Coding Theory Case Study Math 221 Week 6

CASE STUDY APPLICATION PAPER – FOOD WEBS2BackgroundThere are several mathematical techniques that have been in used for many years. While these techniques include both simple and sophisticated graphing, however, these techniques are the foundation of programming and algorithms in computing and discrete mathematics. The techniques are espoused in the food webs case study with the case study enumerating models thatshowcase the relationship between the prey and the predator in an ecosystem. While this relationship is very competitive, however, discrete mathematics offers various assumptions and computational rules a natural balance.Food WebsThese are abstract representations of feeding relationships in ecosystems and serve as a key to understanding the functioning of the ecosystem. A food web is an essential conceptual toolthat illustrates the feeding relationships among various species within an ecosystem (Smith and Smith 2009). While it reveals interactions among species, community structure as well as the dynamics of energy transfer within a community, it is essentially a graphical representation of feeding relationship among species in an ecosystem. That is, networks of who eats whom in

2 In this paper I will be using a case study on food webs to explain competition, food webs, boxicity, and trophic status. I will also give you an example of how you can apply the knowledge learned from food webs to a real world situation. I will first begin with an explanation on competition and then move on to the other concepts. Every species of animals and plants within the ecological system have their own consumers/competitors and resources. These resources consist of temperature, humidity levels, seasons, and the nutrients that they receive. For example, we know that certain types of species cannot survive in harsh temperatures. We also know that species are going to only go to places where there is ample food and water (nutrients). This would be considered a constraint on the species. When looking at an ecological phase space we know that it consists of many different factors that can affect a species niche. Ecological phase space is meant for only one animal unless it is in a non-empty intersection. These then lead to the competition of these two animals and the principle of competitive

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