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The conventional allometric power function, with its slope near 2/3, works well for interspecific scaling of brain vs. body weight in all groups of vertebrates. It fails, however, in extrapolation to vertebrates of the largest size within their groups: these have smaller brains than the equation would predict. We propose a correction, the hyperbolic tangent, to linearize the data over all sizes, and we discuss evolutionary reasons for the relatively small brain size of the largest vertebrates.
Roland Bauchot (2008) studied this question.