title: Enrichment in a general class of stoichiometric producer-consumer population growth models.
abstract: This paper presents the derivation and partial analysis of a general producer-consumer model. The model is stoichiometric in that it includes the growth constraints imposed by species-specific biomass carbon to nutrient ratios. The model unifies the approaches of other studies in recent years, and is calibrated from an extensive review of the algae-Daphnia literature. Numerical simulations and bifurcation analysis are used to examine the impact of energy enrichment under nutrient and stoichiometric constraints. Our results suggest that the variety of system responses previously cited for related models can be attributed to the size of the total system nutrient pool, which is here assumed fixed. New, more complicated bifurcation sequences, such as multiple homoclinic bifurcations, are demonstrated as well. The mechanistic basis of the model permits us to show the robustness of the system's dynamics subject to alternate approaches to modeling producer and consumer biomass production.
authors.affiliation: Department of Mathematics and Statistics, University of Minnesota Duluth, USA. hstech@d.umn.edu
authors.forename: Harlan
authors.initials: H
authors.lastname: Stech
authors.forename: Bruce
authors.initials: B
authors.lastname: Peckham
authors.forename: John
authors.initials: J
authors.lastname: Pastor
mesh_terms: D000818:Animals; D000460:Chlorophyta / Q000254:growth & development; D003621:Daphnia / Q000254:growth & development; D008962:Models, Theoretical; D011158:Population Growth