The fallacy of biphasic growth allometry for the vertebrate brain.

The concept of biphasic, loglinear growth of the vertebrate brain is based on graphical displays of logarithmic transformations of the original measurements. Such displays commonly give the appearance of two distinct mathematical distributions – one set of observations following a steep trajectory at the low end of the size range and another set following a shallow trajectory at the high end. However, the appearance of two distributions is an artefact resulting from the logarithmic transformations. Observations of brain mass vs. body mass in each of the eight vertebrate species examined in the current investigation conform to a single mathematical distribution that is well described by a single equation fitted to the original, untransformed data by non-linear regression. Data for carp, chickens, kangaroos and rabbits are described by three-parameter power equations whereas those for dolphins and primates are described by exponential functions that rise rapidly to a maximum. The brain continues to grow throughout life in carp, chickens, kangaroos and rabbits but not in dolphins and primates. Future investigations of relative growth of the brain should be based on graphical and analytical study of observations expressed on the native mathematical scale. [ABSTRACT FROM AUTHOR]