Multiphasic growth models and the evolution of prolonged growth exemplified by human brain evolution

New models for multiphasic growth are presented. They are illustrated by analysis of brain growth in humans and chimpanzees, and the results are used to test the hypothesis of evolution by proportional growth prolongation: that all descendant growth phases are extended by the same factor while each remains at the ancestral growth rate. The results are consistent with the hypothesis and imply that gross brain weight increase towards humans required change in only one growth parameter: prolongation of the nonlinear ancestral growth phases. The restricted and orderly nature of the developmental changes hints at a basis in few genetic changes. Proportional growth prolongation is of general evolutionary importance because it can reorganize body proportions.