Mathematical Models of Pattern Formation in Planktonic Predation-Diffusion Systems: A Review

• Published in: Aspects of Mathematical Modelling pp. 1 - 26
• Main Authors: Malchow, Horst, Hilker, Frank M., Siekmann, Ivo, Petrovskii, Sergei V., Medvinsky, Alexander B.
• Format: Book Chapter
• Language: English
• Published: Basel Birkhäuser Basel 2008
• Series: Mathematics and Biosciences in Interaction
• Subjects: Bioinvasion; Epidemic spread; Fronts; Pattern formation; Plankton dynamics; Reaction-diffusion; Stability; Systems; Waves
• ISBN: 9783764385903; 3764385901
• DOI: 10.1007/978-3-7643-8591-0_1

Plankton form the basis of aquatic food webs. The mathematical modelling of plankton dynamics was initiated by fisheries in the early 20th century. Today, the significant role of plankton in the global carbon cycle and, hence, in climate control has been recognized. The main aim of modelling is to improve understanding of the functioning of food chains and webs and their dependence on internal and external conditions. Population-dynamical models have not only to account for growth and interactions but also for spatial processes like random or directed and joint or relative motion of species as well as the variability of the environment. Early attempts began with exponential growth, Lotka-Volterra type interactions and physico-chemical diffusion. These approaches have been continuously refined to more realistic descriptions of the development of natural populations. The aim of this paper is to give an introduction to the subject of equation-based modelling and the corresponding bibliography, based on and extending previous reviews [1]–[5]. The fascinating variety of temporal, spatial and spatio-temporal patterns in such systems and the governing mechanisms of their generation and further evolution are described and related to plankton dynamics.