92 INBREEDING AND OUTBREEDING 



lation as a whole where any number of factors are con- 

 cerned. In any case, almost complete homozygosity is 

 reached in about the tenth generation. 6 



It must be remembered that this reduction applies only 

 to the whole population, or to a representative sample of 

 the population, in which every member is self ed, in which 

 each individual is equally fertile, and in which all the 

 progeny are grown in every generation. In practice in an 

 inbreeding experiment, usually only one individual in self- 

 fertilization or two individuals in brother and sister mat- 

 ings are used to produce the next generation. Thus the rate 

 at which complete homozygosity is approached depends on 

 the constitution of the individuals chosen. Theoretically in 

 any inbred generation the progenitors of the next genera- 

 tion may either be completely heterozygous or completely 

 homozygous or any degree in between depending upon 

 chance. The only conditions which must follow in self- 

 fertilization is that no individual can ever be more hetero- 

 zygous than its parent, but may be the same or less. Thus 

 it is seen that artificial inbreeding, as it is practiced, may 

 theoretically never cause any reduction in heterozygosity, 

 or it may bring about complete homozygosity in the first 

 inbred generation. In other words, the rate at which 

 homozygosity is approached may vary greatly in differ- 

 ent lines. However, as the number of heterozygous fac- 

 tors at the commencement of inbreeding increases the 

 more nearly will the reduction to homozygosity follow the 

 curve shown, because the chance of choosing a completely 



6 Various formulae dealing \rith inbreeding have been proposed and 

 discussed by Pearson (177), Jennings (102, 104, 105, 106,) Pearl (168, 

 169, 170, 171, 172), Fish (69), Wentworth and Remick (213), Robbina 

 (186, 187) which are useful in predicting the character of inbred genera- 

 tions when certain conditions are fulfilled. 



