Gradual separation of scales in biosystems: examples from tumour spreading and population dynamics

It is quite common and useful to describe physical systems at different levels of resolution: micro-, meso- and macroscopic scales are naturally introduced in their modelling. The macroscopic biosystems are usually made of several small components, so that a similar procedure might be used. Here it is emphasized the role of the growth (multiplication) process which produces a "dynamic" transition between the microscopic initial size to the macroscopic one. Examples of this nontrivial interplay between the micro- and the macroscopic scales will be given, in the context of tumour growth modelling and population dynamics.