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saces
5 Some Experiments with ‘saces’
1. A prey population increases at a rate proportional to the number of prey, but
is simultaneously reduced by predators at a rate proportional to the product
of the numbers of prey and predators.
2. A predator population decreases at a rate proportional to the number of
predators, but increases at a rate proportional to the product of the numbers
of prey and predators.
The following screenshot illustrates the expected behaviour of the simulation
as displayed by the data viewer.
Figure 5.8: Wolves and sheep population diagram
The Lotka-Volterra example supplied with ‘saces’ simulates a population of
wolves preying on sheep, and demonstrates the cyclic behaviour of such a system.
The events occur in the following order.
1. The sheep population increases because there are not many wolves which
prey on them.
2. The wolf population increases due to the increasing abundance of sheep.
3. The wolf population increases until there is not enough sheep to sustain the
wolf population.
4. The wolf population decreases due to the lack sheep.
Vito Volterra and Alfred J. Lotka described this cyclic behaviour in population dynamics using two coupled differential equations, each one representing a
species.
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