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Effect of parity on productivity and sustainability of Lotka–Volterra food chains

Bounded orbits in food chains

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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.

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Acknowledgments

We thank the reviewers for their insightful comments and helpful suggestions. J.P.P. acknowledges support from NSF-DMS-9987594, NSF-DMS-0236637, and NSF-DMS-0552148 for foundational work that led to the formulation of this problem.

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Authors and Affiliations

  1. University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD,  21250, USA

    Nicole Massarelli & Kathleen Hoffman

  2. Penn State Erie, The Behrend College, Station Road, Erie, PA,  16563, USA

    Joseph P. Previte

Authors
  1. Nicole Massarelli
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  2. Kathleen Hoffman
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  3. Joseph P. Previte
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Correspondence to Kathleen Hoffman.

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Massarelli, N., Hoffman, K. & Previte, J.P. Effect of parity on productivity and sustainability of Lotka–Volterra food chains. J. Math. Biol. 69, 1609–1626 (2014). https://doi.org/10.1007/s00285-013-0746-7

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  • DOI: https://doi.org/10.1007/s00285-013-0746-7

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