106 GENETICS AND EUGENICS 



obviously Cc and cc respectively. A checkerboard is scarcely 

 necessary for cases as simple as these, but will be found very 

 clarifying to thought for the beginner, particularly if he is 

 not accustomed to thinking in algebraic terms, when he comes 

 to deal with crosses involving simultaneously three or four 

 independent characters. 



The essential point about which one must first of all be entirely 

 clear in his own mind is this — what kinds of gametes will each 

 parent form. If he is clear as to this question the calculation 

 of expectations by either method will present no difficulties. 

 It should be borne in mind therefore that the fundamental 

 Mendelian assumptions are (1) that homozygotes form only 

 one type of gamete but (2) that heterozygotes form two 

 types of gametes equally numerous, viz., dominants and re- 

 cessives. Further (3) double heterozygotes {i. e., individuals 

 heterozygous for each of two independent characters) form 

 four types of gametes all equally numerous, and (4) triple 

 heterozygotes form eight types of gametes, all equally numer- 

 ous. (5) In general every additional character in which the 

 individual is heterozygous doubles the assortment of gametes 

 which it would otherwise form. See Table 7. 



TABLE 7 



Zygotic Composition of Parents and the Expected Constitution 



0¥ their Gametes 



Parent Gametes which it will form 



Homozygote, AA all A 



AABB allAB 



« AABBCC all ABC 



Heterozygote, Aa A + a 



" Bb B + b 



" Cc C + c 



Double heterozygote, AaBb AB + Ab + aB + ab 



AaCc AC + Ac + aC + ac 



« BbCc BC + Bc + bC + bc 



Triple " AaBbCc 



ABC + ABc + AbC + aBC 

 + Abe + aBc + abC + abc 



Inspection of a typical checkerboard calculation, that 

 for the F2 generation following a dihybrid cross, shows some 



