When P0 is greater than .5Q0 “Q” will reach "0" first and become extinct. If P0 is less than .5Q0 “P” will reach "0" first and become extinct. However, if P0 = .5Q0, the population will eventually reach an equilibrium with 200 “P’s” and 400 “Q’s.” How could this be proven without using iteration?

Population model:

Pn+1 = Pn -.25Qn + 100

Qn+1 = -Pn + Q n+ 200