MATHEMATICAL CONSIDERATIONS 83 



viduals are necessary for reproduction. Applying the 

 formula given above, the Coefficients of Inbreeding for 

 each generation in brother and sister mating are : 



= 100 (2-2)= 



2 

 ^ = 100 (4-2) =50 



4 

 Z 2 = 100 (8-2) = 75 



8 



Z 3 = 100 (16-2) =87.5 

 16 



The figures obtained are the differences between the 

 possible number of ancestors and the actual number ex- 

 pressed as percentages of the former. By plotting these 

 percentages for successive generations on the generation 

 number as a base, a curve of inbreeding is obtained which 

 can be compared to the curves obtained by other systems 

 of matings. This comparison is shown in Fig. 22 for the 

 common types of matings as worked out by Pearl. 



From these curves it is evident that continued brother 

 by sister and double first-cousin matings have the same 

 effect, although the latter is one generation behind the 

 former. Also the curves for parent by offspring and sin- 

 gle first-cousin matings are similar in type, but show the 

 same differences in position. In any case the concentra- 

 tion of the lines of descent in these systems of inbreeding 

 is rapid, until after fifteen generations no individual can 

 have more than a fraction of one per cent, of the number 

 of ancestors theoretically possible. 



The Coefficient of Inbreeding alone tells us nothing 

 as to the relation between the different lines of descent. 



