The Mathematical Biology of Diatoms

2Size-Resolved Modeling of Diatom Populations: Old Findings and New Insights

Jonas Ziebarth¹, Werner M. Seiler² and Thomas Fuhrmann-Lieker¹*

¹ Institute of Chemistry and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, Kassel, Germany

² Institute of Mathematics, University of Kassel, Kassel, Germany

Abstract

The unique size reduction and restitution cycle of diatoms requires special attention in modeling their population dynamics. Matrix models based on distinct size classes are generally necessary to fully address periodic changes in cell size distribution and understand infra-annual algae blooms. Here, different approaches for such size-resolved models are compared, with their conclusions about oscillatory behavior in diatom populations. Particularly, the coupling of model parameters with environmental signals that may act as zeitgebers are discussed.

Keywords: Diatoms, biological clocks, population dynamics, dynamical systems, matrix models

2.1 Introduction

The simulation of ecosystems by population dynamics of contained species has a long tradition [2.12]. Normally, coupled differential equations are used that describe the interdependence of species or the reaction to changing environmental conditions. Mostly, a species is considered as a single compartment characterized by the number of individuals, but in some models age classes such as juvenile, adult, and senescent are distinguished [2.50]. This idea can be transferred ...