- In Excel, create a 2x30 data table with the left columnrepresenting a population of prey and the right column representinga population of predators. Use the population model presentedbelow.
Let the startingvalues of the model parameters be: r = 1.3, k = 1, s = .5, v = 1.6,and u = .7
Let the startingpopulation 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 ofP[t] and Q[t] in a graph.
c. Describe in wordsthe changes in P[t] and Q[t] through time.
d. Build table inexcel and describe in words what happens if you increase the growthrate of prey (r)? What about if we decrease the growth rate?
e. What does urepresent? 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 arealistic assumption?
f. Create a secondExcel worksheet representing another population model. Use theinstructions from question 1, except that your model should nowinclude a term to represent the amount of prey which cannot beeaten because they are hiding in refuges (just like in question 2)represented by the term: w. Also, for the predators, include a termf representing what happens if a constant, external food sourcecontributes to the predator population.
Let w = 0.3 and let f= 0.25
g. Graph the newpopulation levels.
h. Explore differentvalues of w and f. Try setting w = 0, or f = 0 to see what effecteach of these has individually. Describe your results.
