Mechanistically motivated is a term of art in scientific modeling, a description in contrast to phenomenologically motivated. As an abstract from a paper on molecular evolution states
Descriptive models are often said to be phenomenologically motivated whereas explanatory models are said to be mechanistically motivated.
That is, descriptive models of natural phenomena (the phenomenologically motivated) take into account what things are observed, while explanatory models (the mechanistically motivated) take into account why things are observed as they are. The canonical examples of the latter are thermodynamics and quantum mechanics. The former derives its explanations of the workings of heat and work from the axioms of statistical mechanics; the latter derives its explanations of the activity of subatomic particles from the axioms of Hilbert spaces.
Scientific theories are necessarily a mix of the two approaches.