KeyfitzD {popdemo}

Calculate Keyfitz's delta

Description

Calculate Keyfitz's delta for a population matrix projection model.

Usage

KeyfitzD(A, vector)

Arguments

A

a square, irreducible, non-negative numeric matrix of any dimension.

vector

a numeric vector or one-column matrix describing the age/stage distribution used to calculate the distance.

Details

Keyfitz's delta is the sum of the differences between the stable demographic vector (the dominant right eigenvector of A) and the demographic distribution vector of the population (given by vector). KeyfitzD will not work for reducible matrices and returns a warning for imprimitive matrices (although will not function for imprimitive matrices with nonzero imaginary components in the dominant eigenpair).

Value

Keyfitz's delta.

References

• Keyfitz (1968) Introduction to the Mathematics of Populations. Addison-Wesley.

• Stott et al. (2010) Ecol. Lett., 14, 959-970.

See Also

Other DistanceMeasures: CohenD(), projectionD()

Examples

  # Create a 3x3 PPM
  ( A <- matrix(c(0,1,2,0.5,0.1,0,0,0.6,0.6), byrow=TRUE, ncol=3) )

  # Create an initial stage structure
  ( initial <- c(1,3,2) )
  
  # Calculate Keyfitz's delta
  KeyfitzD(A, vector=initial)