Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-28T18:23:02.752Z Has data issue: false hasContentIssue false

Food Webs, Competition Graphs, and Habitat Formation

Published online by Cambridge University Press:  05 October 2011

M. Cozzens*
Affiliation:
DIMACS, Rutgers University, 96 Frelinghuysen Road, Piscataway, NY 08854-8018, USA
*
Corresponding author. E-mail: midgec@dimacs.rutgers.edu
Get access

Abstract

One interesting example of a discrete mathematical model used in biology is a food web. The first biology courses in high school and in college present the fundamental nature of a food web, one that is understandable by students at all levels. But food webs as part of a larger system are often not addressed. This paper presents materials that can be used in undergraduate classes in biology (and mathematics) and provides students with the opportunity to explore mathematical models of predator-prey relationships, determine trophic levels, dominant species, stability of the ecosystem, competition graphs, interval graphs, and even confront problems that would appear to have logical answers that are as yet unsolved.

Type
Research Article
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J. E. Cohen. Food webs and niche space. Princeton University Press, Princeton, New Jersey, 1978.
Cohen, J. E., Komlos, J., Mueller, T.. The probability of an interval graph and why it matters. Proc. Symposium on Pure Math, 34 (1979), 97-115. CrossRefGoogle Scholar
M. B. Cozzens. Integrating mathematics and biology in the high school curriculum. BioMath in the Schools, DIMACS Book Series, American Math Society, 2010.
M. B. Cozzens, N. Crisler, T. Fleetwood. Food webs, COMAP: Lexington MA, 2010.
Cozzens, M. B., S.Roberts, F.. Computing the boxicity of a graph by covering its complement by cointerval graphs. Discrete Applied Math, 6 (1983), 217-228. CrossRefGoogle Scholar
Goldwasser, L., Roughgarden, J.. Construction and analysis of a large Caribbean food web. Ecology, 74 (1993), No. 4, 1216-1233. CrossRefGoogle Scholar
Hastings, A., Palmer, M. A.. A bright future for biologists and mathematicians. Science, 299 (2003), 2003-2004. CrossRefGoogle ScholarPubMed
J. H. Jackson. Bioinformatics and genomics. in Math & Bio 2010: Linking Undergraduate Disciplines, L.A. Steen (ed.), Mathematical Association of America, 2005, 51-61.
Morris, R. W., Bean, C. A., K.Farber, G., Gallahan, D., Hight-Walker, A. R., Liu, Y., Lyster, P. M., Peng, G. C. Y., Roberts, F. S., Twery, M., Whitmarsh, J.. Digital biology: an emerging and promising discipline. Trends in Biotechnology, 23 (2005), 113-117. CrossRefGoogle ScholarPubMed
Paine, R. T.. Food web complexity and species diversity. American Naturalist, 100 (1966), No. 910, 65-75. CrossRefGoogle Scholar
F. S. Roberts, Discrete mathematical models with applications to social, biological, and environmental problems. Prentice-Hall, Engelwood Cliffs, NJ, 1976, 111-140.