Planktonic ecosystems make up the bottom nutritive levels of aquatic food webs, providing a vital source of food to many large marine organisms. Researchers build nutrient-phytoplankton-zooplankton (NPZ) mathematical models in order to describe the bottom trophic levels of aquatic ecosystems, aiding future research of phytoplankton.
In a paper recently published in the SIAM Journal on Applied Mathematics, authors Sue Ann Campbell, Matt Kloosterman and Francis J. Poulin conducted a study of a closed NPZ model to understand the role of maturity in the juvenile zooplankton population within an ecosystem.
Using different forms of the NPZ model, the authors performed a qualitative analysis of the solutions, studying existence and uniqueness, positivity and boundedness, local and global stability of the solutions as well as conditions for extinction. The authors show that an NPZ model can provide a more accurate description of reality and still be able to obtain results analytically. The authors were also able to add size dependence and spatial dependence to the NPZ model. This leads to rich modeling possibilities, such as coupling with external factors like fluid dynamics or higher predation.
In this study, the authors were able to choose the modeling framework that is most convenient for the situation at hand. Furthermore, in a practical sense, the different models offer flexibility in what initial data is required for numerical simulations.
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Source Article: An NPZ Model with State-Dependent Delay Due to Size-Structure in Juvenile Zooplankton. SIAM Journal on Applied Math, 76(2). (Online publish date: March 8, 2016)
About the authors:
Sue Ann Campbell is Professor, Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo; Matt Kloosterman is a PhD applied mathematics student, University of Waterloo; Francis J. Poulin is Associate Professor, Department of Applied Mathematics, University of Waterloo.