popbio (version 2.7)

vitalsens: Vital rate sensitivities and elasticities

Description

Calculates deterministic sensitivities and elasticities of lambda to lower-level vital rates using partial derivatives

Usage

vitalsens(elements, vitalrates)

Value

A dataframe with vital rate estimates, sensitivities, and elasticities

Arguments

elements

An object of mode expression with all matrix elements represented by zeros or symbolic vital rates

vitalrates

A list of vital rates with names matching expressions in elements above

Author

Chris Stubben. Based on code posted by Simon Blomberg to R-help mailing list

Details

Vital rate sensitivities and elasticities are discussed in example 9.3 and 9.6 in Caswell (2001). Also see Chapter 9 and Box 9.1 for Matlab code in Morris and Doak (2002).

References

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

Morris, W. F., and D. F. Doak. 2002. Quantitative conservation biology: Theory and practice of population viability analysis. Sinauer, Sunderland, Massachusetts, USA.

Examples

## emperor goose in Morris and Doak 2002.
goose.vr <- list( Ss0=0.1357,  Ss1=0.8926,  Sf2=0.6388,  Sf3= 0.8943)
goose.el <- expression(
0,  0,  Sf2*Ss1,Sf3*Ss1,
Ss0,0,  0,      0,
0,  Ss1,0,      0,
0,  0,  Ss1,    Ss1)
## first plot effects of changing vital rates -- Figure 9.1
n <- length(goose.vr)
vr <- seq(0,1,.1)
vrsen <- matrix(numeric(n*length(vr)), ncol=n, dimnames=list(vr, names(goose.vr)))
for (h in 1:n) {
   goose.vr2 <- list(  Ss0=0.1357,  Ss1=0.8926,  Sf2=0.6388,  Sf3= 0.8943)
   for (i in 1:length(vr))
   {
      goose.vr2[[h]] <- vr[i]
      A <- matrix(sapply(goose.el, eval,goose.vr2 , NULL), nrow=sqrt(length(goose.el)), byrow=TRUE)
      vrsen[i,h] <- max(Re(eigen(A)$values))
   }
}
matplot(rownames(vrsen), vrsen, type='l', lwd=2, las=1,
ylab="Goose population growth", xlab="Value of vital rate",
main="Effects of changing goose vital rates")
vrn <- expression(s[0], s["">=1], f[2], f["">=3])
legend(.8, .4, vrn, lty=1:4, lwd=2, col=1:4, cex=1.2)
## then calculate sensitivities  -- Table 9.1
x <- vitalsens(goose.el, goose.vr)
x
sum(x$elasticity)
barplot(t(x[,2:3]), beside=TRUE, legend=TRUE, las=1, xlab="Vital rate",
main="Goose vital rate sensitivity and elasticity")
abline(h=0)
## Table 7 endangered lesser kestral in Hiraldo et al 1996
kest.vr <-  list(b = 0.9321, co = 0.3847, ca = 0.925, so = 0.3409, sa = 0.7107)
kest.el <- expression( co*b*so, ca*b*so, sa, sa)
x <- vitalsens(kest.el, kest.vr)
x
sum(x$elasticity)
barplot(t(x[,2:3]), beside=TRUE, las=1, xlab="Vital rate",
main="Kestral vital rate sensitivity and elasticity")
legend(1,1, rownames(t(x[,2:3])), fill=grey.colors(2))
abline(h=0)