Organisms are composed of chemical elements such as carbon, hydrogen, oxygen, nitrogen, and phosphorus. Research in the area known as ecological stoichiometry (ES) has highlighted the ecological importance of the relative abundance of chemical constituents, known to vary considerably among species and across trophic levels. ES deals with how the balance of energy and elements affect and are affected by organisms and their interactions in ecosystems. It has proven to be an important new lens through which to view and understand ecological interactions and has gained momentum by explicitly linking the elemental physiology of organisms to their food web interactions and ecosystem function. Thus, ES 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 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 distanced from mainstream empirical biology. There is not enough effort and attention on marrying empirical results with theoretical findings. The investigators will extend and generalize existing well-received 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 ES, 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 these parameterized 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 may motivate challenging but tractable problems in areas of qualitative and computational studies of nonlinear differential equations and delay differential equations.

This project will have a broad impact in both local and global environs. The biological findings of this project may have a number of practical applications to issues such as eutrophication, biofuel production, global change, and biodiversity. Its theoretical outcomes will provide a solid and user-friendly framework to build mathematical models that allow quantitative prediction of ecological interactions. Moreover, it will find many ready applications in cancer and other within host diseases dynamics and treatment modeling since one can view cancer cells and pathogens as invading species in a host ecosystem. The investigators' collaborative efforts will provide undergraduate and graduate students of diverse ethnic/racial backgrounds with first-hand educational experience in cross-disciplinary communication and exploration. Finally, the investigators are partnering with Arizona State University's School of Life Sciences award-winning Ask-A-Biologist program to develop articles and virtual experiments related to this project to enhance middle- and high school student learning of biological and mathematical concepts.