eMB: Mathematical Classification of Complexity in Population Dynamics

As Darwin famously observed, life is a struggle with various limiting resources constantly inhibiting its growth. With unlimited nutrients and space, a single E. coli cell can multiply into the size of planet Earth in two days. In reality, population growth is a complex nonlinear process influenced by environmental cues and constrained by numerous factors. All cell growth is dependent upon the availability of various essential nutrients and space. The complex dynamics of life is thus shaped by ubiquitous multiple resource limitation (MRL) from gene expression up to the global ecosystem level. Such dynamics may be described in the forms of nonlinear mathematical models based on laws of conservation that govern nutrient limitations. These models may embody rules of life that exhibit emerging systematic properties applicable to multiple temporal and spatial scales. Discovering such rules is the goal of this team of researchers. This project will generate a variety of biological and mathematical modeling resources for the scientific community. The project will produce uniquely trained graduate students and undergraduates with experiences in integrating studies across ecology, evolutionary biology, and applied mathematics fields. The research will further advance society's ability to predict, design and engineer controllable population dynamics in laboratory and natural settings. In addition, the project's intimate association of modeling with experimental work affords the scientific community an opportunity to develop both modeling and experimental approaches in synchrony to better understand the complexity observed in experiments. Motivated by and based on complex time series data sets from existing and ongoing experiments of flour beetle (Tribolium) populations, it is anticipated that this proposed work will address one specific and compelling question about how the MRL shapes the spatiotemporal organization of life. More specifically, the investigators seek to classify complex population dynamical patterns according to three main stages: 1) the transient and seemingly chaotic dynamics characteristic of the initial exponential growth stage that may be subject to influence by random factors to 2) the stable intermediate growth stage, and 3) final or asymptotical growth stage. It is expected that new hidden interactions will emerge between organisms and these stages due to competition for shared limiting resources, leading to complex and highly nonlinear properties that are rare under a single resource limitation concept but could lead to catastrophic problems in real-world ecosystems. Understanding the rules of behavior of these emergent properties consisting of the nutrient state of living individual, living systems, their environments and interactions will help the society to identify early-warning signals and formulate control strategies to address the issues of resilience and sustainability in evolving environments. The main objective of this proposal is to formulate a family of MRL population growth models, validate them via experimental data and understand their complex dynamics with the help of emergent mathematical theories. 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.