Competition between populations: In this exercise we consider the question of competition between two populations that vie for resources but do not prey on each other. Let m be the size of the first...

Competition between populations: In this exercise we consider the question of competition between two populations that vie for resources but do not prey on each other. Let m be the size of the first population and n the size of the second (both measured in thousands of animals), and assume that the populations coexist eventually. Here is an example of one common model for the interaction:

Per capita growth rate for m = 5(1 − m − n),

Per capita growth rate for n = 6(1 − 0.7m − 1.2n) .

a. An isocline is formed by the points at which the per capita growth rate for m is zero. These are the solutions of the equation 5(1 − m − n) = 0. Find a formula for n in terms of m that describes this isocline.

b. The points at which the per capita growth rate for n is zero form another isocline. Find a formula for n in terms of m that describes this isocline.

 c. At an equilibrium point the per capita growth rates for m and for n are both zero. If the populations reach such a point, they will remain there indefinitely. Use your answers to parts a and b to find the equilibrium point.