Mth 221 - Food Webs

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In this way, the competition graph that was mentioned earlier will have en edge between vertices representing organisms A and B if and only if the intersection of the ecological niche sets relating to these organisms is non-empty (ie. the two sets do intersect). This concept is represented by intersection graphs, which have vertices corresponding to ecological niche sets and there is an edge between set A and set B if and only if the intersection of the two sets is non-empty.

An intersection graph can also be represented using boxes, which is perhaps more consistent with the ecological niche set theory. In this way, each set is represented by a box and two boxes intersect if and only if the intersection of the two sets that they represent is non-empty.

Figure 3: Box representation of an intersection graph

[pic 3]

In this way, boxicity is defined; the boxicity of a graph G is the smallest n such that G is the intersection graph of a family of boxes in Euclidean n-space. As such, the boxicity of the intersection graph above is 2. This is a way of expressing the complexity of an ecological community in that it is a measure of the number of factors that have a large impact on the ecological community.

Generally, the more complex the ecological community, the more stable that ecological community is because this usually indicates that organisms have multiple food sources, which means that changes in conditions of the community will have less of an effect because different organisms (ie. food sources) thrive in different conditions. Therefore, the concept of trophic status was introduced to define the status of an organism on a food web. The more complex the ecological community defined by that food web is, the higher number of organisms there will be at each trophic level. The trophic level of an organism is essentially how high up on the food chain that organism is. For example, in the food web demonstrated by figure 1, the shrimp is at trophic level 1. In mathematical terms, the trophic level is defined as “the length of a directed path from the vertex to the bottom”.

Understanding food webs and the applications of food webs are important to knowing the world around us. One can use food webs to describe direct relationships among two organisms, as well as to illustrate how species can affect each other indirectly. By understanding all of the different parameters that can affect an ecological community, one can truly understand the varying relationships within an ecosystem.

References:

Robert A. McGuigan. (n.d.). Food webs. Retrieved from University of Phoenix, MTH/221 website.

Cohen, J. E., & Cohen, J. E. (1978). Food webs and niche space. Princeton N.J: Princeton University Press.

Michaels, J. G., & Rosen, K. H. (1992). Applications of discrete mathematics. New York: McGraw-Hill.

Predation and food webs. (n.d.). Retrieved from http://Predation and Food Webs. (n.d.). Retrieved June 04, 2017, from http://www.lifeinfreshwater.org.uk/web%20pages/ponds/Predation %20Comms.htm