GENETICS IN RELATION TO AGRICULTURE 



TABI.K XV. PHENOTYPIC RATIOS OBTAINED BY EXPANSION OP THE BINOMIAL 



(3 + 1)-. 



For three pairs of factors, therefore, we interpret this table to mean 

 that the distribution with respect to phenotypes is as follows : 



27ABC:QABc:9AbC:9aBC:ZAbc:3aBc:3abC:labc 



If it is desired now to write down the numbers of each particular geno- 

 type in a given phenotype, the procedure according to the method of pro- 

 gression is very simple. Let us select the class 27 ABC the genotypes of 

 which are as follows: 



1AABBCC 

 2AABBCc 

 2AABbCC 

 2AaBBCC 



4AABbCc 

 4AaBBCc 

 4AaBbCC 

 SAaBbCc 



It may be noted that there is one phenotype in each class homozygous 

 for all its factors. In this class starting with this phenotype, we double 

 the number of individuals each time an additional pair of factors becomes 

 heterozygous. Thus there are three genotypes possible with only one 

 heterozygous factor, and there will be two individuals of each of these, 

 there will be three different genotypes having two heterozygous factors, 

 and each of these will be represented by four individuals, and finally 

 there is only one genotype with three heterozygous factors and it is 

 represented by eight individuals. The method of progression is based 

 upon the symmetrical relations which exist in the phenotypic ratios and 

 in the ratios of genotypes within a phenotype and is a very convenient 

 method for general use. 



For illustrative purposes when it is desired to bring out relations 

 graphically the checkerboard method of Punnett is much used. This 

 method has already been employed in this book and needs no extended 

 discussion here. The accompanying general checkerboard for three 

 pairs of factors will illustrate the relations obtaining when this method is 

 employed consistently. As shown in Fig. 48 the gametic series is written 



