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Students will analyze graphs of hare and lynx populations produced by the predator-prey spreadsheet model. This analysis will provide students with the opportunity to observe the relationships between the two populations, and how each population changes in relation to the other. Ultimately, students will formulate and state a principle about how the two populations change in response to each other. Students will make connections between the graphs and mathematical model and the basic behaviors of lynx and hares that generate the patterns observed in the graphs.
Ask students to look at some specific sections of the graph of hare and lynx populations (Figure 3 below).
Ask students to estimate the average hare population over the 600-month range of the graph. Students should readily observe that the average hare population is around 100 or slightly higher.
Ask students what they expect to happen to the lynx population when there are lots of hares. Students should surmise that when there are many hares, the lynx have plenty to eat and have more offspring, increasing the lynx population.
Draw students’ attention to the first section of the graph where the hare population is above average, from the start of the graph until just before 100 months. Ask students what is happening with the lynx population during those first 90 or 100 months. As shown in Figure 3, the lynx population is rising during that timespan, as was predicted would happen when food for lynx is plentiful.
Figure 3: Lynx Population Increases when Hare Population is High
Ask students what they expect to happen to the lynx population when the hare population is low. Students should realize that lack of food should cause a decrease in the lynx birth rate, and thus also a decrease in the lynx population.
Draw students’ attention to the segment of the graph between 100 and 200 months, when the hare population was below average. Students should observe that, as expected, the lynx population decreased when there were fewer hares to eat. Figure 4 highlights that portion of the graph.
Figure 4: Lynx Population Decreases when Hare Population is Low
Ask students what they expect to happen to the lynx population when the hare population is low. Students should realize that lack of food should cause a decrease in the lynx birth rate, and thus also a decrease in the lynx population.
Draw students’ attention to the segment of the graph between 100 and 200 months, when the hare population was below average. Students should observe that, as expected, the lynx population decreased when there were fewer hares to eat. Figure 4 highlights that portion of the graph.
Ask students to estimate the average lynx population during the 600-month span of the graph. Students should see that the average number of lynx was around 40. Ask students to hypothesize the effect on the hare population when the number of lynx is high. Students should reason that more hares get eaten when there are more lynx around, and thus the hare population should decrease.
Encourage students to look closely at the first section on the graph where the lynx population is high, between months 50 to 150. Ask students to observe the change in hare population during that timespan. As shown in Figure 5, students should realize that the hare population did indeed drop when there were plenty of lynx, as one would expect.
Figure 5: Hare Population Decreases when Lynx Population is High
Figure 6: Hare Population Increases when Lynx Population is Low
