METHODS FOR TESTING LINKAGE 61 



In cases such as this where segregations are abnormal, the methods of measuring 

 recombination which will be considered below may not be applicable. For methods 

 dealing with disturbed segregations the reader is referred to Mather, 858 Fisher and 

 Bailey, 376 Bailey, 45 and Carter. 160 



USE OF MAXIMUM-LIKELIHOOD METHODS FOR THE DETECTION AND ESTIMATION 

 OF LINKAGE 



The methods most widely in use for the estimation of linkage are those based on 

 Fisher's maximum-likelihood method of estimation. A simple example will illustrate 

 the principle of the method. 



Consider a coupling single backcross ABjab x Ab\ab. If p is the probability of 

 recombination, the expected proportions or probabilities of the four types of offspring 

 in terms of p can be determined from table 15. Combining the like phenotypes, we 

 obtain 



AB Ab aB ab 



K2-/0 \{\-p) iP i(i-/>). 



Table 15 



Expected proportions of different genotypes among offspring of a single 



backcross 



The expected proportions of offspring for the other types of matings are given in 

 table 16. 



If we represent the expected proportions or probabilities of the four classes by 

 m ls m 2 , m 3 , and ra 4 , and the observed number of offspring in the corresponding classes 

 by a 1} a 2 , a 3 , and a 4 , then the probability, P, of getting such a set of observed numbers 

 from such a mating is proportional to the product of the probabilities for each in- 

 dividual, or 



P = Cm 1 al m 2 a2 m 3 a3 m i , a *. 



