Theoretical Frameworks for Ecological Dynamics Subject to Stoichiometric Constraints

All organisms are composed of multiple chemical elements such as carbon, nitrogen, and phosphorus. Recent research in the area known as ecological stoichiometry has highlighted the ecological importance of the relative abundance of chemical constituents, known to vary considerably among species and across trophic levels. However, most theoeretical studies in ecology have until very recently ignored the sources and consequences of this chemical heterogeneity. The investigator and his colleagues undertake theoretical investigations of ecological stoichiometry. They develop a relatively new theoretical framework for ecological dynamics that explicitly incorporates stoichiometric constraints. This base model involves a stoichiometric counterpart of the familiar Rosenzweig-MacArthur equations in which the effective carrying capacity of the resource species and the transfer efficiency of the consumer species are constrained by stoichiometric principles. Introduction of stoichiometric considerations in these equations (here, akin to "food quality") allows for a rich array of ecologically realistic dynamics, including deterministic extinction of the consumer species when resources are abundant but of poor quality. They expand this model in five different directions, to explore ecological realities (i.e., complications) whose consideration has proved illuminating in other, non-stoichiometric settings. Specifically, they analyze the dynamics of 1) a multi-nutrient model; 2) trophically complex models in which multiple consumer species share a resource; 3) time delays in nutrient recycling that are a realistic component of terrestrial ecosystems; 4) two patch models featuring habitat heterogeneity and dispersal of the consumer; and 5) age structured models in which juvenile and adult consumers differ in their nutrient requirements. The project aims to provide an analytically rigorous foundation for burgeoning empirical research into ecological stoichiometry. All living things, including humans, are constructed of approximately the same set of basic building blocks, chemical elements such as carbon (C), nitrogen (N), phosphorus (P), and several dozen more in smaller amounts. However, different organisms contain different proportions of these key elements in their biomass and thus must extract these elements from their environment to differing degrees. In many situations, the environment does not provide these key nutrient elements in the abundance and proportions that are optimal for organism growth and reproduction. Thus, the chemical environment of life may set limits on the success of organisms in various situations. In this project the investigators use mathematical models to simulate the flow of multiple chemical elements in natural food webs to better understand how the requirements of living things for multiple chemical elements establish key feedbacks between the living and non-living world. This work is important for two reasons. First, it may provide a better fundamental understanding of how chemical elements move through food webs. Second, improved fundamental knowledge of how nutrients move in the environment and how to simulate those movements with mathematical tools may help predict and manage natural and human-dominated ecosystems, including those affected by nutrient inputs from human activities (e.g. N and P inputs from fertilizer, sewage) or by global change (e.g. effects of increased atmospheric carbon dioxide on C and nutrient flow in the environment).

Collaborative Research: Towards an Integrative Mechanistic Theory of Within-Host Disease Dynamics

Principal Investigators: Yang Kuang, Val Smith, Marilyn S. Smith This multi-campus team is studying processes within a single biological host that can be described by models inspired by ecological stoichiometry, the study of the balance of energy and multiple chemical resources (usually elements) in ecological interactions. These concepts have been broadened by their extension to biological stoichiometry, which has proven to be an important new lens through which we can view and understand complex biological interactions. Within this general theory, the cycling and utilization of energy and multiple nutrients by organisms and their constituent cells occupies a central position. With its emphasis on the flow of elemental matter, such as carbon, nitrogen, and phosphorus, stoichiometric theory covers multiple biological scales. It also allows, via rigid physical and chemical constraints, the construction of robust mechanistic and predictive models. Originally formulated and verified in the fields of limnology and plant ecology, biological stoichiometry has recently been applied at physiological scales to such diverse areas as organism development and tumor growth. In this proposal we aim to synthesize and apply theoretical and empirical approaches to biological stoichiometry within the grand framework of internal disease. Recent headline-grabbing findings that connect nutritional factors to disease dynamics indicate there is an increasing need for stoichiometry-based mathematical models of internal disease that track the effects of potentially limiting resources. The proposed work weaves together threads of theoretical and experimental research. Our primary aim is the construction of predictive and verifiable theoretical models which can begin to explicitly deal with the effects of stoichiometric interactions in within-host disease dynamics. Such models will be built in a modular fashion, starting with simple deterministic models, and then progressively adding stochasticity, spatial heterogeneity, and genetics. At each step the models will be challenged, calibrated, and tested by in vitro laboratory experiments. The proposed work will have a broad impact in both science research and education, and eventually in internal disease management and treatment. Regarding the former, our research team is truly interdisciplinary, with group members in mathematics, theoretical physics, ecology, and biomedicine. Our collaborative efforts will provide undergraduate and graduate students and junior scientists of diverse ethnic/racial backgrounds with first-hand educational experience in cross-disciplinary communication and exploration. The current proposal is a step towards new ways to understand disease, aiming to develop robust and experimentally calibrated mathematical theories of disease-host interactions that can be applied to a wide variety of diseases. We firmly believe that such theories have a central role to play in present and future research. These grants for proposals submitted as a collaborative proposal from three institutions are made under the Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology. This is a joint competition sponsored by the Division of Mathematical Sciences and the Directorate for Biological Sciences at the National Science Foundation and the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health.

UBM: Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences at ASU

An interdisciplinary team of investigators carry out an undergraduate training initiative at Arizona State University. The training plan intimately combines new cross-disciplinary courses and summer research programs. The former are constructed to allow maximal participation among undergraduate cadres, and facilitate life science majors to achieve a minor in mathematics, and, likewise, mathematics majors to enrich their education with a minor in bioscience. The summer research program is a competitive enterprise involving at least eight ASU faculty members from life sciences, mathematics, and biophysics. Research projects span modeling of ecological and evolutionary processes through the new lens of stoichiometric constraints, bio-economics, chemostat theory, and modeling of visual perception. This project has potential to make broad impact in both local and global education environs. Regarding the former, the ASU UBM team is truly interdisciplinary, with members in mathematics, biology and biophysics, exceptionally well suited for interdisciplinary training for undergraduates in biological and mathematical sciences. Its collaborative efforts can provide undergraduate and graduate students of diverse ethnic/racial backgrounds with first-hand educational experience in cross-disciplinary communication and exploration. As for global impact, the proposed holistic approach (involving mathematical biology courses at various levels and summer research projects) in mathematical biology training can vertically integrate all the components in the ASU education system. It is therefore expected that this proposed program may yield many invaluable lessons to serve mathematical bioscience education and research nationwide, enriching the experience for the next generation of students in this integrative and interdisciplinary scientific endeavor.