22 GENETIC STOCKS AND BREEDING METHODS 



The mean length L of heterozygous chromosome on each side of the locus of 

 interest after n generations of backcrossing is 



/•1/2 



L = (1 - c)«- l de 



= -[1 -(1/2)"] 

 n 



1 

 n 



if n is large and if ? = 1 . This means, for example, that 40 generations of backcrossing 

 will be expected to reduce the mean length of heterozygous chromosome, on both 

 sides of the locus of interest, to about 5 centimorgans or 2.5 centimorgans on each side. 

 Several mutations in mice have been put on standard inbred backgrounds by use 

 of the backcross system. A few examples are: C57BL/6J-/1 3 ', C57BL/6J-Ca.S>, 

 C5im,'S]-Mi^ h ,Cbim,^yW v , BALB/cGnSn-FwC, C3HeB/FeHu-Z^, DBA/1 Hu-Z)j. 

 Complete lists of these strains are given by Lane. 751 Some strains have been propa- 

 gated by brother-sister matings with forced heterozygosis after 5 or more generations 

 of backcrossing to a standard inbred strain. Examples are: C57BL/6J-Pf, C57BL/6J- 

 Ra, and BALB/c-Ts. 



THE CROSS-INTERCROSS SYSTEM 



The cross-intercross system is used to put a recessive, viable gene r on a standard 

 inbred background. The inbred strain is presumably homozygous, A A or aa, for all 

 loci with heterozygosity in question after the onset of crossing. The inbred strain 

 is also presumably RR. Mutant-bearing animals of a stock, inbred or not, are on hand 

 carrying rr at the locus of interest. The objective is to replace the RR of the inbred 

 strain with rr of the mutant stock, while otherwise preserving the homozygosity of the 

 inbred strain. 



The matings proceed in cycles of two generations. The first mating of each cycle 

 is a cross, RR x rr; and the second is an intercross, Rr x Rr, with respect to the 

 locus of interest (figure 5) . 



There are three mating types among the crosses and three among the inter- 

 crosses. The mating types and their probabilities in cycle m (C m ) are : 



Forr-locus: For a-locus: 



CROSSES 



. _ [ARlAR x Ar\Ar\ 



Incrosses P / = p 



\aRjaR x ar/ar J r 



Crosses P ( AR I AR x ar l ar \ _ „ 



Crosses P ^^ ^ ^ _ q m , 



D . _ (ARIAR x Arlar\ 



Backcrosses P ' „ ' = r m , 



\aRjaR x Ar/ar J m ' 



