Intellectual merit of the proposed activity. Ecological stoichiometry has proven to be an important new lens through which to view and understand ecological interactions. Within this general theory, the cycling and utilization of energy and multiple chemical elements (such as carbon, nitrogen, and phosphorus) between organisms and their environment occupies a central position. Thus, stoichiometric theory covers multiple biological scales and allows, via rigid physical and chemical constraints, the construction of robust mechanistic and predictive mathematical models. While biology has a research tradition that is almost exclusively empirical in nature and often only weakly connected to formal quantitative analyses, mathematical and theoretical biology on the other hand has had a research agenda that has often been somewhat disconnected from mainstream empirical biology. There is not enough effort and attention on marrying empirical results with theoretical findings. Building on the investigators recent fruitful collaborations analyzing theoretical frameworks for ecological dynamics subject to stoichiometric constraints, the investigators plan to aggressively extend and generalize our wellstudied stoichiometry-based mathematical models to encompass a broader range of ecological situations, including cell quota dynamics, consumer age- or size-structures, variable consumer stoichiometry, and delayed nutrient cycling. Once such a generalized theoretical framework is established, the investigators will construct and evaluate models inspired by recent empirical discoveries in ecological stoichiometry, including one considering the effects on consumer dynamics of not only insufficient food nutrient content but also of excess food nutrient content, and another considering the effects of stoichiometric dietary mixing. Finally, the investigators will challenge our parameterized basic stoichiometric models against observed population growth dynamics qualitatively and quantitatively. In doing so, the investigators hope to achieve a far-reaching synthesis between model and experiment in the form of new theoretical applications that may allow for direct and quantitative predictions of the effects of stoichiometric constraints on ecosystem processes. The models the investigators will investigate are novel and significant mathematically and computationally as they may motivate challenging problems in areas of qualitative and computational studies of nonlinear differential equations and delay differential equations. Nevertheless, the investigators expect these models will have biologically meaningful cases that will pose interesting and tractable mathematical and computational questions.
|Effective start/end date||9/15/09 → 8/31/13|
- National Science Foundation (NSF): $498,940.00