untitled

CONSERVATION IN THEORY 301

50

45

40

35

30

Year

Number of female grizzlies

1960 1965 1970 1975 1980

Fig. 17.2Population
dynamics over time of
female grizzly bears in
Yellowstone National
Park during 1959–82.
(After Eberhardt et al.
1986.)

50

40

30

20

10

0 20 40 60 80 100

Time

Number of female grizzlies

Fig. 17.3Simulated
dynamics of a grizzly
bear population with
mean and variance in
population growth rate
similar to that of the
Yellowstone population
during 1959–82 and
starting with the
population size recorded
in 1982. Note that the
simulated population
has just reached the
critical “quasi-
extinction” threshold of
10 animals in year 97.

in Yellowstone. The average exponential rate of population change (r) recorded over

this period was −0.00086, with a standard deviation of 0.08. Since rwas negative

there was cause for concern because if it was negative for long enough there would

be extinction.

One can use these demographic data, simple as they are, to set up a simple stochas-

tic simulation of the population dynamics of Yellowstone grizzlies, following the Monte

Carlo approach outlined in Chapter 8:

Nt+ 1 =Nteμ+εt

where μis the mean exponential growth rate recorded in the past (−0.00086) and

εtis the magnitude of environmental variation simulated for year t, drawn from a

normal distribution with a mean of zero and a residual standard deviation equiva-

lent to that recorded in the past (σ=0.08).

We assume that a value of 10 bears is the lower critical threshold. By setting the

lowest value on the y-axis to 10, we can readily monitor when our simulated bear

population falls below the critical threshold (Fig. 17.3). Repetition of this process