Space structures and different scales for many-component biosystems

The right scale of description, and more generally, the matching between different scales, in modelling physical or biological systems, presents a substantial interest and related difficulties. "This applies for instance to competition/diffusion models of different species, or to the invasion process by an aggressive population against a native one, like tumor cells in a normal tissue. Under a suitable scaling the system may be described by PDE's where space structures are visible, as is shown and discussed here in a tumor growth model. "On the other hand, the separation of scales may be not so sharp: events occurring in `microscopic' regions may affect the macroevolution considerably. This is shown here in a model of metastatic spreading which can be studied like a collection of `proliferating' random walks on the positive one-dimensional lattice