It has been proposed that natural selection occurs on a hierarchy of levels, of which the organismic level is neither the top nor the bottom. This hypothesis leads to the following practical problem: in general, how does one tell if a given phenomenon is a result of selection on level X or level Y. How does one tell what the units of selection actually are?
It is convenient to assume that a unit of selection may be defined as a type of entity for which there exists, among all entities on the same "level" as that entity, an additive component of variance for some specific component F of fitness which does not appear as an additive component of variance in any decomposition of this F among entities at any lower level. But such a definition implicitly assumes that iff (x, y) depends nonadditively on its arguments, there must be interaction between the quantities which x and y represent. This assumption is incorrect. And one cannot avoid this error by speaking of "transformability to additivity" instead of merely "additivity".
A general mathematical formulation of the concepts of interaction and non-interaction is proposed, followed by a correspondingly modified approach to the definition of a unit of selection. The practical difficulty of verifying the presence of hierarchical selection is discussed.