extCDF: Count-based extinction time cumulative distribution function
In popbio: Construction and Analysis of Matrix Population Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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

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

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

Chris Stubben

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

countCDFxt for bootstrap confidence intervals

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")