VIII GROWTH AND EVOLUTION 25 1 



to increase in the evolutionary series not continually but by jumps. This corre- 

 sponds to different values of b of the allometric equation in the several orders 

 of mammals. In this way, relative size of the brain (reduced to standard body 

 size) in the series of shrews, moles, primitive ungulates {Tragulidae), higher 

 ungulates, anthropoids, Pithecanthropus, and man stands in a proportion 1:2:4: 

 8 : 16 : 32 : 64. Dubois' theory has been severely criticized both for statistical 

 reasons because his data (as well as the similar ones of Brummelkamp, 1939) do 

 not justify the generalizations drawn (Sholl, 1948; Geiger, 1956); and from the 

 anatomical viewpoint because Dubois' theory neglects the changes in the archi- 

 tecture of the brain (Portmann, 1948; C. Schulz, 1951). 



Other mathematical formulations of the evolutionary allometry of the brain are 

 those of Brummelkamp (1939) according to which, in the transition of a mam- 

 malian order to a higher one, brain size increases not with an integer exponent 

 but rather by \ 2-jumps of cephalization; and that of Count (1947) who proposed 

 an empirical equation : 



However, the good approximation of data by this formula is rather due to 

 the increased number of constants than to a particular significance of the equation 

 for which no theoretical explanation is given (Count and Jerison, 1955). In 

 contrast to Count's formulation, the simple allometric equation well applies in 

 birds but, in contrast to Dubois, with a wide variation of the allometry constant 

 in the different orders (Portmann, 1946-47). Intraspecifically, a wide variation 

 of the allometry constants (a = 0.23-0.74) of brain growth is found in teleosteans; 

 brain size is connected with ecological factors and activity, rather than dependent 

 on the phylogenetic rank (Dubois' cephalization factor) of the species concerned 

 (Geiger, 1956). 



At present, hardly more can be stated than that interspecific increase of brain 

 size in mammals is roughly proportional to the 2/3-power of body weight, and 

 that intraspecific, ontogenetic allometry of the brain shows, as a rule, a much 

 smaller allometry exponent {cf. Table 16, p. 242). 



The cycles in human growth and the unique characteristics of the human brain 

 can also be seen in the allometric growth of the brain. While the relative growth of, 

 e.g., the rat brain, is represented by an unbroken allometric line (Fig. 32, p. 230), 

 that of the human brain follows a curve that can be approximated by 3 allometric 

 lines; the allometric curve being steep in early childhood, subsequently flattening 

 and showing a further break at about 30 kg body weight (Fig. 33, p. 231). 



Another interesting pecularity of considerable significance for the unique 

 position of man, concerns postembryonic development. In mammals and birds, 

 nidifugous and nidicolous species can be distinguished; i.e. such where the young are 

 born relatively mature and capable of independent activity, and such born 

 immature and hence dependent on parental care. This distinction is connected 

 with the index of cerebralization, i.e. the ratio between hemispheres and brain 

 stem. According to Portmann (1944), man represents the unique case of a 

 secondary nidicolous (Table 17). Corresponding to his high cerebralization and 

 owing to a long gestation period, he is born at a stage that would anatomically 



Lileralure p. 253 



