164 Linkage and Crossing Over 



a case of independent assortment, do they tell us what is the 

 reason for the peculiar ratio? Unfortunately, the answer is 

 no. All we can learn from applying x^ is that we probably do 

 not have two genes on separate chromosomes. 



AVe must then find another explanation for our unusual re- 

 sults. The student must be given a word of caution here. Just 

 any explanation that seems to fit the data will not do except, 

 of course, as a preliminary hypothesis which we are willing to 

 abandon. The explanation must be consistent with known bio- 

 logical observations and should, preferably, be one that can be 

 used to predict future results. Actually, Bateson and Punnett 

 offered an explanation based on the reduplication of parental 

 gametes in excess of nonparental. Although it agreed with the 

 data it was not founded on sound biological facts, and ultimately 

 it was abandoned in favor of the much more accurate explana- 

 tion of linkage and crossing over. 



Could the x^ method be used to show that Brink's testcross 

 data did not indicate independent assortment? Let us retabu- 

 late these data and calculate %^. 



Rg A Rg a rg A rg a 



Observed frequencies 160 103 115 142 



Expected frequencies 130 130 130 130 



d 30 -27 -15 12 



d Vexpected frequencies 6 . 92 5.61 1 . 73 1.11 



x^ = 15.37; n = 3 



Again we have three degrees of freedom, and again our value 

 of x^ is so large that this ratio could be found as the result of 

 chance alone in less than one per cent of our cases. Again, the 

 hypothesis of independent assortment must be abandoned. 



It was stated previously that there was 41.9 per cent crossing 

 over between these two genes. Could the method of x^ be applied 

 to determine whether this observed ratio was a true example of 

 the ratio to be expected if there were 41.9 per cent crossing over? 

 The method is appHcable and is applied just as in the previous 

 case except that the expected frequencies would be different. 

 Since our total population included 520 plants, the expected fre- 

 quency of each crossover class (20.45 per cent of 520) would be 

 108.94, whereas the expected frequency of each parental class 

 (29.55 per cent of 520) would be 151.06. 



