600 



GENETICS IN RELATION TO AGRICULTURE 



down the A 4 generation we meet with Lord Raglan as a primary reappear- 

 ance as the sire of Mistletoe and further down as the sire of The Czar, also. 

 The total number of primary and secondary reappearances in At is, 

 therefore, 6; and since the expression p n+i q n +i is merely a measure 

 of the total number of reappearances, the value of Z 3 Y\= 37.5 

 per cent. In A 5 we know the total number of secondary reappearances 

 will be 6 X 2 = 12. There is one primary reappearance, that of Will 

 Honeycomb, which must be added to this value, making the total number 

 of reappearances in this generation thirteen. This gives the value 

 Z^ = 40.625 per cent. If we have, therefore, at hand an extended 

 pedigree of an animal it is a simple matter by this method to determine 

 its coefficient of inbreeding for any number of generations. 



100 



60 



40 



20 



// 



8 



10 



12 



14 



246 



Generations 



Fio. 233. Curves of inbreeding: B X S, continued brother X sister matings; P X O, 

 continued parent X offspring matings; C 2 X C 2 , continued double-cousin matings; C 1 X C 1 , 

 continued single-cousin matings. Continued matings of uncle X niece give a curve iden- 

 tical with C 1 X C 1 . (After Pearl.) 



In Fig. 233 are shown a number of curves of inbreeding which show 

 graphically the rate of concentration of blood lines with different types 

 of matings. Continued brother X sister matings give the maximum 

 values for the coefficient of inbreeding. In this connection Pearl calls 

 attention to the similarity of form of the brother-sister and double cousin 

 curves and of the parent-offspring and single cousin curves. 



The Coefficient of Relationship. Obviously it is necessary for 

 determining the significance of the coefficient of inbreeding to know how 

 the reappearances occur in the pedigree. Thus if animals appear on 

 both sire's and dam's line of descent sire and dam are related in some degree. 

 But it is possible as Pearl points out to have a high coefficient of inbreed- 

 ing without any relationship whatever between sire and dam. In fact, 

 specifically the limiting value of the coefficient of inbreeding where sire 



