Geoscience Reference
In-Depth Information
sistence because these values determine the standard deviation of
R
. The
smaller the standard deviations, the more the model approaches the demo-
graphic variation case, and thus, as
N
t
approaches infinity, the deterministic
case. As the standard deviation increases, the more the variation in
N
t
, regard-
less of population size, and the less likely the population is to persist. Thus a
standard deviation of 0.2 for both the birth and death rates results in only 28.5
percent persistence for
N
0
= 100. Compare this to the 77.4 percent persistence
achieved for a standard deviation of 0.1 (figure 9.5) or to the 98.0 percent per-
sistence when no variation in birth and death rates occurred but demographic
variation is still present.
This second source of variation in our simple model is temporal variation,
that is variation in the parameters of the model across time. As the example
shows, increasing temporal variation decreases persistence. The simple model
illustrated assumed that no correlation existed between the birth rate and the
death rate, that is, that the two rates were independent. However, in real pop-
ulations there is probably a high correlation between birth rates and death rates
across years. Good years with lots of high-quality resources available to the ani-
Figure 9.5
Persistence of a population of 100 animals at t= 0 to t= 100 years as a function of the
standard deviation of birth (mean = 0.5) and death (mean = 0.5) rates (temporal variation). Demo-
graphic variation is still included in the model.
