Abstract
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 [fishes, amphibians, reptiles, birds and mammals]. It fails in extrapolation to vertebrates of the largest size within their groups: these have smaller brains than the equations would predict. A correction, the hyperbolic tangent, is proposed to linearize the data over all sizes. Evolutionary reasons for the relatively small brain size of the largest vertebrates are discussed.

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