popbio (version 2.8)

elasticity: Elasticity analysis of a projection matrix

Description

Calculate the elasticities of eigenvalues to changes in the projection matrix elements

Usage

elasticity(A)

Value

An elasticity matrix

Arguments

A

A projection matrix

Author

Chris Stubben

Details

see section 9.2 in Caswell (2001)

References

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

See Also

sensitivity

Examples

elas <- elasticity(teasel)
image2(elas, mar=c(1,3.5,5,1) )
 title("Teasel elasticity matrix", line=2.5)
# Summed elasticities for teasel.
# fertility in last column, stasis P on diagonal, and growth in bottom-left triangle
c(F=sum(elas[,6]), P=sum(diag(elas)), G=sum(elas[row(elas)>col(elas)]))

elas <- elasticity(tortoise[["med.high"]])
image2(elas, mar=c(1,3.5,5,1),  log=FALSE)
 title("Tortoise elasticity matrix", line=2.5)
# Summed elasticities for tortoise (see example 9.4)
# fertility in top row, stasis on diagonal, and growth on subdiagonal
c(F=sum(elas[1,]), P=sum(diag(elas)), G=sum(elas[row(elas)==col(elas)+1]))