The Holling type 1 function is described by g(x) = ax, where x is the amount of prey available and a>0 is the rate at which the predator meets the prey for consumption The Holling type II function is described by f(x)= where x is the amount of prey available and b0 is the maximum consumption rate of the predator (a) Graph the Holling type I and the Holling type II function on the same graph, given a -0.5, 6-2.5 and n-1. bx n+x 2.5 2.5 2.3 2.0 20 20 1.5 1.5 1.3 1.0 1.0 1.0 0.5 0.5 0.5 y 2.5 2.0 1.5 8 10 10 What are the differences between the Holling type I and II functions? The Holling type I function is linear (b) Find the first derivative of the Holling type II function. 12.5 f'(x) = (5+ x)² Interpret the physical meaning of the derivative of the Holling type II function. When the amount of prey increases, the predator growth decreases X (c) Verify that f(n) = -b and interpret the meaning of the parameter n. 2 The parameter n measures the level of prey at which f(x) is half the maximum (d) Find the second derivative of the Holling type II function. -25 F"(x) = x Interpret the meaning of the second derivative of the Holling type II function. As the amount of prey increases, the rate at which the predator growth increases is decreasing What makes the Holling type II function more realistic than the Holling type I function? We see saturation of the amount of food both predator and prey can consume. We see saturation of the amount of prey that can be processed by the predator. We see saturation of the number of predators available in a given area. O We see saturation of the amount of land it takes to sustain a predator and prey population. We see saturation of the number of prey available in a given area. X ✔and the Holling type II function is non-linearv consumption rate of the pr