The influence of spatially heterogeneous mixing on the spatiotemporal dynamics of planktonic systems

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Titel: The influence of spatially heterogeneous mixing on the spatiotemporal dynamics of planktonic systems
Autor(en): Bengfort, Michael
Erstgutachter: Prof. Dr. Horst Malchow
Zweitgutachter: Prof. Dr. Jean-Christophe Poggiale
Zusammenfassung: This thesis focuses on the impact of spatially heterogeneous environments on the spatio-temporal behavior of planktonic systems. Specific emphasis placed is on the influence of spatial variations in the strength of random or chaotic movements (diffusion) of the organisms. Interaction between different species is described by ordinary differential equations. In order to describe movements in space, reaction–diffusion or advection–reaction–diffusion systems are studied. Examples are given for different approaches of diffusive motion as well as for the possible effects on the localized biological system. The results are discussed based on their biological and physical meanings. In doing so, different mechanisms are shown which are able to explain events of fast plankton growth near turbulent flows. In general, it is shown that local variation in the strength of vertical mixing can have global effects on the biological system, such as changing the stability of dynamical solutions and generating new spatiotemporal behavior. The thesis consists of five chapters. Three of them have been published in international peer-reviewed scientific journals. Chapter 1. Introduction: This chapter gives a general introduction to the history of plankton modeling and introduces basic ideas and concepts which are used in the following chapters. Chapter 2. Fokker-Planck law of diffusion: The influence of spatially in- homogeneous diffusion on several common ecological problems is analyzed. Dif- fusion is modeled with Fick’s law and the Fokker–Planck law of diffusion. A discussion is given about the differences between the two formalisms and when to use the one or the other. To do this, the discussion starts with a pure diffusion equation, then it turns to a reaction–diffusion system with one logistically growing component which invades the spatial domain. This chapter also provides a look at systems of two reacting components, namely a trimolecular oscillating chemical model system and an excitable predator–prey model. Contrary to Fickian diffusion, spatial inhomogeneities promote spatial and spatiotemporal pattern formation in the case of Fokker–Planck diffusion. A slightly modified version of this chapter has been published in the Journal of Mathematical Biology (Bengfort et al., 2016). Chapter 3. Plankton blooms and patchiness: Microscopic turbulent motions of water have been shown to influence the dynamics of microscopic species. Therefore, the number, stability, and excitability of stationary states in a predator– prey model of plankton species can change when the strength of turbulent motions varies. In a spatial system these microscopic turbulent motions are naturally of different strength and form a heterogeneous physical environment. Spatially neighboring plankton communities with different physical conditions can impact each other due to diffusive coupling. It is shown that local variations in the physical conditions can influence the global system in the form of propagating pulses of high population densities. For this, three local predator–prey models with different local responses to variation in the physical environment are considered. The degree of spatial heterogeneity can, depending on the model, promote or reduce the number of propagating pulses, which can be interpreted as patchy plankton distributions and recurrent blooms. This chapter has been published in the Journal Ecological Complexity (Bengfort et al., 2014). Chapter 4. Advection–reaction–diffusion model: Here, some of the models introduced in chapter 1 and 2 are modified to perform two dimensional spatial simulations including advection, reaction and diffusion. These models include assumptions about turbulent flows introduced in chapter 1. Chapter 5. Competition: Some plankton species, such as cyanobacteria, have an advantage in competition for light compared to other species because of their buoyancy. This advantage can be diminished by vertical mixing in the surround- ing water column. A non–spatial model, based on ordinary differential equations, which accounts for this effect is introduced. The main aim is to show that vertical mixing influences the outcome of competition between different species. Hystersis is possible for a certain range of parameters. Introducing a grazing predator, the system exhibits different dynamics depending on the strength of mixing. In a diffusively coupled horizontal spatial model, local vertical mixing can also have a global effect on the biological system, for instance, destabilization of a locally stable solution, or the generation of new spatiotemporal behavior. This chapter has been published in the Journal Ecological Modelling (Bengfort and Malchow, 2016).
Schlagworte: Plankton; Competition; Reaction-diffusion equation; Diffusion; Pattern formation; Movement behavior; predator–prey systems
Erscheinungsdatum: 17-Mai-2016
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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