popdemo (version 0.1-2)

Keyfitz.delta: Calculate Keyfitz's delta

Description

Calculate Keyfitz's delta for a given population projection matrix (PPM) model.

Usage

Keyfitz.delta(A, vector)

Arguments

A

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

vector

a specified initial age/stage distribution of class vector or class matrix.

Value

• Keyfitz's delta.

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). Keyfitz.delta 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).

References

Keyfitz (1968) Introduction to the Mathematics of Populations. Addison-Wesley. Stott et al. (2010) Ecol. Lett., 14, 959-970.

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)
    A

    # Create an initial stage structure
    initial <- c(1,3,2)
    initial

    # Calculate Keyfitz's delta
    Keyfitz.delta(A, vector=initial)