Two controversies exist regarding the appropriate characterization of hierarchical and adaptive evolution in natural populations. In biology, there is the Wright-Fisher controversy over the relative roles of random genetic drift, natural selection, population structure, and interdemic selection in adaptive evolution begun by Sewall Wright and Ronald Aylmer Fisher. There is also the Units of Selection debate, spanning both the biological and the philosophical literature and including the impassioned group-selection debate. Why do these two discourses exist separately, and interact relatively little? (...) We postulate that the reason for this schism can be found in the differing focus of each controversy, a deep difference itself determined by distinct general styles of scientific research guiding each discourse. That is, the Wright-Fisher debate focuses on adaptive process, and tends to be instructed by the mathematical modeling style, while the focus of the Units of Selection controversy is adaptive product, and is typically guided by the function style. The differences between the two discourses can be usefully tracked by examining their interpretations of two contested strategies for theorizing hierarchical selection: horizontal and vertical averaging. (shrink)