popbio (version 2.4.4)

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)

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.

Value

A dataframe with vital rate estimates, sensitivities, and elasticities.

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. 2nd ed. Sinauer, Sunderland, Massachusetts.

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

Examples

# NOT RUN {
## 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)

# }