perturb_matrix {Rage}

Perturbation analysis of a matrix population model

Description

Perturbs elements 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.

Usage

perturb_matrix(
  matA,
  pert = 1e-06,
  type = "sensitivity",
  demog_stat = "lambda",
  ...
)

Arguments

matA

A matrix population model (i.e., a square projection matrix).

pert

Magnitude of the perturbation. Defaults to 1e-6.

type

Whether to return sensitivity or elasticity values.

demog_stat

The demographic statistic to be used, as in "the sensitivity/elasticity of demog_stat to matrix element 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 sensitivity or elasticity matrix.

Author(s)

Rob Salguero-Gomez <[e-mail]>

References

Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Sinauer Associates; 2nd edition. ISBN: 978-0878930968

See Also

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

Examples

matA <- rbind(
  c(0.1, 0, 1.5, 4.6),
  c(0.5, 0.2, 0.1, 0),
  c(0, 0.3, 0.3, 0.1),
  c(0, 0, 0.5, 0.6)
)

perturb_matrix(matA)

# use a larger perturbation than the default
perturb_matrix(matA, pert = 0.01)

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

perturb_matrix(matA, demog_stat = "damping")