# loop.elas: loop.elas In demogR: Analysis of Age-Structured Demographic Models

## Description

Calculate and plot loop elasticities for a demographic projection matrix .

## Usage

 ```1 2 3 4 5 6 7``` ```loop.elas(A, draw.plot = TRUE, peryear = 5, xlab = "Loop Elasticity", ylab = "Age", xlim = c(0, (maxe + 0.02)), ...) ```

## Arguments

 `A` demographic projection matrix `draw.plot` should a plot be drawn? default: `draw.plot=TRUE` `peryear` width of the age-class/projection interval `xlab` x-axis label; default `ylab="Age"` `ylab` y-axis label; default `ylab="Loop Elasticity"` `xlim` plotting limits for x-axis `...` arguments to be passed to/from other methods

## Details

Calculates and plots the life-cycle decomposition of van Groenendael et al (1994).

## Value

A vector of length k (the rank of the projection matrix A) giving the loop elasticities for each of the loops in the life-cycle graph.

## References

Van Groenendael, J., H. De Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. Ecology 75 (8):2410-2415.

`eigen.analysis`, `leslie.matrix`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```data(goodman) ven <- with(goodman, life.table(x=age, nKx=ven.nKx, nDx=ven.nDx)) ven.mx <- with(goodman, ven.bx/ven.nKx) A <- leslie.matrix(lx=ven\$nLx,mx=ven.mx) usa <- with(goodman, life.table(x=age, nKx=usa.nKx, nDx=usa.nDx)) usa.mx <- with(goodman, usa.bx/usa.nKx) B <- leslie.matrix(lx=usa\$nLx,mx=usa.mx) eav <- eigen.analysis(A) eau <- eigen.analysis(B) ## Compare the loop elasticities of Venezuela (1965) and the USA (1967) le.usa <- loop.elas(A) le.usa <- loop.elas(B) ```