W'rio-ht: Rates' Duchess Cattle 



413 



100% 





^ 



80 



60 



0i/ch€55 I 



-S40 



V) 



■J 20 





-5 -4 -3 -2 -I ] 2 3 4 

 Qenerations from Duchess I 



RELATIONSHIP BETWEEN SIRES AND DAMS OF THE DUCHESSES 



Figure 21. The degrees of relationship between the sires and dams of the eight genera- 

 tions of Duchesses bred by Thomas Bates and six earlier generations in the straight female 

 line. The coefficients of relationship are theoretically equal to the coefficients of correlation 

 with respect to characters which are wholly hereditary and lacking in dominance. 



sister. He constantly introduced fresh 

 blood but only to such an extent as to 

 prevent the relationship from rising 

 above this level. 



The Degree of Inbreeding Used 

 by Bates 



The coefficients of inbreeding of the 

 thirteen generations of Duchesses are 

 shown in the solid line in Figure 

 34. That of their dams (also, of 

 course, Duchesses, but in a differ- 

 ent order) and of their sires are 

 given in dotted and broken lines 

 respectively. The striking feature of 

 this diagram is the similarity of the 

 three lines at a constant level of about 

 40 ]ier cent beginnino- with Duchess I. 

 Duchess by Daisy Bull, two genera- 

 tions earlier, is the first Duchess which 



shows an appreciable amount of in- 

 breeding (30 per cent). Duchess by 

 Favourite in the next generation rises 

 to 33 per cent. Duchess I, bred by 

 Colling and purchased by Bates, rises 

 to 41 per cent. From this point on no 

 generation rises above 47 per cent or 

 falls below 36 per cent. The coefficient 

 for the last generation, 43 per cent, is 

 l)ractically the same as that for Duch- 

 ess 1 and for the average of the first 

 two generations which Bates himself 

 bred. This level of inbreeding is ap- 

 proxmiately equivalent to two genera- 

 tions of straight lirother-sister mating, 

 something over four generations of 

 pure breeding within a herd (half 

 brother-sister mating) and six genera- 

 tions of double first-cousin mating. In 

 maintaining it. Bates used 1)ulls. wheth- 



