Results/Conclusions Here we present an evolutionary explanation of species body size diversity that is not based on optimal body-size theory or allometry. Instead, the model is based on constrained cladogenetic diffusion in morphospace, and omits explicit mechanisms for inter-specific competition and other ecological processes. We present new empirical results supporting this explanation of body size diversity, and discuss the model's macroecological and evolutionary implications. For instance: species body size distributions are shaped by a fundamental tradeoff between the short-term selective advantages for (Cope's rule) -- and long-term selective risks of -- increased species body size, in the presence of a taxon-specific lower limit on body size.