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iterate dynamic transition functions

Source: R/iterate_dynamic_function.R
iterate_dynamic_function.Rd

Calculate the stable population size for a stage-structured dynamical system, encoded by a transition function, the value of which changes at each iteration, given by function of the previous state: state[t] = f(state[t-1]).

Usage

iterate_dynamic_function(
  transition_function,
  initial_state,
  niter,
  tol,
  ...,
  parameter_is_time_varying = c(),
  state_limits = c(-Inf, Inf)
)

Arguments

transition_function

a function taking in the previous population state and the current iteration (and possibly other greta arrays) and returning the population state at the next iteration. The first two arguments must be named 'state' and 'iter', the state vector and scalar iteration number respectively. The remaining parameters must be named arguments representing (temporally static) model parameters. Variables and distributions cannot be defined inside the function.

initial_state

either a column vector (with m elements) or a 3D array (with dimensions n x m x 1) giving one or more initial states from which to iterate the matrix

niter

a positive integer giving the maximum number of times to iterate the matrix

tol

a scalar giving a numerical tolerance, below which the algorithm is determined to have converged to a stable population size in all stages

...

optional named arguments to matrix_function, giving greta arrays for additional parameters

parameter_is_time_varying

a character vector naming the parameters (ie. the named arguments of the function that are passed via ...) that should be considered to be time-varying. That is, at each iteration only the corresponding slice from the first dimension of the object passed in should be used at that iteration.

state_limits

a numeric vector of length 2 giving minimum and maximum values at which to clamp the values of state after each iteration to prevent numerical under/overflow; i.e. elements with values below the minimum (maximum) will be set to the minimum (maximum).

Value

a named list with four greta arrays:

  • stable_population a vector or matrix (with the same dimensions as initial_state) giving the state after the final iteration.

  • all_states an n x m x niter matrix of the state values at each iteration. This will be 0 for all entries after iterations.

  • converged an integer scalar indicating whether all the matrix iterations converged to a tolerance less than tol (1 if so, 0 if not) before the algorithm finished.

  • iterations a scalar of the maximum number of iterations completed before the algorithm terminated. This should match niter if converged is FALSE

Details

Like iterate_dynamic_matrix this converges to absolute population sizes. The convergence criterion is therefore based on growth rates converging on 0.

The greta array returned by transition_function must have the same dimension as the state input and initial_state should be shaped accordingly, as detailed in iterate_matrix.

To ensure the matrix is iterated for a specific number of iterations, you can set that number as niter, and set tol to 0 or a negative number to ensure that the iterations are not stopped early.

Note

because greta vectorises across both MCMC chains and the calculation of greta array values, the algorithm is run until all chains (or posterior samples), sites and stages have converged to stable growth. So a single value of both converged and iterations is returned, and the value of this will always have the same value in an mcmc.list object. So inspecting the MCMC trace of these parameters will only tell you whether the iteration converged in all posterior samples, and the maximum number of iterations required to do so across all these samples

Examples

if (FALSE) { # \dontrun{
# density-dependent (logistic) growth towards a carrying capacity of 100,
# for two independent populations
transition_function <- function(state, iter) {
  state + 0.2 * state * (1 - state / 100)
}

initial_state <- as_data(matrix(c(2, 30), nrow = 2, ncol = 1))

results <- iterate_dynamic_function(
  transition_function = transition_function,
  initial_state = initial_state,
  niter = 100,
  tol = 1e-6
)

# both populations converge on the carrying capacity
calculate(results$stable_population, results$converged, results$iterations)
} # }