grizzly {popbio}

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

grizzly

Format

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

year

Year of census

N

Estimated number of female grizzlies

Source

Table 3.1 in Morris and Doak 2002. Original data from Eberhardt et al. 1986 and Haroldson 1999.

References

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

Examples

grizzly
## plot like Fig 3.6 (p. 66)
plot(grizzly$year, grizzly$N,
  type = "o", pch = 16, las = 1, xlab = "Year",
  ylab = "Adult females", main = "Yellowstone grizzly bears"
)
## calcualte  log(Nt+1/Nt)
nt <- length(grizzly$N) ## number transitions
logN <- log(grizzly$N[-1] / grizzly$N[-nt])
## Mean and var
c(mean = mean(logN), var = var(logN))
## or using linear regression
## transformation for unequal variances (p. 68)
x <- sqrt(grizzly$year[-1] - grizzly$year[-length(grizzly$year)])
y <- logN / x
mod <- lm(y ~ 0 + x)
summary(mod)
## plot like Fig 3.7
plot(x, y,
  xlim = c(0, 1.2), ylim = c(-.3, .3), pch = 16, las = 1,
  xlab = expression(paste("Sqrt time between censuses ", (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(grizzly$N[-nt], logN,
  pch = 16, xlim = c(20, 100), ylim = c(-.3, .3), las = 1,
  xlab = "Number of females in year T",
  ylab = expression(log(N[t + 1] / N[t])),
  main = "Grizzly log population growth rates"
)
cor(grizzly$N[-nt], logN)
abline(lm(logN ~ grizzly$N[-nt]), lty = 3)