CALCULATING MENDELIAN EXPECTATIONS 105 



in a different horizontal row. The contributions of the other 

 parent are then written in the same squares, but in vertical 

 rows, instead of horizontal ones (since their distribution con- 

 stitutes a separate contingency) each gametic combination 

 being entered in a different vertical row. The checkerboard 

 will then show (within its individual squares) what factorial 

 combinations are to be expected among the zygotes (progeny 

 of the parents in question) and with what frequencies. 



For the example chosen, the cross between homozygous 

 colored and albino guinea-pigs, all the gametes of each parent 



Egg3 



Eggs 



C c 



01 



a 



a 



C/2 



a 



Fig. 49, Checkerboard method of cal- 

 culating a Mendelian F2 expectation. 



Fig. 50. Checkerboard method of calcu- 

 lating the result of a back-cross between 

 Fi and the recessive parent. 



being alike, the Fi zygotes would be all of one sort, Cc. But 

 since the gametes formed by each Fi parent are of two sorts, 

 C and c, it is evident that the checkerboard must contain 

 two horizontal and two vertical rows, or a total of four 

 squares. (See Fig. 49.) Let us enter C in the upper horizon- 

 tal row and c in the lower row as the gametic contributions 

 of one parent, then enter C in the left vertical row of squares 

 and c in the right vertical row as the contributions of the 

 other parent. We then have the table as shown, one square 

 containing CC, two containing Cc, and one cc, the same result 

 given by the algebraic method. 



For the back-cross of Fi with the recessive parent, only 

 two squares are required. (See Fig. 50.) The recessive parent 

 contributes always c, which we enter in the two squares 

 placed in a horizontal row. The Fi parent contributes C to 

 one square, c to the other. The resulting combinations are 



