Data-driven modelling approaches, including those inspired by statistical physics of complex and disordered systems, are rapidly gaining importance in modern computational biology. In this report we propose approaches to the modelling of experimental evolution protocols like directed evolution, which proceed by alternating cycles of mutation (by error-prone polymerase chain reaction) and selection (e.g. for antibiotic resistance) for some protein of interest. Recently it has been shown in two independent articles that sequence ensembles generated by this approach can be used to gain important structural and functional information about the studied proteins. However, the basic understanding of the potential and the limitations of the experimental approaches remains limited, and the reasons leading to significant differences between the papers remain unclear.