600 GENETICS IN RELATION TO AGRICULTURE 
down the A, 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 A, is, 
therefore, 6; and since the expression p,+1 — Gn+1 18 merely a measure 
of the total number of reappearances, the value of Z; = ®{¢= 37.5 
per cent. In A; 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 
Zs = 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. 
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Generations 
Fie. 233.—Curves of inbreeding: B X S, continued brother X sister matings; P X O, 
continued parent X offspring matings; C? X C?, continued double-cousin matings; C1 X C}, 
continued single-cousin matings. Continued matings of uncle X niece give a curve iden- 
tical with C! x Cl. (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 
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