrying capacity values for each population at time step.
stage_abundance: Matrix of abundance for each stage (rows) and population (columns) at time step.
occupied_indices: Array of indices for populations occupied at time step.
simulator: SimulatorReference object with dynamically accessible attached and results lists.
additional attributes: Additional attributes when the transformation is optionally nested in a list.

returns the post-dispersal abundance matrix

dispersal_stages

Array of relative dispersal (0-1) for each stage to indicate the degree to which each stage participates in dispersal (default is 1 for all stages).

dispersal_source_n_k

Dispersal proportion (p) density dependence via source population abundance divided by carrying capacity (n/k), where p is reduced via a linear slope (defined by two list items) from n/k <= cutoff (p = 0) to n/k >= threshold (aliases: dispersal_n_k_cutoff & dispersal_n_k_threshold).

dispersal_target_k

Dispersal rate (r) density dependence via target population carrying capacity (k), where r is reduced via a linear slope (through the origin) when k <= threshold (alias: dispersal_k_threshold).

dispersal_target_n

Dispersal rate (r) density dependence via target population abundance (n), where r is reduced via a linear slope (defined by two list items) from n >= threshold to n <= cutoff (r = 0) or vice versa (aliases: dispersal_n_threshold & dispersal_n_cutoff).

dispersal_target_n_k

Dispersal rate (r) density dependence via target population abundance divided by carrying capacity (n/k), where r is reduced via a linear slope (defined by two list items) from n/k >= threshold to n/k <= cutoff (r = 0) or vica versa.

abundance_threshold

Abundance threshold (that needs to be exceeded) for each population to persist.

simulation_order

A vector of simulation process names in configured order of execution (default is "transition", "translocation", "harvest" (plus harvested results), "mortality", "dispersal", "results" (except harvested).

additional transformation functions

Additional user-defined abundance transformation functions (optionally nested in lists with additional attributes) are utilised when listed in simulation_order (function as per translocation).

results_selection

List of results selection from: "abundance" (default), "ema", "extirpation", "extinction_location", "harvested", "occupancy"; "summarize" (default) or "replicate".

result_stages

Array of booleans or numeric (0, 1, 2, ...) for each stage to indicate which stages are included/combined (each unique digit > 0; optionally named) in the results (default is 1 for all stages).

Value

Selected simulation results as a nested list summarized (mean, sd, min, max) across multiple replicates (default), or 2-3D arrays including results for each replicate:

abundance: Matrix or 3D array of simulation abundance: populations rows by time_steps columns (by replicates deep).
abundance_stages: List of matrices or 3D arrays of simulation abundance for unique stage combinations when present: each populations rows by time_steps columns (by replicates deep).
all$abundance: Array or matrix of total abundance across populations: time_steps (rows by replicates columns).
all$abundance_stages: List of arrays or matrices of total abundance across populations for unique stage combinations when present: each time_steps (rows by replicates columns).
all$ema: Array of expected minimum abundance at each time step (averaged across replicates).
extirpation: Array or matrix of extirpation times: populations (rows by replicates columns).
all$extirpation: Array of extirpation time across populations for each replicate.
all$extinction_location: The weighted centroid of cells occupied in the time-step prior to the extirpation of all populations (if it occurred) for each replicate.
harvested: Matrix or 3D array of individuals harvested: populations rows by time_steps columns (by replicates deep).
harvested_stages: List of matrices or 3D arrays of individuals harvested for unique stage combinations when present: each populations rows by time_steps columns (by replicates deep).
all$harvested: Array or matrix of individuals harvested across populations: time_steps (rows by replicates columns).
all$harvested_stages: List of arrays or matrices of individuals harvested across populations for unique stage combinations when present: each time_steps (rows by replicates columns).
all$occupancy: Array or matrix of the number of populations occupied at each time-step: time_steps (rows by replicates columns).
additional results: Additional results may be attached via user-defined functions (using params$simulator$results).

Examples

# U Island example region
coordinates <- data.frame(
  x = rep(seq(177.01, 177.05, 0.01), 5),
  y = rep(seq(-18.01, -18.05, -0.01), each = 5)
)
template_raster <- Region$new(coordinates = coordinates)$region_raster # full extent
template_raster[][-c(7, 9, 12, 14, 17:19)] <- NA # make U Island
region <- Region$new(template_raster = template_raster)
# Harvest function
harvest <- list(
  rate = 0.3,
  function(params) round(params$stage_abundance * (1 - params$rate))
)
# Population model
stage_matrix <- matrix(c(
  0, 2.5, # Leslie/Lefkovitch matrix
  0.8, 0.5
), nrow = 2, ncol = 2, byrow = TRUE)
pop_model <- PopulationModel$new(
  region = region,
  time_steps = 10, # years
  populations = region$region_cells, # 7
  stage_matrix = stage_matrix,
  initial_abundance = rep(10, 7),
  carrying_capacity = array(70:1, c(7, 10)),
  harvest = harvest,
  results_selection = c("abundance", "harvested")
)
# Simulations
population_simulator(pop_model) # model
#> $all
#> $all$abundance
#>  [1]  79  91 102 122 132 145 119  88  55  18
#> 
#> $all$harvested
#>  [1] 35 38 43 54 59 64 52 38 22 10
#> 
#> 
#> $abundance
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,]    9    9   14   15   18   24   17   14   10     5
#> [2,]    9   15   12   21   19   24   19   14    9     4
#> [3,]   12   12   10   14   16   23   18   13    8     3
#> [4,]   13   15   20   19   27   22   18   13    8     2
#> [5,]   13   19   24   29   26   22   16   12    8     2
#> [6,]   13   13   12   14   11   16   16   11    6     1
#> [7,]   10    8   10   10   15   14   15   11    6     1
#> 
#> $harvested
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,]    3    3    5    7    7   11    8    7    4     2
#> [2,]    4    6    5   10    9   10    8    6    4     2
#> [3,]    6    5    5    6    8   10    8    6    4     2
#> [4,]    6    6    9    9   12   10    7    5    3     2
#> [5,]    6    8   11   13   12    9    7    5    2     1
#> [6,]    5    6    4    5    5    7    7    5    3     1
#> [7,]    5    4    4    4    6    7    7    4    2     0
#> 
inputs <- pop_model$get_attributes()
population_simulator(inputs) # list
#> $all
#> $all$abundance
#>  [1]  85 117 123 126 126 131 110  84  56  20
#> 
#> $all$harvested
#>  [1] 36 48 53 55 55 54 48 34 21  8
#> 
#> 
#> $abundance
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,]   11   19   18   20   18   25   19   14   10     5
#> [2,]    9   12   12   13   14   10    7    9   10     4
#> [3,]   13   25   28   28   28   23   18   13    9     3
#> [4,]   14   16   17   17   13   22   17   13    8     3
#> [5,]   12   15   15   15   15   14   17   12    7     2
#> [6,]   12   15   15   12   18   16   16   12    6     2
#> [7,]   14   15   18   21   20   21   16   11    6     1
#> 
#> $harvested
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,]    5    7    8    9    7   10    9    7    4     2
#> [2,]    4    4    5    6    6    4    3    4    3     2
#> [3,]    6   10   12   13   12   10    8    5    3     2
#> [4,]    6    7    8    7    5   10    8    5    3     1
#> [5,]    5    6    6    6    7    5    7    5    3     1
#> [6,]    5    7    6    4    8    7    7    4    3     0
#> [7,]    5    7    8   10   10    8    6    4    2     0
#>