popdemo (version 1.3-3)

stoch: Project population dynamics

Description

Analyse long-term dynamics of a stochastic population matrix projection model.

Usage

stoch(
  A,
  what = "all",
  Aseq = "unif",
  vector = NULL,
  Astart = NULL,
  iterations = 10000,
  discard = 1000,
  PREcheck = FALSE
)

Value

A numeric vector with three possible elements: "lambda" (the geometric mean stochastic population growth rate) "log_lambda" (the arithmetic mean of the logarithm of the stochastic population growth rate) and "var" (the variance of the logarithm of the stochastic population growth rate). Values returned depend on what's passed to what.

Arguments

A

a list of matrices. stoch uses project to perform a stochastic' projection where the matrix varies with each timestep. The sequence of matrices is determined using Aseq. Matrices must be square, non-negative and numeric, and all matrices must have the same dimension.

what

Deprecated: later versions will always return all values of growth, log growth and variance in growth. This argument determines what should be returned. A character vector with possible entries "lambda" (to calcualate stochastic growth), "log_lambda" (to calcualate logarithm of stochastic growth), "var" (to calculate variance in log stochastic growth) and/or "all" (to calculate all values).

Aseq

the sequence of matrices in a stochastic projection. Aseq may be either:

• "unif" (default), which results in every matrix in A having an equal, random chance of being chosen at each timestep.

• a square, nonnegative left-stochastic matrix describing a first-order markov chain used to choose the matrices. This should have the same dimension as the number of matrices in A.

• a numeric vector giving a specific sequence which corresponds to the matrices in A.

• a character vector giving a specific sequence which corresponds to the names of the matrices in A.

vector

(optional) a numeric vector describing the age/stage distribution used to calculate the projection. If vector is not specified, a random vector is generated. Long-term stochastic dynamics should usually be the same for any vector, although if all the matrices in A are reducible (see isIrreducible), that may not be the case.

Astart

(optional) in a stochastic projection, the matrix with which to initialise the projection (either numeric, corresponding to the matrices in A, or character, corresponding to the names of matrices in A). When Astart = NULL, a random initial matrix is chosen.

iterations

the number of projection intervals. The default is 1e+5.

discard

the number of initial projection intervals to discard, to discount near-term effects arising from the choice of vector. The default is 1e+3

PREcheck

many functions in popdemo first check Primitivity, Reducibility and/or Ergodicity of matrices, with associated warnings and/or errors if a matrix breaks any assumptions. Set PREcheck=FALSE if you want to bypass these checks.

Details

Calculates stochastic growth and its variance for a given stochastic population matrix projection model.

Examples

  # load the Polar bear data
  ( data(Pbear) )

  # Find the stochastic info for a time series with uniform probability of each
  # matrix
  ( all_unif <- stoch(Pbear, what = "all", Aseq = "unif") )

  # Find the stochastic growth for a time series with uniform probability of each
  # matrix
  ( lambda_unif <- stoch(Pbear, what = "lambda", Aseq = "unif") )

  # Find the variance in stochastic growth for a time series with uniform 
  # probability of each matrix
  ( var_unif <- stoch(Pbear, what = "var", Aseq = "unif") )
                 
  # Find stochastic growth and its variance for a time series with a sequence of
  # matrices where "bad" years happen with probability q
  q <- 0.5
  prob_seq <- c(rep(1-q,3)/3, rep(q,2)/2)
  Pbear_seq <- matrix(rep(prob_seq,5), 5, 5)
  ( all_q <- stoch(Pbear, what = "all", Aseq = Pbear_seq) )