Population dynamics with internal and external structures

All situations considered in population dynamics have a common problem that could be characterized as the "structure" distribution problem. The objects forming a population, like polymers, cell structures, single cells, cells in a tissue, animals or people can be modelled with different degrees of internal structure, like age, energy content, metabolic activity, or health status. On the other side the individual's environment has in general itself a structure, bacteria in the soil live in a porous medium, oceanic populations must cope with turbulent diffusion and oceanic currents, human populations are mixed by various processes affecting for example the spread of diseases, and trees experience self-induced vertical solar energy gradients. It is clear that any realistic structuring of a population gives rise to arbitrary complex models. It is important to find consistent frameworks which allow a sufficient projection of the real-world problem into mathematical equations and furthermore are sufficiently tractable by analytical and numerical methods. In the talk I will give some concrete (mostly ecological and biotechnological) examples how such a modelling program can be followed. Here the mathematical restriction will be to use deterministic models, i.e. PDE and integral equations.