title: Enrichment in a stoichiometric model of two producers and one consumer.
abstract: We consider a stoichiometric population model of two producers and one consumer. Stoichiometry can be thought of as the tracking of food quality in addition to food quantity. Our model assumes a reduced rate of conversion of biomass from producer to consumer when food quality is low. The model is open for carbon but closed for nutrient. The introduction of the second producer, which competes with the first, leads to new equilibria, new limit cycles, and new bifurcations. The focus of this paper is on the bifurcations which are the result of enrichment. The primary parameters we vary are the growth rates of both producers. Secondary variable parameters are the total nutrients in the system, and the producer nutrient uptake rates. The possible equilibria are: no-life, one-producer, coexistence of both producers, the consumer coexisting with either producer, and the consumer coexisting with both producers. We observe limit cycles in the latter three coexistence combinations. Bifurcation diagrams along with corresponding representative time series summarize the behaviours observed for this model.
authors.affiliation: Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812, USA. linx0275@d.umn.edu
authors.forename: Laurence Hao-Ran
authors.initials: LH
authors.lastname: Lin
authors.forename: Bruce B
authors.initials: BB
authors.lastname: Peckham
authors.forename: Harlan W
authors.initials: HW
authors.lastname: Stech
authors.forename: John
authors.initials: J
authors.lastname: Pastor
mesh_terms: D002244:Carbon / Q000378:metabolism; D020387:Food Chain; D008954:Models, Biological; D013997:Time Factors
chemical_list: D002244:Carbon