CH. XV VARIATION AND EVOLUTION 169 



primarily upon the number and variety of the 

 factors that existed in the two gametes that went 

 to its building. Now most species exhibit consider- 

 able variation and exist in a number, often very 

 large, of more or less well-defined varieties. How 

 far can this great variety be explained in terms 

 of a comparatively small number of factors if the 

 number of possible forms depends upon the number 

 of the factors which may be present or absent ? 



In the simple case where the homozygous and 

 heterozygous conditions are indistinguishable in 

 appearance the number of possible forms is 2, 

 raised ^to the power of the number of factors con- 

 cerned. Thus where one factor is concerned there 

 are only 2^ = 2 possible forms, where ten factors are 

 concerned there are 2^°= 1024 possible forms differ- 

 ing from one another in at most ten and at least one 

 character. Where the factors interact upon one 

 another this number will, of course, be considerably 

 increased. If the heterozygous form is different in 

 appearance from the homozygous form, there are 

 three possible forms connected with each factor ; 

 for ten such factors the possible number of indi- 

 viduals would be 3^^=59,049; for twenty such 

 factors the possible number of different individuals 

 would be 3^^=3,486,784,401. The presence or 

 absence of a comparatively small number of factors 

 in a species carries with it the possibility of an 

 enormous range of individual variation. But every 

 one of these individuals has a perfectly' definite con- 

 stitution which can be determined in each case by 

 the ordinary methods of Mendelian analysis. For 

 in every instance the variation depends upon the 



