# Characteristics of the (i,j)-Step Competition Graphs of Real Food Webs

**Mentor:** Dr. Kim Factor

**Description:** Mathematics is used to model many aspects of the “real” world. One such area is ecology. Traditionally, food webs are used to model the predator-prey relationship of an ecosystem. In the past, the competition graph of a food web has been used by both ecologists/biologists and mathematicians to provide information regarding the strengths and weaknesses of certain ecosystems. This not only relates to a current ecosystem, but can be expanded to investigating the possible effects of either a species being added to the system or a species becoming extinct within the system. In this project, the participants will choose an ecosystem and extend previous research on the characteristics of the (i,j)-step competition graphs of food webs.

**Expected knowledge:** The applicant should have at least one course that deals with proofs in mathematics. More, in this case, is better. Knowledge of graph theory may be helpful, but is not necessary, as we can take time at the beginning of the summer to establish the necessary base. An interest in ecosystems is nice, but not necessary. This is a project dealing with pure mathematics, which has ecosystems as an application (with the emphasis on “mathematics”). The applicant should definitely be interested in and excited by the prospect of finding and/or developing something completely new in the area of graph theory. Applicants with an interest/ability in math who are also involved with computer science would be quite welcome to apply—we are doing computational research and a computer-savvy team member adds a lot!

**Previous Student Researcher:** Nathan Sponberg