## A Predator-Prey Simulation

Let there be two fishes named Kernighans and Ritchies. The only fish know to prey on Ritchies and to be able to digest them is the colour-blind Kernighan. The Kernighan has adapted to a diet of Ritchies, and won't prey on any other species. No other fish or sea animal could prey on the Ritchies.

So with he above information, could a simulation be created to calculate the two population at different time intervals. I have done something but i belive that i could be on the wrong track.

Some other information to follow would be:

The population of Kernighans and Ritchies can be fully determined by the population size of Kernighans and Ritchies. Suppose that in a given month the number of Kernighan is pop_k, and the population of Ritchies is pop_r. The population of Kernighans and Ritchies is measured in multiples of 1000. This means a population size of 1.0 corresponds to 1000 fish. For the number of Kernighans in the next month we have:

 The population pop_k decreases by alpha_k  pop_k. This is the number of Kernighans that would starve if there were no Ritchies to eat.
The population pop_k increases by beta_k  pop_k  pop_r. This is the number of new Kernighans because they can feed on Ritchies.
The population pop_k decreases by gamma_k  pop_k2. This decrease in the number of Kernighans is due to competition between Kernighans.

Hence, given a population pop_k, the population in the next month is
pop_k - alpha_k  pop_k + beta_k  pop_k  pop_r - gamma_k.pop_k2
If the result of this computation is smaller than 0.001, then there are no Kernighan fish left

For the number of Ritchies in the next month we have

The population pop_r increases by alpha_r  pop_r. This is the number of new Ritchies, if there were no Kernighan to eat them..
 The population pop_r decreases by beta_r  pop_k  pop_r. This is the number of Ritcchies eaten by Kernighans.
 The population pop_r decreases by gamma_r  pop_r2. This decrease in the number of Ritcchies tis due to competition between Ritchies.

Hence, given a population pop_r the population in the next month is

 pop_r + alpha_r.pop_r - beta_r.pop_k.pop_r - gamma_r.pop_r 2
 If the result of this computation is smaller than 0.001, then there are no Ritchie fish left.

Measurements have shown that the constants have the following values:
 alpha_k = 0.4;
 beta_k = 0.4
 gamma_k=0.036
 alpha_r = 0.2;
 beta_r = 0.2
 gamma_r=0.036