project.leslie {demogR}

project.leslie

Description

Projects an population vector tmax intervals by pre-multiplication with a Leslie matrix.

Usage

project.leslie(A, no, tmax, pop.sum = FALSE)

Arguments

A

a k x k projection matrix

no

a k x 1 population vector

tmax

number of time steps to project the vector

pop.sum

logical; If 'TRUE', the age-classes of the projected population are summed, yielding a single total population vector

Details

Takes an initial population vector, no, and pre-multiplies by the demographic projection matrix, A, tmax times. This projection will be tmax*n years into the future, where n is the width of the age-classes in the Leslie matrix, A.

Value

If pop.sum=FALSE (the default), the value will be a k x tmax+1 matrix. The first column of the matrix is no and each subsequent column represents the population structure at time step 1, 2, ..., tmax.

If pop.sum=TRUE, the value will be a vector of length tmax+1, where each element of the vector is the total population at time t=0, 1, ..., tmax.

See Also

leslie.matrix, eigen.analysis

Examples

data(goodman)
ult <- with(goodman, life.table(x=age, nKx=usa.nKx, nDx=usa.nDx))
mx <- goodman$usa.bx/goodman$usa.nKx
usa <- leslie.matrix(lx=ult$nLx,mx=mx)

## initial population is the age structure in 1967
## this includes the number of 0-1 year-olds and the number of 1-4
## year-olds, which need to be combined into a single 5-year wide
## element 

no <- goodman$usa.nKx[3:11]
no <- c(sum(goodman$usa.nKx[1:2]),no)/1e6

N <- project.leslie(usa,no,tmax=20)
plot( seq(1967,2067,by=5), apply(N,2,sum), 
         type="l", 
	 xlab="Years", 
	 ylab="Projected Population (millions)")
title("Projected Total Population Size (Ages 0-45) of the United States")

##   Note that this is a lousy projection since it assumes constant
##   demographic rates and a closed population and only accounts for
##   ages 0-45