Food Webs, Competition Graphs, and Habitat Formation

M. Cozzens

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 6, page 22-38
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Cozzens, M.. "Food Webs, Competition Graphs, and Habitat Formation." Mathematical Modelling of Natural Phenomena 6.6 (2011): 22-38. <http://eudml.org/doc/222274>.

@article{Cozzens2011,
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. },
author = {Cozzens, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {food web; predators and prey; dominance; trophic level; trophic status; mathematical model; graph; directed graph; competition graph; interval graph; boxicity; prey-predator; directed graphs; interval graphs},
language = {eng},
month = {10},
number = {6},
pages = {22-38},
publisher = {EDP Sciences},
title = {Food Webs, Competition Graphs, and Habitat Formation},
url = {http://eudml.org/doc/222274},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Cozzens, M.
TI - Food Webs, Competition Graphs, and Habitat Formation
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 22
EP - 38
AB - 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.
LA - eng
KW - food web; predators and prey; dominance; trophic level; trophic status; mathematical model; graph; directed graph; competition graph; interval graph; boxicity; prey-predator; directed graphs; interval graphs
UR - http://eudml.org/doc/222274
ER -

References

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

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