popbio (version 2.7)

pop.projection: 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)

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

Arguments

A

A projection matrix

n

An initial age or stage vector

iterations

Number of iterations

Author

Chris Stubben

Details

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

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