grizzly: Population sizes of grizzly bears in Yellowstone from...

In popbio: Construction and Analysis of Matrix Population Models

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)

Example output

   year  N
1  1959 44
2  1960 47
3  1961 46
4  1962 44
5  1963 46
6  1964 45
7  1965 46
8  1966 40
9  1967 39
10 1968 39
11 1969 42
12 1970 39
13 1971 41
14 1972 40
15 1973 33
16 1974 36
17 1975 34
18 1976 39
19 1977 35
20 1978 34
21 1979 38
22 1980 36
23 1981 37
24 1982 41
25 1983 39
26 1984 51
27 1985 47
28 1986 57
29 1987 48
30 1988 60
31 1989 65
32 1990 74
33 1991 69
34 1992 65
35 1993 57
36 1994 70
37 1995 81
38 1996 99
39 1997 99
      mean        var 
0.02134027 0.01305092 

Call:
lm(formula = y ~ 0 + x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.21371 -0.07773 -0.02134  0.07740  0.24692 

Coefficients:
  Estimate Std. Error t value Pr(>|t|)
x  0.02134    0.01853   1.152    0.257

Residual standard error: 0.1142 on 37 degrees of freedom
Multiple R-squared:  0.0346,	Adjusted R-squared:  0.008506 
F-statistic: 1.326 on 1 and 37 DF,  p-value: 0.2569

    mean.x        var 
0.02134027 0.01305092 
        2.5 %     97.5 %
x -0.01620969 0.05889023
[1] 0.008674359 0.021844393
       25 
0.3807524 
[1] 0.04120517

popbio documentation built on March 26, 2020, 8:44 p.m.