popbio (version 1.0.1)

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)

Arguments

A

A projection matrix

n

An initial age or stage vector

iterations

Number of iterations

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

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

stages<-c("seedling", "vegetative", "flowering")
A<-matrix(c(
0,    0,    6,
0.4,  0.6,  0.02,
0.01, 0.2,  0.25
), nrow=3, byrow=TRUE, 
    dimnames=list(stages,stages) 
)

n<-c(25,25,25)
pop.projection(A,n, 15)

eigen.analysis(A)$damping.ratio
pop.projection(A,n, 50)$pop.changes



data(whale)
A<-whale$T+whale$F
n<-c(4,38,36,22)

## convergence is slow with damping ratio close to 1
pop.projection(A,n, 10)

eigen.analysis(A)$damping.ratio

pop.projection(A,n, 250)$pop.changes