Energy equivalence, the notion that population energy flux is independent of body mass, has become a key concept in ecology. We argue that energy equivalence is not an ecological ‘rule’, as claimed, but a flawed concept beset by circular reasoning. In fact, the independence of mass and energy flux is a null hypothesis. We show that our mechanistic understanding of size–density relationships (SDRs) follows directly from this null model and the assumption that energy limits abundance. Paradoxically, without this assumption energy equivalence has no meaning and we lack a mechanistic understanding for SDRs. We derive an expression for the strength (r 2) of SDRs under the null model, which provides a framework within which to compare published SDRs. This confirms that tight correlations between mass and abundance are a trivial consequence of the span of body masses considered. Our model implies that energy flux varies by five to six orders of magnitude among similarly sized mammals and to a far greater extent in birds. We conclude that the energetic paradigm can be strengthened by considering alternative, non-energetic, hypotheses.