Collaborative Research: RUI: Structured Population Dynamics Subject to Stoichiometric Constraints

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As human activities continue to alter environmental balances and nutrient cycles, it is becoming vital to understand how these changes can impact the environment. Ecological processes depend on the flow and balance of essential elements such as carbon, nitrogen, and phosphorus. These essential elements can affect juvenile consumers differently than adult consumers. Such age/stage-specific effects affect population dynamics, suggesting age/stage-structured mathematical models are needed to accurately capture and understand population dynamics. The development of age/stage-structured population models over the decades has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, current models fail when fertility and maturation play important roles in nutrient recycling and ecosystem function. Here, investigators will design and conduct laboratory experiments in conjunction with developing mathematical models that incorporate age/stage-specific nutritional constraints on growth, time to maturation, and reproduction. This will result in the development of new theoretical applications in ecology that investigate how varying nutrient levels help shape ecological communities. The project is a collaboration between Texas Tech University, Haverford College, and California State University Northridge, and offers valuable educational, training, and outreach opportunities. Specifically, undergraduate and graduate students will receive interdisciplinary training and mentorship in the fields of mathematics and ecology to gain the ability to ask, answer, and achieve broad understandings of scientific problems, that is necessary to communicate effectively across disciplines. Investigators and students will be involved in K-12 outreach initiatives. This project seeks to understand the interactive effects of stoichiometric constraints and population dynamics, particularly, how organismal stage structures and ecosystem function influence each other. To this end, the investigators will develop and analyze a series of empirically testable and robust mathematical models of population dynamics structured under the framework of Ecological Stoichiometry. The theory of Ecological Stoichiometry emphasizes the balance of essential elements throughout ecological interactions. Compartmental systems of ordinary differential equations and delayed integro-differential equations will be developed to address complex questions about stage-specific nutritional constraints, and their consequences on maturation and reproductive output. Dynamical systems theory and tools will be used to interpret and analyze the models including analytical, numerical, as well as bifurcation analysis. The synthesis of the models and experiments will integrate the field of structured population mathematical modeling with the theory of Ecological Stoichiometry. The resulting theoretical frameworks and their findings will help shed light on the interplay between elemental constraints and stage-structures within ecological systems and broaden the types of ecological questions that models can answer.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.