Effect of parity on productivity and sustainability of Lotka–Volterra food chains: Bounded orbits in food chains

Nicole Massarelli, Kathleen Hoffman, Joseph Peter Previte

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Hairston, Slobodkin, and Smith conjectured that top down forces act on food chains, which opposed the previously accepted theory that bottom up forces exclusively dictate the dynamics of populations. We model food chains using the Lotka–Volterra predation model and derive sustainability constants which determine which species will persist or go extinct. Further, we show that the productivity of a sustainable food chain with even trophic levels is predator regulated, or top down, while a sustainable food chain with odd trophic levels is resource limited, which is bottom up, which is consistent with current ecological theory.

Original languageEnglish (US)
Pages (from-to)1609-1626
Number of pages18
JournalJournal of Mathematical Biology
Volume69
Issue number6-7
DOIs
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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