pop.projection {popbio} | R Documentation |
Calculates the population growth rate and stable stage distribution by repeated projections of the equation n(t+1)=An(t)
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pop.projection(A,n,iterations=20)
A |
A projection matrix |
n |
An initial age or stage vector |
iterations |
Number of iterations |
Eventually, structured populations will convergence to a stable stage distribution where each new stage vector is changing by the same proportion (lambda).
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 |
Chris Stubben
see section 2.2 in Caswell 2001
stage.vector.plot
to plot stage vectors
## 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 eigen.analysis(A)$damping.ratio stage.vector.plot(p$stage.vectors, col=2:4) #### data(whale) A<-whale$T+whale$F #n<-c(4,38,36,22) n<-c(5,5,5,5) p<-pop.projection(A,n, 15) p stage.vector.plot(p$stage.vectors, col=2:4, ylim=c(0, 0.6)) ## convergence is slow with damping ratio close to 1 eigen.analysis(A)$damping.ratio pop.projection(A,n, 100)$pop.changes