eigen.analysis {popbio}R Documentation

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

Details

The calculation of eigenvalues and eignvectors in Matlab is listed in section 4.8.1 (p. 107) in Caswell (2001). In addition, the damping ratio is described in section 4.7.1, sensitivities in section 9.1, and elasticities in section 9.2

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

Note

If matrix A is singular, then eigen.analysis will return elasticities, sensitivities, and reproductive values with NAs

Author(s)

Original code by James Holland Jones, Stanford University, Department of Anthropological Sciences, 12 August 2005 at http://popstudies.stanford.edu/summer_course/

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()


[Package popbio version 1.1.2 Index]