232 PROBLEMS OF RELATIVE GROWTH 



cross-section across a series of curves for a number of similar 

 processes occurring at different rates, such as are actually 

 visible in Gammarus, but could in Drosophila only be detected 

 by chemical means or by deduction. 



The Gammarus eye-colour curves also show the phenomenon 

 of an equilibrium-position — i.e. the degree of pigmentation 

 finally ceases to change. This merely means that pigment 

 and eye-area are now increasing at the same rate, instead of 

 the pigment-formation proceeding at a more rapid rate as at 

 first — in other words, it corresponds to a change from heter- 

 ogony to isogony, such as we have seen to occur in regard to 

 the size-relations of many organs (Chapter I, etc.). In the 

 case of rate-genes, when this change occurs before birth, we 

 get an apparently fixed character ; but we may either observe 

 (Gammarus wild-type eye) or deduce (human black eyes) that 

 rate-factors have been operative in the prenatal period. 



With all these similarities, we may with some confidence 

 assume that the proportions of parts, at least in so far as they 

 are determined during the period of auxano-differentiation and 

 not during that of histo-differentiation, will be found to be 

 determined by rate-factors operating according to the same 

 rules as have been found to hold for the rate-factors controlling 

 pigmentation in the eye of Gammarus. 



For an interesting corollary of this, we may look to the work 

 of Davenport (1923 ; his p. 151) on human body-build. He 

 has plotted the frequency for relative chest-girth (chest-girth : 

 stature) in man at various ages in a three-dimensional form. 

 If the mean values alone were taken, the age-change would 

 consist in a marked downward slope of the curve from birth 

 to late adolescence, followed by a slight upward tendency, 

 and then often a stable equilibrium-position. When the fre- 

 quency model is examined, however, it is seen not only that 

 there is very great variation at all ages, but that there is a 

 well-marked multimodality. The general shape of the curve 

 indicates that we are dealing with interrelated rate-factors ; 

 the multimodality shows that there exist a few main genetic 

 types, each corresponding to one sort of body-build and 

 determined by a particular gene or set of genes influencing 

 relative growth of chest-girth and/or stature (Fig. 101). 



An important corollary of all this is that we should expect 

 numerous genetically-determined characters concerning relative 

 size of parts to alter with absolute size of body, without there 

 being any change in their genetic basis. The unusual propor- 



