538 



Cytogenetics and Evolution 



can form and develop, that they are all equally fertile, and that 

 the population is large. Selection of mates and mutations of 

 the genes must also be excluded. This condition would be met if 

 equal numbers of AA and aa organisms were suddenly placed 

 together in the same area so that each would have an equal 

 opportunity of mating with one like itself or with one of the 

 other type. All the offspring from all these organisms would 

 then be found in a ratio of lAA : 2Aa : laa, and repeated suc- 

 cessive generations, provided that the original conditions were 

 unchanged, would also show the same ratio of the three types. 

 This constant ratio is always found because the ratio of A to 

 a gametes is always 1 : 1 for all generations. A checkerboard 

 for any one generation would be the same as for the heterozy- 

 gote, because the two types of gametes would be present in the 

 same frequency both in a heterozygous organism and in a popu- 

 lation of many organisms in which there were originally equal 

 numbers of both the AA and aa types. This principle, discov- 

 ered in 1904 by Pearson, is a special case of a general rule 

 formulated independently in 1908 by Hardy and Weinberg. 



In most natural populations, however, it is highly improbable 

 that the original number of AA and aa organisms would be equal. 

 Let us suppose that some cataclysm opened for invasion a new 

 territory and that AA and aa plants were near enough to in- 

 vade. If four times as many AA as aa plants became estab- 

 lished in the new territory, the frequency of the A gene would 

 be four times as great as of the a gene. The ratio of the off- 

 spring of these plants could be determined by the checkerboard 

 method by merely indicating that the gene frequency of A was 

 0.8 and of a 0.2. The percentage of the offspring of each of the 

 three types would then be 64AA : 32Aa : 4aa. 



Provided that the offspring formed a sufficiently large popula- 

 tion, the ratio of A and a gametes would again be 4 : 1, and the 



