Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1 – R[t]/K) - sR[t]W[t] W[t+1] = (1-u)W[t] + vR[t]W[t] Where the carrying capacity of rabbits is 1 million. The growth rate of rabbits is 10% a year and s is equal to 0.00001, v is 0.0000001, and u is equal to 0.01. How many wolves and how many rabbits exist in the equilibrium? Use the equations for the
- Given is a population of wolves (W) and rabbits (R).
R[t+1] = R[t]+ g*R[t] * (1 – R[t]/K) - sR[t]W[t]
W[t+1] = (1-u)W[t] + vR[t]W[t]
Where the carrying capacity of rabbits is 1 million. The growth rate of rabbits is 10% a year and s is equal to 0.00001, v is 0.0000001, and u is equal to 0.01. How many wolves and how many rabbits exist in the equilibrium? Use the equations for the co-existence equilibrium.
Implement the model into Google Sheets with the initial populations of 200,000 rabbits and 10,000 wolves.
Show the dynamics over time. It may take a few hundred steps to get to an equilibrium
Look at the effect of the carrying capacity of rabbits. Suppose environmental pollution decrease the carrying capacity for the rabbits. After trying different values of K, what can you conclude is the minimum carrying capacity needed to have a population of wolves surviving in this environment?
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