The food webs case study introduces mathematical techniques used for many years, including simple and sophisticated graphing, and how it relates to modern world computing and technology. Today, these mathematical techniques form the basis for programming and algorithms used in computing and research and better known as discrete mathematics. The basis of each theory discusses relationships of elements involving two or more sets and any subsets of these sets. The graphs used to follow food webs help establish a requiem of vertices, edges, and links that an information system closely adheres to in modern computing. The food web case study uses annotations that adequately provide models that depict the predator and prey relationship found in the ecological environment. This relationship is very competitive and discrete mathematics provides different assumptions and computational rules to maintain a natural balance. Competition within the food web describes the parameters needed for each element to exist and coexist within a given environment.
These parameters consist of elements such as Ph balance, temperature (or climate), food availability, and so forth. For each animal or plant represented, these parameters provide a niche for survival in the ecological system of nature. These niches prove to be superior to some species and inferior to others. Competition graphs utilize each element within the food web exhibiting how species feed and prey upon others. The graphs capabilities include how more than any single species may prey or be prey to more than any single species and still coexist. These directed, simple graphs prove sufficient when studying limited numbers of elements. The Euclidean space provides an n dimensional view of the components needed to support the life of the species.