Enrichment in a general class of stoichiometric producer–consumer population growth models

Abstract

Abstract. This paper presents the derivation and partial analysis of a general producer--consumer model. The model is stoichometric 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.

Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models

“…Although this does not significantly complicate the numerical simulation of solutions, general conclusions regarding the system persistence, the existence of co-existence states (constant, and otherwise), and the response of such systems to environmental change often rely on simplifying assumptions permitting the reduction of the original model to a system of lower dimensionality. See, for example, [5,25,28], and the references therein. total amount of nutrient N T .…”

“…See [25] for details. For the purpose of generality, we do not specify algebraic forms for the undefined functions on the right of Equations (1)- (3).…”

“…For the special case when the producer's growth is independent of nutrient availability, we take q p = 0 and interpret μ p (l p ) ≡ 1 in Equations (1) and (3). See [25] for a full discussion.…”

“…Model parameter default values and ranges are given in Table 1. See [25] for a discussion of model parameterization and the supporting literature.…”

“…The surface is defined over the biologically feasible region q c C + q p P ≤ N T . See [25] for a discussion of parameter values and units. The system is essentially a periodic behaviour for t ≥ 100 days.…”