PredatorPrey Analysis In some western state wilderness areas

Predator-Prey Analysis

In some western state wilderness areas, deer and mountain lion populations are interrelated, because the mountain lions rely on the deer as a food source. The population of each species goes up and down in cycles, but out of phase with each other. A wildlife management research team estimated the respective populations in a particular region every 2 years over a 16 month period, which the results as shown in the following table:

Years

0

2

4

6

8

10

12

14

16

Deer

1,272

1,523

1,152

891

1,284

1,543

1,128

917

1,185

Lions

39

47

63

54

37

48

60

46

40

Perform the following steps to determine the relationship between the predator and prey:

Deer Population Analysis

a.Enter the data for the deer population for the time interval [0, 16] in a graphing calculator and produce a scatter plot of the data.

b.A function of the form y = k + Asin(Bx + C) can be used to model these data. Use the data in the table to determine k, A, and B. Use the graph in part a to visually estimate C to one decimal place.

c.Plot the data from part a and the equation from part b in the same viewing window. If necessary, adjust the value of C for a better fit.

d.Use your graphing calculator sine regression feature to check your results from parts b and c.

e.Write a summary of the results describing fluctuations and cycles of the deer population.

Mountain Lion Population Analysis

Repeat the steps from the Deer Population Analysis using the Mountain Lion data.

Interrelationship of the Two Populations

a.Discuss the relationship of the maximum predator populations to the maximum prey populations relative to time.

b.Discuss the relationship of the minimum predator populations to the minimum prey populations relative to time.

c.Discuss the dynamics of the fluctuations of the two interdependent populations. What causes the two populations to rise and fall, and why are they out of phase with one another?

Solution

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