popbio (version 2.4.4)

grizzly: Population sizes of grizzly bears in Yellowstone from 1959-1997

Description

Estimated number of adult female grizzly bears in the Greater Yellowstone population from 1959-1997.

Usage

data(grizzly)

Format

A data frame with 39 observations on the following 2 variables.

year

Year of census

N

Estimated number of female grizzlies

Details

The grizzly bear data set is used in count based PVAs in chapter 3 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

# NOT RUN {
data(grizzly)
attach(grizzly)
## plot like Fig 3.6 (p. 66)
plot(year, N, type='o', pch=16, las=1, xlab="Year", 
ylab="Adult females", main="Yellowstone grizzly bears")
## calcualte  log(Nt+1/Nt)
nt<-length(N)  ## number transitions
logN<-log(N[-1]/N[-nt])
## Mean and var
c(mean=mean(logN), var=var(logN))
## or using linear regression
## transformation for unequal variances (p. 68)
x<-sqrt(year[-1]-year[-length(year)])
y<-logN/x
mod<-lm(y~0 + x )
## plot like Fig 3.7
plot(x,y, xlim=c(0,1.2), ylim=c(-.3,.3), pch=16, las=1,
xlab=expression((t[t+1]-t[i])^{1/2}),
ylab=expression(log(N[t+1]/N[t]) / (t[t+1]-t[i])^{1/2}) ,
main=expression(paste("Estimating ", mu, " and ", sigma^2, " using regression")))
abline(mod)
## MEAN (slope)
mu<- coef(mod)
## VAR (mean square in analysis of variance table)
sig2<-anova(mod)[["Mean Sq"]][2] 
c(mean= mu , var= sig2)
## Confidence interval for mean  (page 72)
confint(mod,1)
## Confidence interval for sigma 2  (equation 3.13)
df1<-length(logN)-1
df1*sig2 /qchisq(c(.975, .025), df= df1)
## test for outliers using dffits (p.74)
dffits(mod)[dffits(mod)> 2*sqrt(1/38) ]
## plot like  fig 3.11
plot(N[-nt], logN, pch=16, xlim=c(20,100), ylim=c(-.3, .3),las=1,
xlab="Number of females in year T",
ylab=expression(log(N[t+1]/N[t])),
main="Grizzly log population growth rates")
cor(N[-nt], logN) 
abline(lm(logN ~ N[-nt]), lty=3 )
detach(grizzly)

# }