In Montana there is a population of Elk Coyote and Grizzle i

In Montana, there is a population of Elk, Coyote, and Grizzle in the wild. In the absence of Grizzle, the Elk and Coyote follow the L-V model E’ = aE – bEC, and C’ = -dC + hEC Since the Grizzle does not hunt (nor be hunted by) Elk or Coyote, the above equations hold for any Grizzle population. However, Grizzle is a scavenger and their population depends on the population of the other species. Its population can be defined by: G’ = -kG + mGEC – nG2 All time frames are one year. All lower case constants are positive. Start with d=.07, k=.09, m=.21, n=1, a=1, b=2, h=1. Assume a starting population of E0 = 150,000, C0 = 700, and G0 = 400. Track the population of each species for 25 years. Make adjustments to starting populations and constants to see if any changes in patterns come up.

Solution

In Montana, there is a population of Elk, Coyote, and Grizzle in the wild. In the absence of Grizzle, the Elk and Coyote follow the L-V model E’ = aE – bEC, and C’ = -dC + hEC Since the Grizzle does not hunt (nor be hunted by) Elk or Coyote, the above equations hold for any Grizzle population. However, Grizzle is a scavenger and their population depends on the population of the other species. Its population can be defined by: G’ = -kG + mGEC – nG2 All time frames are one year. All lower case constants are positive. Start with d=.07, k=.09, m=.21, n=1, a=1, b=2, h=1. Assume a starting population of E0 = 150,000, C0 = 700, and G0 = 400. Track the population of each species for 25 years. Make adjustments to starting populations and constants to see if any changes in patterns come up.