The reconstruction of genealogical relationships between languages is traditionally performed through lexical comparison and the establishment of regular sound changes. The historical analysis of other aspects of linguistic structure, like syntactic patterns or the function of grammatical elements, is normally understood to depend on a previously established thorough understanding of the genealogical structure of the family. In this article we show that it is possible to reconstruct historical changes in morphosyntactic function without assuming detailed knowledge about the genealogical developments of the languages involved. Even more surprisingly, we are able to accurately reconstruct the genealogical structure of a language family using only a limited amount of morphosyntactic variation. As a case study, this article focuses on the nonspatial usage of spatial case marking in the Tsezic languages, a subgroup of Nakh-Daghestanian, spoken in the Caucasus. A new semantic-map-like visualization is developed to represent functional differences in case marking between the various Tsezic languages. Using MAXIMUM PARSIMONY, a reconstruction is proposed for the historical development of the case marking, and the same visualization is used to present the reconstructed historical developments in an insightful manner. Besides various new insights regarding the development of Tsezic case marking, the approach used in this article presents a generally applicable method for the reconstruction of morphosyntactic function.