100 GENETICS 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 /; individuals and in their union to form the PF» 
zygotes. It is assumed throughout that one factor of each pair of 
allelomorphs is dominant. 
Taste XVI.—Proportrions Existing IN MmnpreuiAN EXPERIMENTS INVOLVING 
Various Numpers oF Factor DIrrERENCES 
Number of pairs of factors | 1 | 2 Glee Hi oy§ S| Cee n 
— ee ! oa 1 = | 
Number of different kinds of gametes... | 2 | 4 | 8 | 16 | 32 | 64 2” 
Number of combinations of gametes...... | 4 | 16 | 64 }256 |1,024 4,096 4” 
Number of homozygotes in Py........... 2 4 | 8 | 16 | 32 | 64 ae 
Number of heterozygotes in Fy.......... 2 | 12 | 56 |240 | 992 |4,032 |4" — 2 
Number of kinds of genotypes in F2...... | 3 | 9} 27] 81 | 243 | 729 3” 
Number of kinds of homozygous genotypes) 2 4 | 8 | 16 | 32 | 64) 2" 
.Number of kinds of heterozygous geno- | | | 
EVES aes see cout eee 1 Sei RON GS 21a GG slo ale 
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 /’, 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 248. 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 = +1/N(K—N 
where N represents a particular term of a Mendelian ratio and K repre- 
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