Reply to: Comparisons of static brain-body allometries across vertebrates must distinguish between indeterminate and determinate growth

Allometric growth in mass by the brain of mammals

I re-examined published data for ontogenetic change in relative mass of the brain in six species of mammal (i.e., sheep, pig, cow, horse, rat, cat) to illustrate an insidious problem with conventional analyses of brain-body allometry. Graphical displays of logarithmic transformations of the original data for each species give the appearance of two discrete mathematical distributions, but untransformed observations nonetheless conform to a single distribution that is well described by a single, nonlinear equation. The concept of biphasic, allometric growth by the brain consequently is an artifact of transformation. The notion of Rapid and Slow phases in relative growth by the brain also is an artifact, because the notion is based explicitly on the concept of biphasic growth allometry. Relative growth by the brain in sheep, pigs, cows, and horses follows the path of a power curve with an exponent less than 1, so relative growth declines progressively as animals grow to their maximum size, at which point growth effectively ends for both brain and body. Relative growth by the brain in rats and cats follows the path of an exponential curve and consequently is more like relative growth by the brain of odontocoete cetaceans and primates, with the brain growing rapidly relative to the body early in ontogeny and attaining maximum (cats) or near-maximum (rats) mass well before the body reaches its maximum. An exponential pattern of relative growth by the brain appears to have evolved independently in rodents, carnivores, odontocoetes, and primates.