100 



(1KNKTICS IN RELATION TO AGRICULTURE 



and in methods of testing the mathematical validity of segregation ratios. 

 Table XVI gives the mathematical relations which obtain in the pro- 

 duction of gametes in F\ individuals and in their union to form the F z 

 zygotes. It is assumed throughout that one factor of each pair of 

 allelomorphs is dominant. 



TABLE XVI. PROPORTIONS EXISTING IN MENDELIAN EXPERIMENTS INVOLVING 

 VARIOUS NUMBERS OF FACTOR DIFFERENCES 



From this table it is clearly apparent how rapidly Mendelian. problems 

 increase in complexity with increases in the number of factor differences. 

 With only five pairs of factors the number of individuals necessary to 

 represent the F z population is 1024 and in order to be sure to have all 

 classes represented it would be necessary to grow four or five times as 

 many individuals as this. In such an experiment there would be 243 

 different genotypes distributed among thirty-two phenotypes. Natu- 

 rally the chances of selecting a homozygous individual would vary ac- 

 cording to the phenotype within which such selection was made, but the 

 average chance of selecting a homozygote would be one in thirty-two, 

 and the chance of selecting such an individual in the class displaying all 

 five dominant characters would be only one in 243. The practical diffi- 

 culties of dealing with large numbers of factor differences are there- 

 fore of considerable importance in planning and carrying out Mendelian 

 experiments. 



Methods of testing the "goodness of fit" of Mendelian ratios depend 

 upon the application of the mathematical theory of probabilities. It 

 is beyond the province of this book to enter into any exhaustive treat- 

 ment of this subject, the present discussion is intended merely to point 

 out the mathematical requirements which must be fulfilled, if no factors 

 are present which tend to disturb the ratio constantly in a given direc- 

 tion. For most problems of this kind it is sufficiently accurate to con- 

 sider the standard deviation of a Mendelian ratio = +\/N(KN 

 where N represents a particular term of a Mendelian ratio and .Krepre- 



