48 BREEDING CROP PLANTS 



existence in a cross-fertilized species through heterozygosis may be 

 isolated by its means. Weak types appear in self-fertilized species, but 

 are eliminated because they must stand or fall by their own merits." 



Biologists commonly believe that internal or external agencies 

 do occasionally modify the germ plasm. It is also commonly 

 accepted that somatic modifications do not impress themselves 

 upon the germ plasm. From the facts of segregation as explained 

 by the Mendelian law and the acceptance of the theory of factor 

 stability, we may next consider what may be expected in self- 

 pollinating a naturally cross-fertilized plant, such as corn, or 

 what will result in later generations after making a cross in 

 naturally self-fertilized plants. 



Several slightly different formulae have been advanced to show 

 the theoretical expectation. The simplest formula for the per- 

 centage of homozygous types in any generation following a cross 



/2 n l\ m 

 between different forms is f ) . In this formula n is the 



number of segregating generations which has elapsed since the cross 

 was made and m is the number of separately inherited allelomor- 

 phic pairs of factors involved. In self-fertilized organisms this 

 would not absolutely hold unless all the progeny of each genotype 

 were equally productive numerically. 



In artificially self-fertilizing naturally cross-pollinated plants, 

 such as corn, it is theoretically possible to select a completely 

 heterozygous individual in each generation for self-fertilization 

 and thus obtain no reduction in heterozygosis. Jones (1919) 

 has worked out theoretical curves for 1, 5, 10, and 15 allelo- 

 morphic pairs of factors for from one to 10 generations of self- 

 fertilization following a cross. 



Some facts regarding the effects of self-fertilization in genera- 

 tions following a cross are apparent from a consideration of this 

 figure. When only a single allelomorphic pair is concerned, the 

 first generation of selfing reduces the percentage of heterozygous 

 individuals by half. When a number of factor pairs are con- 

 cerned reduction of the percentage of heterozygous individuals is 

 comparatively slow for the first few years of selfing. At the end 

 of 10 years the percentage of heterozygotes is veiy low whether 

 the Initial cross was heterozygous for 15 allelomorphic pairs or 

 for a single allelomorphic pair. From the above discussion it is 

 apparent that after several years of self-fertilization following a 



