THE PROBLEM OF INBREEDING 147 



mating organisms, and is, properly speaking, 

 nothing else. Furthermore, precise methods of 

 measuring, and hence of comparing, systems of 

 mating which are inbreeding have been sug- 

 gested in these preceding sections of the paper. 



The other two phases or elements of the general 

 problem are logically consequences or effects of the 

 first. The second phase demands for its solution 

 mathematical analysis, falling in the field of 

 probability, with, of course, the limitations implied 

 by general Mendelian principles. The third phase 

 demands experimental investigation. 



I have been at considerable pains to endeavor 

 to make entirely clear and sharply defined the 

 logical elements of the problem of inbreeding for 

 the reason that the distinctions between them seem 

 not always to have been kept in mind. 



The investigation of the second phase of the 

 problem has barely been begun. It has been 

 shown by East and Hayes ^ and Jennings ^ that 

 the proportion of homozygotes increases steadily 

 with continued self-fertilization, which represents 

 the absolutely closest possible form of inbreeding. 

 Jennings summarizes his mathematical results 



1 East, E. M., and Hayes, H. K. "Heterozygosis in Evolution 

 and in Plant Breeding." U. S. Dept. Agr. Bur. Plant Ind. Bulletin 

 No. 243, pp. 1-58, 1912. 



2 Jennings, H. S. "Production of Pure Homozygotic Organisms 

 from Heterozygotes by Self-Fertilization." Amer. Nat., Vol. XLVI, 

 pp. 487-491, 1912. 



