CONTINUOUS VARIATION 



contimtoHs. In any family where the gene of major effect was not 

 segregating, the variation must have been wholly of this continuous 

 kind. 



The variation that we normally see in stature in man, or indeed 

 of size in any organism, is continuous in this way. Stature may vary 

 between wide extremes, and every height between those extremes 

 is represented. There is no discontinuity in the range of statures: 

 the gradations are imperceptible. As a consequence we cannot 

 classify people into tails and shorts in the way that Mendel was able 

 to do with his peas. It is therefore impossible either to specify a 

 family or population in respect of stature by a mendelian ratio of 

 tall to short, or to investigate the inheritance of stature in man by 

 the mendelian method. What method can we use to take its place ? 



The Specification of Continuous Variation 



Where variation in a character is continuous, the number of . 

 classes into which individuals can be divided according to the mani- | 

 festation of the character is limited only by the fmeness of the means 

 we possess for measuring it. Each observation is unique or poten- 

 tially so. We may, however, defme classes with arbitrarily chosen 

 limits and describe any group of individuals by recording the num- 

 bers which fall into each of these classes. Thus we might describe 

 a human population by recording the numbers o£ people with 

 heights between 4 feet 6 inches and 4 feet 7 inches, 4 feet 7 inches 

 and 4 feet 8 inches, 4 feet 8 inches and 4 feet 9 inches, and so on. The 

 members of each class will not, of course, all have exactly the same j 

 height. The representation is therefore only approximate, and a .' 

 closer approximation would be obtained by classifying into ranges 

 of 1^ inch instead of i inch; for the frequency distribution of stature, 

 as it is called, would then approach more closely to the true state . 

 of continuity. The fmer the gradations we use, however, the fewer f 

 individuals will fall into each class, and the more erratic will the 

 distribution appear when limited numbers of individuals are avail- 

 able for measurement. To overcome this difficulty we need a means 

 of specifying the frequency distribution as a whole. We need a means 

 of representing it by a few constants (known as parameters), know- 

 ledge of whose values would enable us to determine the proportion 



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