Haller's rule is that larger animal species though having absolutely larger brains have relatively smaller brains than related smaller species. It was first proposed by Albrecht von Haller in 1762. It applies both to brains of invertebrates and vertebrates. The rule also applies to eyes.
Most parts of the body, especially the outer and inner surfaces, innervated by the brain grow by the square, but the brain grows by the cube. Therefore the brain of larger animals may be relatively smaller without diminishing its central nervous functions since these functions only expand with area. The surface area to volume ratio. Likewise this is the case of the retina which is part of the central nervous system and determines the size of the eyes.
It was confirmed by Georges Cuvier in 1801 in his Leçons d'anatomie comparée that contains a comparative table of the ratio of brain weight to body weight. Johann Friedrich von Brandt in 1867 linked reduction in brain mass to body mass to the changing ratio of volume and surface area.
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.
- Haller, von A. (1762). Elementa physiologiae corporis humani.
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- Cuvier, G. (1801). Leçons d'anatomie comparée
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