The non-forking independence relation is not hard to describe in DLO : one can show that C is independent from B over A if and only if every point of C avoid those B-definable intervals which are bad, ie those that are closed, bounded, and disjoint from A. The main result that I will present in this talk is that this very simple characterization of forking also holds in DOAG : we have independence if and only if every point from dcl(AC) avoids the AB-definable intervals that are closed, bounded, and disjoint from dcl(A). In order to establish this characterization of forking by singletons, we will need to manipulate some group valuations which might seem weird at first, but actually interact very well with the model theory. In particular, the notion of a separated family (in a valued vector space) will naturally correspond to orthogonality of types, and thus allow us to restrict our problem to smaller subfamilies, which you can guess will be relevant, given the unary nature of our result. If time allows, we will show that our result naturally extends to every regular ordered Abelian group, one just has to additionnally check the divisibility conditons which characterize non-forking in the stable reduct of torsion-free Abelian groups.