Geoscience Reference
In-Depth Information
Figure 9.2
Three examples of the outcome of the population model with only demographic varia-
tion. The smaller population goes extinct at time 93. Birth and death probabilities are both 0.5, mak-
ing the expected value of R= 0.
population does not persist for 100 years without
N
t
becoming 0 for some
t
.
These estimates were determined by running the population model 10,000
times and recording the number of times the simulated population went
extinct before 100 years had elapsed. Lowering the initial population to
N
0
=
20 results in persistence of only 53.2 percent of the populations, again based
on 10,000 runs of the model. Setting
N
0
= 500 improves the persistence rate
to nearly 100 percent. Note that the persistence is not linear in terms of
N
0
(figure 9.3). Initial population size has a major influence on persistence.
DEMOGRAPHIC VARIATION
Other considerations affect persistence. The value of
R
(the birth rate minus the
death rate) is critical.
R
can be negative (death rate exceeds birth rate) and the
population can still persist for 100 years, which may seem counterintuitive.
Furthermore,
R
can be positive (birth rate exceeds death rate) and the popula-
tion can still go extinct. For example, suppose
R
is increased to 0.02 by making
the birth rate 0.51 and the death rate 0.49. The persistence for
N
0
= 20 increases
