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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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Methods are proposed for modeling the population-level effects of endocrine-disrupting chemicals on age-structured populations. We present a framework for representing xenobiotic-induced impacts to reproductive, life-stage transition, and mortality rates. Numerical simulations are described addressing delayed disturbance and recovery dynamics and potential transgenerational effects. [ABSTRACT FROM AUTHOR]

A cyclic, constant parameter epidemiological model is described for a closed population divided into susceptible, exposed and infectious classes. Distributed delays are introduced and the model is formulated as two coupled Volterra integral equations. The delays do not change the general nature of thresholds or asymptotic stability; in all cases considered the disease either dies out, or approaches an endemic steady state. [ABSTRACT FROM AUTHOR]

A detailed analysis of a general class of SIRS epidemic models is given. Sufficient conditions are derived which guarantee the global stability of the endemic equilibrium solution. Further conditions are found which ensure instability for the equilibrium. Finally, the dependence of the stability on the contact number and the ratio of the mean length of infection to the mean removed time is considered. [ABSTRACT FROM AUTHOR]

A scalar integrodifferential equation is considered which describes a single self-regulating species. Three results are presented towards showing that the 'carrying capacity' equilibrium state becomes unstable as the self-regulating mechanism acts after a longer time lag. [ABSTRACT FROM AUTHOR]