CHAPTER X 



CALCULATING MENDELIAN EXPECTATIONS 



Mendelian expectations may be calculated either by the 

 algebraic method used by Mendel himself or by the ingenious 

 checkerboard method devised by Punnett. The first step 

 in either process consists in ascertaining what factorial com- 

 binations are to be expected among the gametes formed by 

 either parent. By the algebraic method, we ascertain the 

 product of the gametic combinations of the two parents, 

 which will give the zygotic combinations to be expected 

 among their Fi offspring. A repetition of this process, con- 

 sidering the Fi individuals now as parents, will give the 

 combinations to be expected among the F2 offspring, etc. 



For example, if a homozygous colored guinea-pig is crossed 

 with an albino, the gametes formed by the parents contain 

 C and c respectively. The Fi zygotes will contain the two in 

 association, Cc. The gametes formed by the Fi individuals 

 will contain either C or c, or collectively will be C -f e. The 

 Fi female will produce gametes (eggs), C -f- c; the Fi male 

 will produce gametes (sperms), C -f c; the F2 zygotes will 

 correspond with their product or CC 4- 2Cc -t- cc, or one 

 homozygous colored (CC), two heterozygous colored (Cc) 

 and one homozygous albino (cc), or altogether three colored 

 to one albino, the observed average result. 



Suppose now we wish to calculate the result to be expected 

 from a back-cross of Fi with the recessive (albino) parent. 

 The Fi gametes, we have assumed, are C -f- c; the gametes 

 of the recessive parent are all c. Their product is Cc -\- cc 

 or equal numbers of heterozygous colored individuals and 

 albinos, the observed experimental result. 



The checkerboard method of calculating Mendelian ex- 

 pectations consists in writing the gametic contributions of 

 one parent in a series of horizontal squares, each combination 



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