THE BIOMETRICAL ANALYSIS 



true-b reeding lines and of their F^'s is all non-heritable, but the 

 lines and the F/s differ from one another in their genotypes. Then, 

 if comparable environmental differences are to contribute to the 

 variation (or rather to the quantities representing it) independently 

 of the gcnetical differences, we must fmd a scale on which the 

 variances of the frequency distributions of the lines and of their 

 Fi's are the same, even though their means differ for genetical 

 reasons. 



If the scale used in taking the measurements fails to satisfy these 

 tests, the measurements may be transformed by taking logs, anti- 

 logs, square-roots, squares, or in any other consistent way, and the 

 tests repeated on the new scale. If, as may sometimes happen, no 

 scale is found to be satisfactory on all counts, some suitable com- 

 promise has to be adopted. 



Constitution of the Statistics 



Mendelian theory thus helps us to cope with this first problem of 

 finding a scale suitable for genetical analysis. It is equally essential 

 for our analysis of the statistics which are obtained from the measure- 

 ments represented on that scale. 



Let us denote by 26.^ the difference in phcnotype between two 

 individuals raised in the same environment and differing genetically 

 only by being homozygous for different allelomorphs of the gene 

 A-a. Then, if neither allelomorph is dominant, their heterozygote 

 will have a phcnotype midway between the homozygotes. If there 

 is dominance then let the heterozygote depart by h^ from this mid 

 point. The phenotypcs corresponding to the three genotypes are 

 then related in the following way : — 



aa Aa AA 



- d. K 4 



The effect of gene B-h can be similarly measured in terms of d^ 

 and h.^, and so on, the convention being adopted that the capital 

 letter denotes the allelomorph making for increased manifestation 

 of the character in all genes. Thus A is not of necessity dominant 

 over a: h^^ may depart from the mid-point in either the positive 

 or the negative direction. The same is true oi \\, and furthermore 



So 



