popbio (version 1.0.1)

eigen.analysis: Eigenvalue and eigenvector analysis of a projection matrix

Description

Calculate population growth rate and other demographic parameters from a projection matrix model using matrix algebra

Usage

eigen.analysis(A, zero=TRUE)

Arguments

A

a projection matrix

zero

Set sensitivities for unobserved transitions to zero

Value

• A list with 6 items
• lambda
  dominant eigenvalue
• stable.stage
  proportional stable stage distribution
• sensitivities
  matrix of eigenvalue sensitivities
• elasticities
  matrix of eigenvalue elasticities
• repro.value
  reproductive value scaled so v[1]=1
• damping.ratio
  dominant eigenvalue divided by second largest eigenvalue

References

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.

See Also

projection.matrix to construct matrix model

Examples

data(whale)
whaleA<-whale$T+whale$F

a<-eigen.analysis(whaleA)

a

ymax<-max(a$repro.value)*1.25
barplot(a$repro.value, col="blue", ylim=c(0,  ymax ), xpd=FALSE, 
       ylab="Reproductive value", xlab="Killer whale stage class")
box()

## display sensitititivies of "impossible" transitions 
## (postreprod -> juvenile, yearling -> mature, etc)
eigen.analysis(whaleA, zero=FALSE)$sensitivities

data(teasel)
teaselA<-teasel$T + teasel$F


a<-eigen.analysis(teaselA)
a
barplot(a$stable.stage, col="green", ylim=c(0,1), 
       ylab="Stable stage proportion", xlab="Teasel stage class")
box()