There is a wealth of data to which the allometric formula has been successfully applied, including measurements of length, volume, weight, and chemical proportions (
It is interesting to note that the allometric formula also describes a number of quantitative relationships between species. Instead of taking pairs of measurements on growing individuals of different species. By this method it can be shown that certain relations of magnitudes obey a simple law that is related to the fundamental phenomena of general growth. Thus, the relation of cerebro-cortical surface in rodents to the weight of their body (Bok, 1959), or the volume of the neocortex to the volume of the brain in all primates(v.Bonin,1950) can be expressed by simple mathematical formulae. The existence of regularities of this kind should warn us not to attach too great importance to certain structural differences found between species, because they may not necessarily be signs of specific adaptations to a unique condition but simply result from changes in over-all size of the animal. As an example we may cite the extent of folding of man’s cerebral cortex or the size of his corpus callosum or certain transcortical fiber connection, or the size and extent of association cortex, which may be the consequence of growth laws expressed by formulae such as the allometric one instead of being a unique specialization for intelligence or language(see also Sholl, 1948). One of these interpretations does not automatically exclude the other but together they point to the complexity of evolutionary events.
The purpose of these excursions was to show that physiological processes are ultimately dependent upon certain structural features of the organism, even though these features may not be obvious upon superficial inspection. This is particularly so in cases where the dependence is upon internal organs or upon the molecular constitution of component tissues and cells. The peculiarities of structure, on the other hand, are entirely a function of developmental growth；and growth is to be described by temporal and directional (spatial) parameters. The great regularity of developmental histories within species indicates that time and direction of grpwth must be controlled by factors that may be traced back to intracellular activities which are under the control of genes and their influence upon the elaboration of certain enzymes at certain times. The route through which genes affect the over-all patterns of structure and function is their action upon and direction of ontogenesis, especially the prolonging and shortening of growth and differentiation periods; genetic variations between species should, therefore, find their immediate and most dramatic expressions in embryological and postnatal developmental histories. Such an idea is not new. It was proposed(sometimes together with far-reaching and even unwarranted by Goldschmidt (1938) and (1952).
Consideration of this type show that it is possible to talk about language in connection with genetics without having to make shaky assumptions about“genes for language.”It is true that we do not know what the direct relationships are between man’s complement of genes and his mode of communication; we merely wish to outline the theoretical possibilities for relation the two. It is in this vein that the observations on twins and pedigrees, cited below, are to be interpreted (cf. Georgacopoulos, 1954; Grothkopp, 1934; Howie et al., 1961). There is in fact, one line of evidence that makes the general line of argument used here even more plausible. If gene-variations are the raw materials for speciation (played upon by selection ) and this is reflected in inter-species differences in ontogenetic history, then a highly species-specific feature such as the capacity for language might well be involved in some fashion in species-specific developmental peculiarities. Marked inter-specific differences in maturational histories are well-documented and reported upon by Altman and Dittmer (1962), and the material on primates is beautifully reviewed by Schultz(1956).
In Chapter Four we have pointed out that man’s history si markedly different from that of other primates. The human neonate is considerably more immature at birth than our closest of kin, with a concomitant prolongation of differentiation periods and increased susceptibility for various factors to impinge upon the direction of further development. The acquisition of language plays a definite part in this developmental history, its emergence occupying a fixed position within the array of developmental milestones, and there are definite indications that its development is contingent upon a certain aspect of what might be called
(3) Transformations of Form and Function
Closely related to Huxley’s method of studying allometric growth is D’Arcy Thompson’s (1917) famous method of transformations in which he compares related forms such as shown in Fig. 6.6 by the distortions of the coordinates may be studied that result from drawing lines through the homologous points on the second form. This method is purely descriptive and difficult to quantify. But it illustrates the topological relationships between certain forms and how certain differences in structure may be accounted for by a single principle, usually changes in growth gradients during ontogeny, in cases where specific dimensions can be compared allometrically, we would find different values for the parameters a and b (compare Needham, 1964. on allomophosis), of the allometric formula. In an important discussion of D’Arcy Thompson’s transformation, Woodger(1945) pointed out that the phenomenon demonstrated here must be understood in the light of genetics and embryology because no mature form can change, by a process of transformation, into any other.
However, there may be intracellular genetic alterations such that ontogenetic histories are altered resulting in two different mature forms. The situation is diagrammed in Fig. 6.7. There are two molecular structures, Σ1 and Σ2, that are at the basis of two developmental histories H1 and H2. Σ1 and Σ2 are related to one another by by the specification of a molecular transformation called Tm. The developmental histories H1 and H2, result in mature structures S1 and S2. In the case described by D’Arcy Thompson, an apparent transformation relation, Ta, persists that is characterized through the distorted coordinate systems. Notice, however, that the biological connection rests entirely in the molecular and “invisible” transformation Tm and that the apparent transformation Ta is more or less incidental－certainly not essential－for it is obvious that some or even most molecular transformations will alter the developmental histories in such a way that the corresponding two mature structures either lose their isomorphism (as in the isolated case of two-headed monsters or other deformities ) or remain the same to the eyes of the unaided observer as in the case of certain inherited diseases such as hemophilia. Thus, D’Arcy Thompson’s transformation
D’Arcy Thompson對Huxley的allometric學習方法有密切的相關，這種方法完全描寫但難確定數量，在D’Arcy Thompson轉變的重要討論裡，Woodger指出這裡的現象必須按照遺傳學和胚胎學來理解，因為沒有一個成熟的形式能改變一個過程成為其他的。不過，可能有細胞內遺傳學的改變，因此個體發生的歷史被改變成兩個不同的成熟形式。