Plenary-06

Yang Kuang

Professor of Mathematics

Arizona State University

Abstract:

In this talk, we will present some of the challenges and approaches we took in three modeling projects in ecology. These projects are all motivated by highly nonlinear data-sets that showcase the complexity of the population dynamics being modeled. We will start with our ongoing work on the dynamics of flour beetles growth which allow us to gain deep insights into population chaos. Next we present some of our work on stoichiometric population growth models as all organisms are composed of multiple chemical elements such as carbon, nitrogen and phosphorus. While energy flow and element cycling are two fundamental and unifying principles in ecosystem theory, population models usually ignore the latter. This negligence makes energy-only based population growth models simplistic in understanding the observed complexity of grazer population growth when producer population such as algae are subject to varying light exposures. We will also present our reaction–diffusion modeling work of E.coli colony growth incorporating nutrient distribution and agar dehydration. The bacterial colony is a powerful experimental platform for broad biological research, and reaction– diffusion models are widely used to study the mechanisms of its formation process. However, there are crucial factors that affect the colony growth but are absent from well-known models, such as the heterogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. We propose two plausible reaction–diffusion models based on the above two factors and validate them against experimental data. Both models outperform the classical Fisher equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, our model captures how a colony’s expansion slows down and the change of a colony’s height profile over time.