Part $2$: Predator$-$Prey Simulation

Spreadsheets can perform simple simulations. One such simulation is to look at the

populations of rabbits and wolves as they interact with each other. As the population of

rabbits grows there is more food available for wolves. Wolves then have more offspring

which eventually means that more wolves are chasing rabbits. This will result in more

predation and the population of rabbits will go down. Wolves will go hungry and produce

fewer offspring. Consequently more rabbits will survive and they will have more offspring

and the cycle continues.

We can simulate this cycle. Biologists have come up with models for this and we will be

exploring one of them. We will simulate the change of these populations as a function of

time.

Let w be the number of wolves and r be the number of rabbits. Let k$1$ be the reproductive

rate of rabbits, k$2$ be the reproductive rates of wolves and let k$3$ be the mortality rate of

wolves. During each time period we will evaluate the change in populations using these

two formulas:

Change in number of rabbits: $\backslash$Delta r$=($k$\_(1)^(*)$r$)-($k$\_(2)^(*)$r$^(**)$w$)$

Change in number of wolves: $\backslash$Delta w$=($k$\_(2)^(*)$r$^(**)$w$)-($k$\_(3)^(*)$w$)$

Thus the new populations will be:

r$^(\text{'})=$r$+\backslash$Delta r

w$^(\text{'})=$w$^(\text{'})+\backslash$Delta w Rabbit Growth Wolf Growth Wolf Mortality

k$1$ k$2$ k$3$

$0\mathrm{.}030\mathrm{.}00050\mathrm{.}05$

Time Rabbits Wolves

r w

$0100100$Your task will be to simulate the change in population over $500$ time periods. The file

preditorPreyStart.xlsx contains the basics of the simulation. You are expected to complete

the simulation and include a chart that shows the two populations as a function of time,

similar to the one below. Name your resulting file LastN$\_$FirstN$\_$simulation.xlsx and

submit it through eClass.