popdemo (version 1.3-1)

eigs: Calculate asymptotic growth

Description

Dominant eigenstuff of a population matrix projection model.

Usage

eigs(A, what = "all", check = TRUE)

Arguments

A

a square, nonnegative numeric matrix of any dimension.

what

what components of the dominant eigenstuff should be returned. A character vector, which may include:

"lambda"

the dominant eigenvalue (lambda)

"ss"

the dominant right eigenvector (stable stage)

"rv"

the dominant left eigenvector (reproductive value)

the default, "all", returns all of the above.

check

(logical) determines whether the dominant eigenvalue is checked for nonzero imaginary component, and largest absolute value. If either of these occur, then the dominant eigenvalue may not be described as truly dominant.

Value

A list with possible components that depends on the contents of what:

lambda

the dominant eigenvalue, which describes asymptotic population growth (if A is primitive; see isPrimitive). A real, nonnegative numeric vector of length 1.

ss

the dominant right eigenvector, which describes the stable age/stage structure (if A is primitive; see isPrimitive). A real, nonnegative numeric vector equal to the dimension of A in length, scaled to sum to 1.

rv

the dominant left eigenvector, which describes the reproductive value (if A is primitive; see isPrimitive). A real, nonnegative numeric vector equal to the dimension of A in length, scaled so that rv

If only one of these components is returned, then the value is not a list, but a single numeric vector.

Details

eigs gives the dominant eigenstuff of a population projection model. This includes the dominant eigenvalue (asymptotic population growth), the dominant right eigenvector (stable age/stage distribution), and the dominant left eigenvector (reproductive value). The dominant eigenvalue is the eigenvalue with the largest real component, and the dominant eigenvectors are the eigenvectors that correspond to this eigenvalue. If the matrix is reducible, then there may be other real or complex eigenvalues whose absolute value are equal in magnitude to that of the dominant eigenvalue. In this case, eigs returns the first one, and gives a warning "More than one eigenvalues have equal absolute magnitude", for information.

Examples

# NOT RUN {
  # load the desert tortoise data
  data(Tort)
  
  # find the dominant eigenvalue
  eigs(Tort, "lambda")
  
  #find the stable stage structure
  eigs(Tort, "ss")
  
  #find the reproductive value
  eigs(Tort, "rv")
  
  #find both dominant eigenvectors
  eigs(Tort, c("ss","rv"))
  
  #find all eigenstuff
  eigs(Tort)

# }