BIOL 4800 Problem Set 1 Problem 1: MacArthur & Wilson (MW) biodiversity model Write an R program that simulates the MW model that we derived in class. Implement the model by calling it as a function inside the for loop. The function should take E, I and S(t) as arguments and return S(t+1), which can then be stored in an array. Simulate this model for 100 iterations using initial condition S(0) 2 and parameters0.5, E- 0.1). Plot S(t) vs time a. b. Re-run the model with S(0) 20 and plot S(t) vs time Despite the different initial conditions used in parts (a) and (b) you should observe a common long-time behavior of the model (that relates back to something we discussed during Lecture #1). Justify this long-time behavior for S(t) by using the recursion equation for the MW model in the limit that S(t+1)S(t) [alternatively, S(t+1)- S(t)0] c. BIOL 4800 Problem Set 1 Problem 1: MacArthur & Wilson (MW) biodiversity model Write an R program that simulates the MW model that we derived in class. Implement the model by calling it as a function inside the for loop. The function should take E, I and S(t) as arguments and return S(t+1), which can then be stored in an array. Simulate this model for 100 iterations using initial condition S(0) 2 and parameters0.5, E- 0.1). Plot S(t) vs time a. b. Re-run the model with S(0) 20 and plot S(t) vs time Despite the different initial conditions used in parts (a) and (b) you should observe a common long-time behavior of the model (that relates back to something we discussed during Lecture #1). Justify this long-time behavior for S(t) by using the recursion equation for the MW model in the limit that S(t+1)S(t) [alternatively, S(t+1)- S(t)0] c