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Nested functions for population density dependence.

Source: R/population_density.R
population_density.Rd

Modular functions for the population simulator for performing density dependent adjustments to transition rates.

Usage

population_density(
  populations,
  stage_matrix,
  fecundity_mask,
  fecundity_max,
  density_dependence,
  growth_rate_max,
  density_affects,
  density_stages,
  density_precision,
  simulator
)

Arguments

populations

Number of populations.

stage_matrix

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

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).

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 abundance 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 (when stages > 1) multipliers to the affected transition rates within a transition array (returns multiplied transition array).

simulator

SimulatorReference object with dynamically accessible attached and results lists.

additional attributes

Additional attributes when density dependence is optionally nested in a list.

returns an adjusted transition array for occupied populations

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).

simulator

SimulatorReference object with dynamically accessible attached and results lists.

Value

Density dependent calculation function, either:

function(carrying_capacity, stage_abundance)

For ceiling density dependence function, OR

function(transition_array, carrying_capacity, stage_abundance, occupied_indices)

For user-defined density dependence function, where:

transition_array

3D array of transition rates: stages by stages by populations.

carrying_capacity

Array of carrying capacity values for each population.

stage_abundance

Matrix of abundance for each stage (rows) and population (columns).

occupied_indices

Array of indices for populations occupied.

Examples

# Ceiling density dependence
stage_matrix <- array(c(0, 0.5, 0, 3, 0, 0.7, 4, 0, 0.8), c(3, 3))
fecundity_mask <- array(c(0, 0, 0, 1, 0, 0, 1, 0, 0), c(3, 3))
simulator <- SimulatorReference$new()
density_function <- population_density(
 populations = 7, stage_matrix = stage_matrix, fecundity_mask = fecundity_mask,
 fecundity_max = NULL, density_dependence = "ceiling",
 growth_rate_max = NULL, density_affects = NULL, density_stages = c(0, 1, 1),
 density_precision = NULL, simulator = simulator
)
carrying_capacity <- rep(10, 7)
stage_abundance <- matrix(c(
 7, 13, 0, 26, 0, 39, 47,
 2, 0, 6, 8, 0, 12, 13,
 0, 3, 4, 6, 0, 9, 10
), nrow = 3, ncol = 7, byrow = TRUE)

# Life cycle stages 2 and 3 (rows 2 and 3) all add up to 10 or less
density_function(carrying_capacity, stage_abundance)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    7   13    0   26    0   39   47
#> [2,]    2    0    6    6    0    6    6
#> [3,]    0    3    4    4    0    4    4