240 



GROWTH 



PRINCIPLES AND THEORY 



(b) Evolutionary allometry 



Thompsonian transformation is essentially typological and does not indicate 

 the law of the evolutionary process. However, many important evolutionary 

 series are governed by the quantitative law of allometry. In the case oi positive 

 allometry, the allometric equation states that the larger the body becomes, the 

 larger is the allometrically growing organ. As long as body size is small, the 

 organ will be rudimentary; it will become more prominent with increasing size. 

 Hence any factor increasing body size will entail enlargement of the organ, 

 not only in absolute size, but also in ratio to the body. The converse applies to 

 negative allometry. 



One classical example is the evolution in titanotheres (Hersh, 1934; Fig. 41). The earliest 

 and smallest forms did not have horns which only appear in later forms. In each of the 

 groups into which the titanotheres split, increasingly larger horns appeared independ- 

 ently, eventually to reach monstrous dimensions. Below a certain body size, an allo- 

 metrically growing organ such as the horn does not appear, as is the case in the earliest 

 and smallest titanotheres. However, although these were too small to develop horns, they 

 transmitted hereditary factors of horn formation to the several descendant groups, which 

 developed horns when a certain body size was reached. 



Evolutionary allometry in the ancestry of the horse was studied by Robb (1935-1937)- 

 Skull and foot show interesting differences. The progressive elongation of the skull (Fig. 42) 

 follows simple allometry; moreover, evolutionary transformation corresponds to the onto- 

 genetic transformation in foetal and postnatal development of the modern horse. Thus, 

 the skull of the 5-month old foetus shows the proportions oi Eohippus; that of the lo-month 

 old those oi Aierychippus; in the newborn the proportions are those oi Pliohippus, and in the 

 one-year old horse, those of Equus scotti. In such way, some 60 million years of evolution 

 appear to be governed by a simple formula, evolutionary increase in body size entailing 

 changes in proportion of the skull. Furthermore, the evolution of the equine skull is a 

 quantitative expression of the biogenetic law, ontogenetic development of the modern 

 horse recapitulating the ancestral series. The latter represents a prolongation of the ontogenetic 

 development of the ancestors inasmuch as, so to speak, new stages are added to the latter in 

 the development of modern horses. 



Total length of skull 



50- 

 40- 



30 

 25 

 20 



15 



10 

 8 

 6 



4- 



I I I \ L_L 



15 202530 4050 80 



Fig. 42. Evolution of the equine skull, a Relative elongation of the preorbital region with 

 increasing body size. Below Eohippus, above Equus. b Allometric plot: correspondence of 



phylogeny and ontogeny. evolution from Hyracotheriiim to Equus; ontogenetic 



development in Equus caballus. After Robb and Simpson from Bertalanffy, 1951a and 



Rensch, 1954. 



