Bulletin of Mathematical Biology

, Volume 77, Issue 10, pp 1833–1853 | Cite as

Dynamics of Simple Food Webs

  • Tomas GedeonEmail author
  • Patrick Murphy
Original Article


We consider a simple food web with commensal relationship, where organisms utilize both external resources and resources produced by other organisms. We show that in such a community with no competition, there is at most one possible equilibrium for each fixed set of surviving species, and develop a natural condition that determines which species survive based on available resource. Our main result shows that among all possible communities described by equilibria, the one which is stable has the largest number of surviving species and largest combined biomass and hence maximizes utilization of available resources.


Microbial consortia Chemostat Commensal relationship 



We would like to thank Jeff Heys and Ross Carlson for many stimulating discussions on microbial consortia. We would also like to thank anonymous referees whose comments significantly improved the presentation of the paper.


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  1. 1.Department of MathematicsMontana State UniversityBozemanUSA

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