pop.projection: Calculate population growth rates by projection

In popbio: Construction and Analysis of Matrix Population Models

Calculate population growth rates by projection

Description

Calculates the population growth rate and stable stage distribution by repeated projections of the equation n(t+1)=An(t)

Usage

pop.projection(A, n, iterations = 20)

Arguments

A	A projection matrix
n	An initial age or stage vector
iterations	Number of iterations

Details

Eventually, structured populations will convergence to a stable stage distribution where each new stage vector is changing by the same proportion (lambda).

Value

A list with 5 items

lambda	Estimate of lambda using change between the last two population counts
stable.stage	Estimate of stable stage distribution using proportions in last stage vector
stage.vector	A matrix with the number of projected individuals in each stage class
pop.sizes	Total number of projected individuals
pop.changes	Proportional change in population size

Author(s)

Chris Stubben

References

see section 2.2 in Caswell 2001

See Also

stage.vector.plot to plot stage vectors

Examples

## mean matrix from Freville et al 2004
stages <- c("seedling", "vegetative", "flowering")
A <- matrix(c(
    0,     0,  5.905,
0.368, 0.639,  0.025,
0.001, 0.152,  0.051
), nrow=3, byrow=TRUE,
    dimnames=list(stages,stages))
n <- c(5,5,5)
p <- pop.projection(A,n, 15)
p
damping.ratio(A)
stage.vector.plot(p$stage.vectors, col=2:4)
A <- whale
#n <- c(4,38,36,22)
n <- c(5,5,5,5)
p <- pop.projection(A,n, 15)
p
stage.vector.plot(p$stage.vectors, col=2:4, ylim=c(0, 0.6))
## convergence is slow with damping ratio close to 1
damping.ratio(A)
pop.projection(A, n, 100)$pop.changes

popbio documentation built on May 29, 2024, 4:35 a.m.