title_body: What is a constructed variety of a natural language called?
upvoted_answer: That would be an a posteriori conlang, in contrast with an a priori one. Wikipedia. The process of changing a language through time is called diachronic conlanging. 
  
  An example of a very well-done a posteriori conlang would be Carisitt which has been developed as if it was a natural language deriving from PIE (that is, it is also an example of diachronic conlanging). Examples of an a priori conlang are abundant, for instance all of Tolkien’s works.