popbio (version 2.8)

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

grizzly

Format

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

year

Year of census

N

Estimated number of female grizzlies

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)