Question

1. In Excel, create a 2x30 data table with the left column representing a population of prey and the right column representing a population of predators. Use the population model presented below.

Let the starting values of the model parameters be: r = 1.3, k = 1, s = .5, v = 1.6, and u = .7

Let the starting population of P = 1.1 and Q = .4

Difference equations: P[t + 1] = P[t](1 + r(1 – P[t]/K)) - sP[t]Q[t]

Qt + 1 = (1-u)Q[t] + vP[t]Q[t]

a. What does sP[t]Q[t] and vP[t]Q[t] represent?

b. Plot the values of P[t] and Q[t] in a graph.

c. Describe in words the changes in P[t] and Q[t] through time.

d. Build table in excel and describe in words what happens if you increase the growth rate of prey (r)? What about if we decrease the growth rate?

e. What does u represent? Why should u be less than 1? What happens if we make u = 1? Can you think of any biological systems in which u = 1 is a realistic assumption?

f. Create a second Excel worksheet representing another population model. Use the instructions from question 1, except that your model should now include a term to represent the amount of prey which cannot be eaten because they are hiding in refuges (just like in question 2) represented by the term: w. Also, for the predators, include a term f representing what happens if a constant, external food source contributes to the predator population.

Let w = 0.3 and let f = 0.25

g. Graph the new population levels.

h. Explore different values of w and f. Try setting w = 0, or f = 0 to see what effect each of these has individually. Describe your results.

Answer 1