Figure 3.30 is a digraph representing a food web in a small ecosystem. A directed edge

Chapter 3, Problem 3.7.70

(choose chapter or problem)

Figure 3.30 is a digraph representing a food web in a small ecosystem. A directed edge from a to b indicates that a has b as a source of food. Construct the adjacency matrix A for this digraph and use it to answer the following questions. (a) Which species has the most direct sources of food? How does A show this? b) Which species is a direct source of food for themost other species? How does A show this?(c) If a eats b and b eats c, we say that a has c as an indirectsource of food. How can we use A to determinewhich species has the most indirect foodsources? Which species has the most direct andindirect food sources combined?(d) Suppose that pollutants kill the plants in this foodweb, and we want to determine the effect thischange will have on the ecosystem. Construct anew adjacency matrix A* from A by deleting therow and column corresponding to plants. Repeatparts (a) to (c) and determine which species arethe most and least affected by the change.(e) What will the long-term effect of the pollution be?What matrix calculations will show this?