popbio (version 2.7)

extCDF: Count-based extinction time cumulative distribution function

Description

Returns the extinction time cumulative distribution function using parameters derived from population counts.

Usage

extCDF(mu, sig2, Nc, Ne, tmax = 50)

Value

A vector with the cumulative probabilities of quasi-extinction from t=0 to t=tmax.

Arguments

mu

estimated value of mean mu

sig2

estimated value of sample variance

Nc

current population size

Ne

quasi-extinction threshold

tmax

latest time to calculate extinction probability, default 50

Author

Chris Stubben

Details

converted Matlab code from Box 3.3 and equation 3.5 in Morris and Doak 2002

References

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

See Also

countCDFxt for bootstrap confidence intervals

Examples

logN <- log(grizzly$N[-1]/grizzly$N[-39])
mu <- mean(logN)
sig2 <- var(logN)
## grizzly cdf (log scale)
ex <- extCDF(mu, sig2, Nc=99, Ne=20)
plot(ex, log='y', type='l', pch=16, col="blue", yaxt='n',
xlab="Years", ylab="Quasi-extinction probability",
main="Yellowstone Grizzly bears")
pwrs <- seq(-15,-5,5)
axis(2, at = 10^pwrs, labels=parse(text=paste("10^", pwrs, sep = "")), las=1)
##plot like fig 3.10  (p 90)
n <- seq(20, 100, 2)
exts <- numeric(length(n))
for (i in 1:length(n) ){
   ex <- extCDF(mu, sig2, Nc=n[i], Ne=20)
   exts[i] <- ex[50]
}
plot(n, exts, type='l', las=1,
xlab="Current population size",
ylab="Probability of quasi-extinction by year 50")