256 GENETICS IN RELATION TO AGRICULTURE 



rapidly toward a homozygous condition in all descendants. Thus, 

 Jennings shows that in the case of the original cross, AA by aa giving all 

 A a, if thereafter all breeding is by self-fertilization, then, after n genera- 

 tions, the proportions of different genotypes in the population may be 

 calculated by the following formulae: 



Aa = ^; 



2" - 1 



aa = n n + i 



Therefore, within six self-fertilized generations after a cross involving a 

 single pair of factors, the proportion of homozygous individuals in the 

 population for one or the other of the two factors will be 98.4 per cent. 

 Hence it is clear that, even though many genetic factors are concerned, 

 as is undoubtedly the case in any crop plant or domestic animal, yet in 

 those species where self-fertilization is the method of reproduction, the 

 fundamental condition necessary to the existence of pure lines is met. 

 Although by definition every pure line is a genotype, yet every genotype 

 is not a pure line, for any heterozygote belongs to some genotype whereas 

 a pure line is necessarily homozygous. Upon the basis of Johannsen's 

 definition, it would be impossible to obtain pure lines from obligatory 

 allogamous species, to which class belong all domestic animals and 

 certain cultivated plants. However, it is clear that continual inbreed- 

 ing in such organisms would tend to produce a homozygous genetic 

 composition. 



Isolation of Pure Lines from Mixed Populations. In order to 

 obtain pure lines from mixed populations the method employed will de- 

 pend upon the method of reproduction of the organism. In autogamous 

 species the method adopted by Johannsen in working with beans is 

 adequate. The individual plant being capable of reproducing the species 

 through self-fertilization and incapable of natural cross-fertilization, 

 it is only necessary to isolate the progeny of single individuals to establish 

 pure lines. However, in supposedly autogamous species natural hybrids 

 sometimes occur. Hence in critical work it is always advisable to pro- 

 tect the flowers even of autogamous plants. In dealing with allogamous 

 species, in which it is necessary to mate two individuals, when starting 

 with a mixed population of unknown genetic factors the original selections 

 must be made on the basis of phenotypic similarity. With domestic 

 animals the repetition of such selection for a large number of generations 

 has produced the "pure" or pedigreed breeds, which approximate more 

 or less closely to pure lines and hence should be expected to breed fairly 



