Rich and realistic dynamics of resource quality based population models

All organisms are composed of multiple chemical elements such as nitrogen (N), phosphorus (P), and carbon (C). P is essential to build nucleic acids (DNA and RNA) and N is needed for protein production. To keep track of the mismatch between P requirement in the consumer and the P content in the producer, stoichiometric models have been constructed to explicitly incorporate food quality and quantity. Most stoichiometric models have suggested that the consumer dynamics heavily depend on P content in the producer when the producer has low nutrient content (low P:C ratio). Motivated by recent lab experiments, researchers explored the effect of excess producer nutrient content (extremely high P:C ratio) on the grazer dynamics. This phenomenon is called the stoichiometric knife edge. However, the global analysis of these resource quality based models is challenging because the phase plane/space is separated into many regions in which the governing nonlinear equations are different. The aim of this talk is to present an overview of the rich and novel dynamics embodied in these stoichiometric population models and its many biological implications and present an alternative framework to build mathematically more tractable and biologically more plausible models.