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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., (Copyright © 2012 Elsevier Inc. All rights reserved.)

This article compares a general closed nutrient, stoichiometric producer-consumer model to a two-dimensional 'quasi-equilibrium' approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare-Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.

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.

Functional-structural plant models (FSPMs) typically integrate suites of detailed physiological and phenological processes to simulate the growth of individual plants. Recent advances in high-performance computing have allowed FSPMs to be extended to patches of interacting trees. Here, we describe a parallel modelling strategy to run simultaneous individual tree models across an 8 × 8 patch of trees. The 64 'core' trees are surrounded by multiple rings of neighbour trees to remove edge effects. A sensitivity analysis of the patch model demonstrates that computational factors such as the number of independently simulated trees (9 v. 36) or number of neighbour rings (3 v. 6) did not significantly influence model estimates of tree volume growth. Updated submodels for phenology and redistribution of overwinter carbohydrate storage allow the simulation to be more responsive to above ground competition among trees in a patch over multiple growing seasons. An 8-year patch-scale simulation of aspen clones 216 and 259 was conducted using high-resolution environmental data from the Aspen FACE Experiment, a long-term free-air carbon dioxide enrichment (FACE) study. Tree heights and volumes were comparable to 8-year growth measurements made at the Aspen FACE site.