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.

Examples

Run this code

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")

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