56 1 GENETIC STOCKS AND BREEDING METHODS 



to exceed 95 per cent incross matings, starting with q — 1 ; 22 generations are required 

 to exceed 99 per cent incross matings. For c = 1/10,26 and 39 generations, respectively, 

 are required to exceed 95 per cent and 99 per cent incross matings. It should be noted, 

 however, that when c is not zero this system ensures eventual attainment of animals 

 homozygous and heterozygous at the locus of interest, and otherwise coisogenic, aside 

 from recent mutations. 



Examples of strains of mice produced by this system of mating are: SEC/IGn — se, 

 FS/Gn -fs, and QV/Gn - qv. See Lane 751 for a complete list. 



BROTHER-SISTER INBREEDING WITH HETEROZYGOSIS FORCED BY INTERCROSSING 



This system, brother-sister inbreeding with heterozygosis forced by intercrossing, 

 is useful in putting a recessive lethal mutation on an inbred background. Similarly, 

 any recessive mutation with low viability or fertility when homozygous and its normal 

 allele may be put on a common inbred background. If the new recessive mutation 

 has recently arisen in an already inbred strain, this system provides a way of continued 

 inbreeding. All matings are between heterozygotes, Rr x Rr, with respect to the locus 

 of interest. It will commonly be necessary to determine which are Rr x Rr matings 

 by observing which matings of/?- x R- produce rr progeny. The system is also useful 

 for inbreeding with a semidominant lethal. In this case, all matings are Dd x Dd, 

 DD being lethal, and dd being rejected. 



Let A/a be any other gene pair whose heterozygosity is in question and let c 

 be the probability of crossing over between the a-locus and the r-locus (or ZMocus). 

 Five types of matings may occur with probabilities in G n denoted as follows : 



„ I AR/Ar x AR/Ar\ 

 intercrosses Incrosses P I ' ' ] = p n , 



\aRjar x aR/ar ) 



Crosses P (AR/Ar x aR/ar) = q n , 



(AR/Ar x AR/ar\ 

 aR/ar x aR/Ar 

 AR/Ar x aR/Ar 

 aR/ar x AR/ar I 



Intercrosses 1 AR/ar x AR/ar\ 



(first kind) [aR/Ar x aR/Ar) = V "' 



Intercrosses P (AR/ar x aR/Ar) = w n . 



(second kind) 



The incrosses yield incrosses exclusively in the next generation. The crosses yield 

 intercrosses of the first kind and intercrosses of the second kind in the ratio 1/2: 1/2 in 

 the next generation. The backcrosses each produce three kinds of progeny and then 

 yield four kinds of matings — incrosses, backcrosses, intercrosses of the first kind, and 

 intercrosses of the second kind — in the ratio (1/4) : (1/2) : (1/4)(1 - 2k):(\/2)k, where 

 k = c(\ — c), in the next generation. The intercrosses of the first kind produce four 

 kinds of progeny and all five kinds of matings in the ratio 2k 2 :2k 2 :4k(l — 2k): 



