SYSTEMS OF MATING 19 



The mating types and their probabilities in G n are : 



Incrosses : 



lAdjAd x ADjAd\ 

 [ad/ad x aDjad ) ~ Pn 



Crosses- (Ad/Ad x aD/ad \ _ 



Crosses. F y^ x AD/Ad ) - <7», 



Backcrosses p lAdjAd x ADjad\ 



(first kind) : W/arf x ai)/^/ = : r "' 



Backcrosses p /Ad/Ad x aD/Ad\ 



(second kind) : \adjad x AD /ad J ™ n ' 



The standard inbred strain is given on the left, the mutant bearer on the right in each 

 mating type. For the case of a recessive mutation, replace each D by r and each d by 

 R. The probability of crossing over between the a- and the ZMocus or the a- and the 

 r-locus is c, where c = 1 /2 when there is no linkage. 



The incrosses each produce one kind of mutant-bearing offspring, which, when 

 mated in turn to the standard strain, yield incrosses in the next generation. The 

 crosses produce doubly heterozygous progeny, considering only the mutant-bearing 

 offspring, which, when mated to the standard inbred strain, yield backcrosses of the 

 second kind. The backcrosses of the first kind produce two kinds of mutant-bearing 

 progeny, ADjAd and aDjAd, or aDjad and ADjad, in the ratio (1 — c):c. The next 

 generation of matings with the standard strain are thus of two types, incrosses and 

 backcrosses of the second kind, in the proportions (1 — c):c. The backcrosses of the 

 second kind produce the same two kinds of progeny, but the ratio is c: (1 — c), so the 

 two types of matings in the next generation, incrosses and backcrosses of the second 

 kind, are in the ratio c: (1 — c). 



These results may be displayed as a set of linear equations, 



from which it is readily seen that the incrosses will steadily increase as n increases, 

 although very slowly He is very small. The initial matings may occasionally be crosses 

 or backcrosses of the first kind. Even so they are converted within one generation into 

 other mating types. Therefore, the equations above may usually be written 



It follows at once that 

 or 



Pn + 1 = Pn + c *n, 



tn + X= (\~c)t n . 



t n = (1 -c)»-% 



t n = (1 -C)"- 1 



when t x = 1 , as is the case if the initial mating is a cross, that is, if q = 1 . 



