Analysis of simulation data

• Re-examination of the source

  How data are collected in the arrays.
  

• Modifications:
  1. Modify the source code (copy it from /home/progClass/src/logistic/logistic.c), so that the programs ask for the user inputs for birthR, deathR, and kk.
  2. Run the simulation (assuming that you compiled the program as logistic):

     ./logistic > out1

     Use birth rate of 0.2, death rate of 0.1, k of 100, and 1 run of simulation.

     To plot the simulation results:

     $ R
     
     > source("/home/progClass/src/logistic/logistic.r")
     > plot.logistic("out1")
     

  3. Now run with the same parameter values, but simulate 100 runs, and make the plot.

  4. Calculate r and K of the simple logistic model from the parameters used for the ``mechanistic'' logistic model (you can calculate this with paper and pencil). Does the Carrying capacity of simulation matches with deterministic model?

  5. There seems to be slight difference in the two models (density dependent birth model vs density dependent death model). Can you think what is making this differences?

     Running the simulation with various combinations of parameters may give you a hint. In other words, you may observe more difference between the two models under certain parameter sets.

  6. After observing the behavior of the system, try running with birth rate of 0.2, death rate of 0.1, k of 20, and 1 run of simulation. Also run 100 simulations.

  7. Do you remember the exercise where you counted the number of heads from k flips of biased coin? Can you modify PopChange(), so that you call your coin flip function you made? Does the code look cleaner?

  8. Consider a Model 3, where both birth and death are density dependent.
     $$\begin{eqnarray*} B(N) & = & b N ( 1 - \frac{N}{2 k}) = b N - \frac{b}{2 k} N^2... ...frac{N}{2 \frac{d}{b} k}) = d \cdot N + \frac{b}{2 k} N^2 \\ \end{eqnarray*}$$
     
     

     Add this model to the source code, and analyze the results.