# damping.ratio: Damping ratio In popbio: Construction and Analysis of Matrix Population Models

## Description

Calculates the damping ratio of a projection matrix

## Usage

 `1` ```damping.ratio(A) ```

## Arguments

 `A` A projection matrix

## Details

see section 4.7 in Caswell (2001).

Damping ratio

## Note

The damping ratio is calculated by dividing the dominant eigenvalue by the eigenvalue with the second largest magnitude.

Chris Stubben

## References

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

`lambda`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## whale converges slowly to stable stage distribution data(whale) matplot2(pop.projection(whale, c(1,1,1,1), 60)\$stage.vectors, prop=TRUE, legend=NA, main=paste("whale damping ratio = ", round(damping.ratio(whale),3) ) ) # Calathea - compare to Table 12 in Horvitz and Schemske (1995) data(calathea) x<-sapply(calathea[-17], damping.ratio) x<-matrix(x, nrow=4, byrow=TRUE, dimnames= list(paste("plot", 1:4), 1982:1985)) x matplot2(x, type='b', ylab="Damping ratio", main="Calathea") ```