SOME QUANTITATIVE ASPECTS OF EVOLUTION 



migrate to the coast, plunge into the sea, and swim until they die. The 

 population is re-established by the few which remain in the mountains. 

 Similarly, those many species which have small over-wintering popula- 

 tions must show bottleneck effects. 



Allometry. As an organism grows, the various parts grow at different 

 rates, so that its proportions change. Thus a baby's head is relatively large, 

 but its growth does not keep pace with that of the rest of the body, and 

 hence its proportionate size in the adult is more moderate. One says that 

 the head shows negative allometry (Greek, differential measurement) or 

 heterogony (Greek, unlike development). On the other hand, the adult 

 teeth are larger in proportion to the head than are the milk teeth, and so 

 tooth development is positively allometric. D'Arcy Thompson first showed 

 that trends of allometric growth can be analyzed mathematically. They 

 correspond to the equation y = bx^, where y is the size of the organ 

 studied, x is the size of the animal as a whole ( or of some part used for 

 comparison), Z? is a constant determined by the value of y when x is 1, 

 and k is the exponent of allometric growth. If k is less than 1, allometry 

 will be negative, while if k is more than 1, allometry will be positive. 



The most obvious application of this is to ontogeny. Thus young ba- 

 boons are only moderately prognathous, but the jaws protrude ever more 





Figure 101. Derivation 

 OF Crab Carapaces of 

 Very Different Appear- 

 ances BY Cartesian 

 Transformations of a 

 Single Original Type. 

 ( From Huxley, "Problems 

 of Relative Growth," 

 Methuen & Co., Ltd., 

 London, 1932. ) 





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