Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model

In this thesis, we study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms which represent a plankton dynamics that includes info–chemical mediated trophic interactions. We consider both a simplified two species model which has been studied in the literature (mostly in biological terms) and an extended, four-species model. In the latter, the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external infochemical (C) mediated predation by copepods (Z). We undertake a stability analysis of both the two species model and the four species model and compare the system dynamics. In relation to this, the critical conditions for Turing instability are derived; these are necessary and sufficient. Furthermore, we consider the degenerated situation wherein Turing bifurcation and Hopf bifurcation occur simultaneously. We also consider under what conditions Turing patterns are exhibited and under what conditions spatiotemporal patterns are observed generally. The Transient Turing instability of spatial interactions –exhibited by the two species model–is introduced and investigated in a number of ways. We also study the effects of the paradox of enrichment. This paradox led to a loss of stability in the four species model after this was derived from the two species model by expansion and by the addition of resources. Further, a numerical continuation technique was used to determine the existence of multiple stationary patterns

Joint effects of nutrients and contaminants on the dynamics of a food chain in marine ecosystems

We analyze the joint effect of contaminants and nutrient loading on population dynamics of marine food chains by means of bifurcation analysis. Contaminant toxicity is assumed to alter mortality of some species with a sigmoidal dose-response relationship. A generic effect of pollutants is to delay transitions to complex dynamical states towards higher nutrient load values, but more counterintuitive consequences arising from indirect effects are described. In particular, the top predator seems to be the species more affected by pollutants, even when contaminant is toxic only to lower trophic levels

Analysis of toxic effects and nutrient stress in aquatic ecosystems

Kooijman, S.A.L.M. [Promotor]Kooi, B.W. [Copromotor

Ecological Complex Systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noises role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System to appear in EPJ B, Vol. 65 (2008

Partial Differential Equations in Ecology

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots

Pattern selection models: From normal to anomalous diffusion

“Pattern formation and selection is an important topic in many physical, chemical, and biological fields. In 1952, Alan Turing showed that a system of chemical substances could produce spatially stable patterns by the interplay of diffusion and reactions. Since then, pattern formations have been widely studied via the reaction-diffusion models. So far, patterns in the single-component system with normal diffusion have been well understood. Motivated by the experimental observations, more recent attention has been focused on the reaction-diffusion systems with anomalous diffusion as well as coupled multi-component systems. The objectives of this dissertation are to study the effects of superdiffusion on pattern formations and to compare them with the effects of normal diffusion in one-, and multi-component reaction-diffusion systems. Our studies show that the model parameters, including diffusion coefficients, ratio of diffusion powers, and coupling strength between components play an important role on the pattern formation. Both theoretical analysis and numerical simulations are carried out to understand the pattern formation in different parameter regimes. Starting with the linear stability analysis, the theoretical studies predict the space of Turing instability. To further study pattern selection in this space, weakly nonlinear analysis is carried out to obtain the regimes for different patterns. On the other hand, numerical simulations are carried out to fully investigate the interplay of diffusion and nonlinear reactions on pattern formations. To this end, the reaction-diffusion systems are solved by the Fourier pseudo-spectral method. Numerical results show that superdiffusion may substantially change the patterns in a reaction-diffusion system. Different superdiffusive exponents of the activator and inhibitor could cause both qualitative and quantitative changes in emergent spatial patterns. Comparing to single-component systems, the patterns observed in multi-component systems are more complex”--Abstract, page iv

Tipping points in natural systems. An inventory of types, early warnings, and consequences

Hoe creatief om te gaan met de toenemende druk door de menselijke populatie en de mogelijke belangenverstrengelingen van verschillende belangenhouders die dat met zich meebrengt, bv. door systemen meerdere functies tegelijk te laten vervullen. Het KB IV-programma “groenblauwe ruimte” beoogt te onderzoeken hoe, door goed gebruik te maken van de half-natuurlijke terrestrische (‘groene’) en aquatische (‘blauwe’) ruimte, hier oplossingen kunnen worden geboden. Onderzoek heeft uitgewezen dat er in meerdere natuurlijke en menselijke systemen mogelijke ‘kantelpunten’ (Eng. ‘tipping points’) bestaan: Kleine veranderingen in factoren die van belang voor het systeem zijn, kunnen onverwacht leiden tot plotselinge grote veranderingen

The influence of seasonal forcing on the population dynamics of ecological systems

Seasonal forcing represents a pervasive source of environmental variability and it has been shown to be important in generating the cycles observed in many ecological and epidemiological systems. We use a combination of bifurcation analysis and simulation to understand the impact of seasonality on population dynamics, with a focus on predator-prey and host-macroparasite systems. Multi-year cycles with a wide range of periods, quasi-periodicity and chaos are found. We consider the importance of the unforced dynamics in a predator-prey system by contrasting the e ect of seasonality when the underlying behaviour is oscillatory decay to the equilibrium or limit cycles. The limit cycles case shows a wider range of dynamics and multiple solutions. The e ect of variations in the seasonal forcing term are analysed in a predator-prey model by changing the breeding season length, using the vole system in Fennoscandia as a case study. It is found that the period of the multi-year cycles increases as the breeding season length decreases. By studying a general host-macroparasite system, in which the e ect of seasonality has not previously been explored in detail, we nd a larger potential for multiple solution behaviour compared to predator-prey systems. Overall, we show the critical role that seasonality can play in ecological systems