SHORTER ARTICLES AND DISCUSSION 



ON THE NUMERICAL EXPRESSION OP THE DEGREE 

 OF INBREEDING AND RELATIONSHIP IN A 

 PEDIGREE 1 



Dr. Raymond Pearl has given in a series of papers ("Studies 

 on Inbreeding," I-VIII )• published in the American Natu- 

 ralist during the years 1913 to 1917 a system of measuring 

 numerically the degree of inbreeding and relationship in a 

 pedigree. 



It will not be necessary to describe the method in any length 

 as it may be familiar to most readers or can easily be found in 

 the original papers. 



The starting point is the fact, that all inbred individuals, not- 

 withstanding the special system of inbreeding involved, have 

 fewer different ancestors in a certain generation than the great- 

 est possible number. 



The degree of inbreeding is measured by the extent of this 

 reduction in numbers of different ancestors. For that purpose 

 a coefficient of inbreeding is determined for each generation ac- 

 cording to the formula 



Zm = 10 0(pn + i - qn+O 

 Pn+l ' 



where p n+ i indicates the greatest possible number of different 

 ancestors in the n -f 1st generation and q n+1 means the actual 

 number of different ancestors in the same generation. 



Plotting the series of values obtained for Z over a base indi- 

 cating the series of generations, the inbreeding curve can be 

 drawn. Maximum values for the coefficient of inbreeding are 

 obtained when continuous brother and sister mating is involved. 

 The brother and sister inbreeding curve has therefore the im- 

 portance as the limit, which no other inbreeding curve can 

 surpass. 



The proportion of the actual inbreeding during a number of 

 generations to the highest possible inbreeding in the same num- 

 ber of generations then offers a fairly good measure for the 



Hygiene and Public Health, Johns Hopkins University, No. 12. 



