perturb_vr: Perturbation analysis of vital rates in a matrix population...

In Rage: Life History Metrics from Matrix Population Models

Perturbation analysis of vital rates in a matrix population model

Description

Perturbs lower-level vital rates within a matrix population model and measures the response (sensitivity or elasticity) of the per-capita population growth rate at equilibrium (\lambda), or, with a user-supplied function, any other demographic statistic.

These decompositions assume that all transition rates are products of a stage-specific survival term (column sums of matU) and a lower level vital rate that is conditional on survival (growth, shrinkage, stasis, dormancy, or reproduction). Reproductive vital rates that are not conditional on survival (i.e., within a stage class from which there is no survival) are also allowed.

Usage

perturb_vr(
  matU,
  matF,
  matC = NULL,
  pert = 1e-06,
  type = "sensitivity",
  demog_stat = "lambda",
  ...
)

Arguments

matU	The survival component of a matrix population model (i.e., a square projection matrix reflecting survival-related transitions; e.g., progression, stasis, and retrogression).
matF	The sexual component of a matrix population model (i.e., a square projection matrix reflecting transitions due to sexual reproduction).
matC	The clonal component of a matrix population model (i.e., a square projection matrix reflecting transitions due to clonal reproduction). Defaults to NULL, indicating no clonal reproduction (i.e., matC is a matrix of zeros).
pert	Magnitude of the perturbation. Defaults to 1e-6.
type	Whether to return sensitivity or elasticity values. Defaults to sensitivity.
demog_stat	The demographic statistic to be used, as in "the sensitivity/elasticity of demog_stat to vital rate perturbations." Defaults to the per-capita population growth rate at equilibrium (\lambda). Also accepts a user-supplied function that performs a calculation on a projection matrix and returns a single numeric value.
...	Additional arguments passed to the function demog_stat.

Value

A list with 5 elements:

survival	sensitivity or elasticity of demog_stat to survival
growth	sensitivity or elasticity of demog_stat to growth
shrinkage	sensitivity or elasticity of demog_stat to shrinkage
fecundity	sensitivity or elasticity of demog_stat to sexual fecundity
clonality	sensitivity or elasticity of demog_stat to clonality

Author(s)

Rob Salguero-Gomez <[e-mail]>

Patrick Barks <[e-mail]>

See Also

Other perturbation analysis: perturb_matrix(), perturb_stochastic(), perturb_trans(), pop_vectors()

Examples

matU <- rbind(
  c(0.1, 0, 0, 0),
  c(0.5, 0.2, 0.1, 0),
  c(0, 0.3, 0.3, 0.1),
  c(0, 0, 0.5, 0.6)
)

matF <- rbind(
  c(0, 0, 1.1, 1.6),
  c(0, 0, 0.8, 0.4),
  c(0, 0, 0, 0),
  c(0, 0, 0, 0)
)

perturb_vr(matU, matF)

# use elasticities rather than sensitivities
perturb_vr(matU, matF, type = "elasticity")

# use a larger perturbation than the default
perturb_vr(matU, matF, pert = 0.01)

# calculate the sensitivity/elasticity of the damping ratio to vital rate
#  perturbations
damping <- function(matA) { # define function for damping ratio
  eig <- eigen(matA)$values
  dm <- rle(Mod(eig))$values
  return(dm[1] / dm[2])
}

perturb_vr(matU, matF, demog_stat = "damping")

Rage documentation built on Sept. 30, 2023, 1:06 a.m.