The per capita production of type a is reduced by a factor of 1 - p and the per capita production of type b is reduced by a factor of p. This is a case where a large proportion of type a reduces the production of type a, and a large proportion of type b reduces the production of type b. Do you think that type a will still take over?
The model of selection includes no interaction between bacterial types a and b (the per capita production of each type is a constant). Write a pair of differential equations for a and b with the following forms for the per capita production, and derive an equation for the fraction p of type a. Assume that the basic per capita production for type a is μ = 2, and that for type b is λ =1.5.