title: Effect of parity on productivity and sustainability of Lotka-Volterra food chains: bounded orbits in food chains.
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.
authors.affiliation: University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD,  21250, USA, massa2@umbc.edu.
authors.forename: Nicole
authors.initials: N
authors.lastname: Massarelli
authors.forename: Kathleen
authors.initials: K
authors.lastname: Hoffman
authors.forename: Joseph P
authors.initials: JP
authors.lastname: Previte
mesh_terms: D000818:Animals; D017753:Ecosystem; D053476:Extinction, Biological; D005260:Female; D020387:Food Chain; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D011235:Predatory Behavior