FURTHER DATA ON THE MEASUREMENT OF INBREEDING. 



229 



TABLE I. 



Values of the Successive Coefficients of Inbreedi;ng in the Case 

 of Continued Cousin Mating. 





Ancestral 



Coefficient for 



Coefficient for 



Coefficient for 



Coefficient of 



Generation 



Single Cousins 



Double Cousins 



Brother x 



Inbreeding 



Included 







Sister 



Zo 



1 















Zi 



2 











50.00 



Z2 



3 



25.00 



50.00 



75.00 



Z3 



4 



50.00 



75.00 



87.50 



Z4 







68.75 



87.5(i 



93.75 



Z5 



6 



81.25 



93.75 



96.98 



Z6 



7 



89.06 



96.98 



98.44 



Z7 



8 



93.75 



98.44 



99.22 



Z8 



9 



96.48 



99.22 



99.61 



'Is 



10 



98.05 



99.61 



99.80 



Zio 



11 



98.93 



99.80 



99.90 



Zii 



12 



99.41 



99.90 



99.95 



Z12 



13 



99.68 



99.95 



99.98 



ZlS 



14 



99.83 



99.98 



99.99 



Zl4 



15 



99.91 



99.99 



99.994 



Zl5 



16 



99.95 



99.994 



99.997 



The values of the coefficients of inbreeding (Zo to Z13) for 

 continued single and double cousin matings are shown in Table 

 I. These coefficients are calculated from the usual formula, 



Z = 



100 (p^^^—q^^^) 



(i) 



Pn 



+1 



where /'„ , ^ denotes the maximum possible number of different 

 -individuals involved in the matings of the n~\-i generation, 



Qn+l 



the actual number of different individuals involved in 



these matings. The method of using this formula on a pedigree 

 has been fully explained' and need not be repeated here. 



The data of Table I are given graphically in Fig. 50, together 

 with the curve for brother X sister and parent X offspring. 



From the table and figure it is seen that with continued in- 

 breeding according to any one of these four types the coefficient 

 approaches the value 100. The rate of approach is different, 

 however, in the different cases. The curves fall into two pairs. 

 The brother X sister and the double cousin curves are precisely 

 alike so far as concerns their curvature or shape at any given 

 point. Similarly, the parent X offspring and single cousin curves 



^Me. Agr. Expt. Stat. Bulletin 215, pp. 127-135. 



