converters for the transforming variables R and K. Specify the flow ΔN as a biflow
by clicking on the biflow option in the side-docked panel. Your model should look
like the one in Fig. 2.1.
Set up a graph to plot N and K over time. Specify in the Run Specs menu a DT of
one and the length of the model run to extent from time period 0–120, and specify
the units of time as months. Before you run the model, make an educated guess of
the population size N over time. Will N reach the carrying capacity? Will the
approach be exponential? Will N overshoot K? Here is what you should get when
you run your model (Fig. 2.2).
The population size N asymptotically approaches K, and this approach is at first
fairly rapid—as long as N is far below K—but the increase slows down as K is
approached. The ratio of N/K approaches 1 as N increases, and thus (1 À N/K)
becomes ever smaller. As a result, ΔN approach zero, but it never quite gets there.
Experiment with alternative values for R, K and initial population sizes, and
observe the resulting population dynamics. Always make an educated guess
about the results before you run the model.
Fig. 2.1
Fig. 2.2
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2 Exploring Dynamic Biological Systems
by clicking on the biflow option in the side-docked panel. Your model should look
like the one in Fig. 2.1.
Set up a graph to plot N and K over time. Specify in the Run Specs menu a DT of
one and the length of the model run to extent from time period 0–120, and specify
the units of time as months. Before you run the model, make an educated guess of
the population size N over time. Will N reach the carrying capacity? Will the
approach be exponential? Will N overshoot K? Here is what you should get when
you run your model (Fig. 2.2).
The population size N asymptotically approaches K, and this approach is at first
fairly rapid—as long as N is far below K—but the increase slows down as K is
approached. The ratio of N/K approaches 1 as N increases, and thus (1 À N/K)
becomes ever smaller. As a result, ΔN approach zero, but it never quite gets there.
Experiment with alternative values for R, K and initial population sizes, and
observe the resulting population dynamics. Always make an educated guess
about the results before you run the model.
Fig. 2.1
Fig. 2.2
30
2 Exploring Dynamic Biological Systems