58 GENETIC STOCKS AND BREEDING METHODS 



The two left columns of the intercross are the parental combinations for coupling and 

 the recombinations for repulsion. 



It can be seen that in the double backcross the parental or recombinant type of the 

 gamete can always be recognized from the phenotype of the offspring. The proportion 

 of recombination in the gametes can therefore be estimated directly from the proportion 

 of recombinant phenotypes among the offspring. In the single backcross and inter- 

 cross, however, some of the phenotypes among the offspring result from both parental 

 and recombinant gametes. A direct estimate of recombination is therefore impossible 

 and more elaborate methods become necessary. 



USE OF CHI-SQUARE FOR TESTING SEGREGATIONS AND DETECTING LINKAGE 



Before any effort is expended to detect linkage or estimate recombination, the 

 segregations of the individual genes should be examined to determine whether they are 

 in accordance with expectation, since disturbed segregations may lead to serious errors 

 in estimating recombination. The most useful method for this purpose is that of % 2 . 

 Since explanations of yf are widely available in textbooks on statistical methods, this 

 discussion will be confined to the special formulas useful with linkage data. 



Let a be the observed number of individuals in a class and m be the expected 

 proportion, such that mn is the expected number when n is the total number of in- 

 dividuals. The general formula for % 2 is then 



2 = V ( fl ~ mn ) 



* ^-> mn 

 An algebraically equivalent form which is easier to compute is 



X 2 



*-> \mn) 



If there are two classes of individuals, denoted by 1 and 2, and if the numbers in the 

 two classes, a x and a 2 , are expected to occur in the proportion k:\, % 2 can be more 

 easily calculated from the formula 



{a x - ka 2 ) 2 



X = 



kn 



An example is the segregation of the gene for ruby eye, ru, in the mouse, reported in 

 a cross by Fisher and Snell. 379 An intercross gave the following segregation: 



H — ruru Total 

 Observed number 117 40 157 



Expected proportion 3/4 1/4 



„ (117-120) 2 9 nMn 



y = — = = 019 



1 3 x 157 471 



For one degree of freedom, the deviation from expectation is not significant. 



