I noticed on the early 80s Rush albums, that Peart’s drumming became more like Stewart Copeland’s, he even admitted that The Police were a heavy influence on Rush then.
Oh man... It is as complicated as trying to trace DNA with every artist. We all started at the roots with Jazz like Buddy Rich and adopted more and more complicated licks and styles as we evolved, and as new drummers came out who blew us away with their combinations. I have traced back just a unique cymbal crash sequence back to the first source before, and it was in the 50s yet the particular sequence is still adopted and used by current drummers. All influences amount to the total of ones own individual style. :)