At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them. thus we assume that the rate at which fish are caught is given by ey, where e is a positive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. to include this effect, the logistic equation is replaced by dy/dt = r(1 − y/k)y − ey. (i) this equation is known as the schaefer model after the biologist m. b. schaefer, who applied it to fish populations. (a) show that if e < r, then there are two equilibrium points, y1 = 0 and y2 = k(1 − e/r) > 0. (b) show that y = y1 is unstable and y = y2 is asymptotically stable.