We investigate the emergence of spatio-temporal patterns in ecological systems. In particular we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predatorprey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 TuringTakens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns is observed.

In general, the distributions of nutrients and microorganisms in sediments show complex spatio-temporal patterns, which often cannot be explained asresulting exclusively from the temporal fluctuations of environmental conditions and the inhomogeneity of the studied sediment's material. We studied the dynamics of one population of microorganisms feeding on a nutrient in a simple model, taking into account that the considered bacteria can be in an active or in a dormant state. Using this model, we shoew that the formation of spatio-temporal patterns can be the consequence of the interaction between predation and transport processes. Employing the model on a two-dimensional vertical domain, we show by simulations which patterns can arise. Depending on the strength of bioirrigation, we observe stripes or "hot spots"(or "cold spots")with high (or low) microbiological activity. A detailed study regarding the effect of non-homogeneous (depth dependent) forcing by bioirrigation shows that different patterns can appear in different depths.

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Ecological systems are commonly studied by very concrete conventional models or very abstract random matrix models. Here we review and extend the approach of generalized structural kinetic modeling, that offers an intermediate way between these extremes. Generalized models describe systems with a specific structure, but do not restrict the processes in the model to specific functional forms. The approach is based on the construction of a locally linear model in every point of parameter space, in such a way that each element of the model is directly accessible to measurement and has a well defined ecological interpretation. Here we show that generalized models can be used to study the local asymptotic stability of steady states and reveal certain features of the global dynamics. Among other examples we present results on spatial predator-prey system and a complex food web.

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