.1^0. 643] GBO]yTH IN CHBOMOSOMES 167 



to be so. Theoretically, all the plants are hereditarily 

 exactly alike. When such a hybrid with segregating 

 gametes is again crossed with a similar first generation 

 hybrid but having a different genetic construction, the 

 result is a mixed lot of plants in which practically every 

 individual differs in some degree germinally from every 

 other. 



This statement holds for any numbers that it would be 

 possible to grow. Every inbred strain of maize, that has 

 so far been obtained by continued self-fertilization with 

 one progenitor in each generation, has differed in many 

 ways from every other inbred line, whether they came 

 originally from the same or different varieties. All the 

 inbred strains coming from different individuals at the 

 start show a noticeable increase in vigor when crossed 

 and a rapid reduction of growth and great increase in 

 variability in the immediately following generations when 

 again self-fertilized. It is therefore not at all improbable 

 that most of the self-fertilized strains differ from each 

 other by a large number of genes in every chromosome. 



If such is the case, then the duplex combination will 

 have an extraordinary amount of genetic diversity. This 

 may be made clearer in the following illustration. If, 

 instead of being crossed, a hybrid was self-fertilized and 

 there was only one factor difference in each pair of 

 chromosomes, over one million plants would have to be 

 grown in order to have an even chance of securing all 

 the possible combinations (assuming maize to have 10 

 chromosomes). But with more than one factor in each 

 chromosome the situation is far different. Two factors 

 in each chromosome having a linkage ratio of 10 per cent, 

 would necessitate 20="' individuals in the segregating 

 generations to obtain the same result. This is calculated 

 from the formula [2(r + 1)"-^]'*- where r + 1 is the link- 

 age ratio, in this case 10 per cent., or 9 4-1, v is the 

 number of factors in each chromosome, and c is the num- 

 ber of chromosome pairs. This number of plants to be 

 grown would require an area roughly 57,346 million 

 times the total surface of the earth. But instead of being 



