504 TRANSMISSION 



SECTION XII CHARACTERS TEND TO COMBINE IN 

 DEFINITE MATHEMATICAL PROPORTIONS 1 



The student working with large populations must be struck 

 by the remarkable similarity of the general features of all fre- 

 quency distributions and arrays. Broadly interpreted, this sug- 

 gests a strong mathematical basis in reproduction. 



In all forms of life halving and doubling are basic processes. 

 The number " two," therefore, as a mathematical conception, lies 

 at the bottom of a large share of our biological problems, espe- 

 cially those of variability, and a little consideration will show 

 that the usual form of the frequency distribution is the natural 

 result of the reproductive processes, indeed, that the facts of 

 variability largely, though not exclusively, follow the ordinary 

 mathematical laws of combinations and probabilities. 



The mixing of pure forms. To illustrate this fundamental fact 

 let us undertake to follow the history of two characters brought 

 together for the first time, and the manner in which they will 

 naturally appear in the offspring. 



To put the matter in its simplest form, let us suppose a herd 

 of pure blacks to meet and mingle with a herd (of equal numbers) 

 of pure reds, and that they breed together without restraint, that 

 is, without selection. They will then mate indiscriminately ; that 

 is to say, a black female will mate indifferently with a black or 

 a red male, sometimes with one and sometimes with the other. 



This being true, one half the offspring of the black females 

 will be pure black (designated by B**} and one half will be mixed, 

 black and red (designated by BR). 



The same principle applies to the red females, whose progeny 

 will, in like manner, be equally divided between the mixed off- 

 spring and the pure reds. 



Expressed in tabular form we should then have : 



For every 200 offspring of black females 100 IP + 100 BR 



For every 200 offspring of red females i oo BR + I oo R z 



Total distribution, 400 offspring 100 B z + 200 BR + looT? 2 



In proportion of 2 + 2 BR + K* 



1 This principle was first announced by Quetelet, 1846, in Lettres sur la theorie 

 des probabilites. See Vernon, Variation in Animals and Plants, p. 12. 



