Stoichiometry in Predator-Prey Equations
Irakli Loladze (Mathematical Biosciences Institute, The Ohio State University)
(March 8, 2006 4:30 PM - 5:30 PM)
All organisms are composed of multiple chemical elements such as carbon, nitrogen, and phosphorus. Element cycling and energy flow are two fundamental and unifying principles in ecosystem theory; however, population models rarely take advantage of the former. Instead, they assume chemical homogeneity of all populations by concentrating on a single constituent, generally an equivalent of energy. In this talk, we examine ramifications of an explicit assumption that both predator and prey are chemically heterogeneous. Using stoichiometric principles, we construct a 2D Lotka-Volterra predator-prey type model where both populations are composed of two essential elements: carbon and phosphorous. The analysis shows that indirect competition between two populations for phosphorus can shift predator-prey interactions from a (+, -) type to an unusual (-, -) class. This leads to complex dynamics with multiple positive equilibria, where bistability and deterministic extinction of the predator are possible. Rosenzweig's paradox of enrichment holds only in the part of the phase plane where the predator is energy (food quantity) limited; a new phenomenon, the paradox of energy enrichment, arises in the other part, where the predator is phosphorus (food quality) limited. Subsequent laboratory experiments validated the outcomes of this model.