Biology

There a few applications of graph theory in biology. Trees are the things that are used the most in biology. These trees are used as ways to display information. There are two types of tress that occur, natural trees and conceptual tress

(Wilson & Watkins, 1990)

. Natural tress often look like the following.

Conceptual tree do not have a well-defined physical structure like natural tress do. A familiar example is the tree of life, which represent the evolutionary relationships between various animal or vegetable species. Below is an example of this type of tree.

Genetics

One application of graph theory in genetics is the proof to Benzer's Problem

(Singh, 2010)

. The structure of genes is considered to be a linear arrangement, Benzer's problem asks whether the structure inside of the gene is also linearly arranged. Graph theory was used to prove that for phage T4, a bacterial virus, the inside structure is also linear. The way that this was proved was by using by study the mutations, the changes of structure in a given gene. When studying these mutations, Benzer looked at the missing parts. When the missing parts overlapped, he was able to express the results in the form of an adjacency matrix. Below you can find a part of the adjacency matrix..

The graph from the entire 19x19 adjacency matrix, looks like:

Note that he was not able to strictly draw the conclusion that the fine structure was linear based solely on these results, it only helped him to prove it.

Ecology

Ecology is the study of the relationship between species and their surroundings. They often study thing like what animals eat which. Examining questions like this, it is especially useful if they can represent the relationships in some way. They often do this with directed graphs called food webs

Often these graphs are much larger than the one shown, so to interpret these graphs, they break them down into competition graphs. Competition graphs are graphs that are broken down into pairs of vertices that share common edges. Here is are a few examples of competition graphs from the above food web.