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Food Webs, Competition Graphs, and HabitatFormation

Published online by Cambridge University Press:  05 October 2011

M. Cozzens
M. Cozzens*
Affiliation:
DIMACS, Rutgers University, 96 Frelinghuysen Road, Piscataway, NY 08854-8018, USA
*
⋆ Corresponding author. E-mail: [email protected]
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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 ofa food web, one that is understandable by students at all levels. But food webs as part ofa larger system are often not addressed. This paper presents materials that can be used inundergraduate classes in biology (and mathematics) and provides students with theopportunity to explore mathematical models of predator-prey relationships, determinetrophic levels, dominant species, stability of the ecosystem, competition graphs, intervalgraphs, and even confront problems that would appear to have logical answers that are asyet unsolved.

Keywords

food webpredators and preydominancetrophic leveltrophic statusmathematical modelgraphdirected graphcompetition graphinterval graphboxicity
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 6: Biomathematics Education , 2011 , pp. 22 - 38
Copyright
© EDP Sciences, 2011

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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.