QUANTITATIVE INHERITANCE 215 



an estimate of the total genetic variance in this particular F 2 generation. The estimate 

 of the number of genes that cause this genetic variation then comes from a comparison 

 of the amount of genetic variance with the difference of mean between the parental 

 lines that were crossed. It is easy to see that if there are very few genes segregating — 

 say one or two — then the parental values will be easily recovered in the F 2 ; but if there 

 are any more than a few genes the parental values will not be recovered. Therefore 

 the greater the variance in relation to the parental difference, the fewer are the genes 

 segregating. The relationship that estimates the number of genes is 



1 R 2 



n = •= 



where R is the difference between the parental strains, and V (F2) and V (Fl) are the 

 variances of the F 2 and F x generations respectively. This relationship, however, is 

 based on a number of assumptions, and if these do not hold it is not valid. The 

 conditions for its validity are : 



1 . All the + genes are concentrated in one of the parental strains and all the — 

 genes in the other. 



2. The parental strains are highly inbred (or long selected), so that the genes 

 segregating in the F 2 are all at frequencies of one half. 



3. There is no dominance. 



4. There is no linkage. 



5. All the genes have effects of equal magnitude on the character. 



The first of these conditions will hardly ever be met unless the parental strains 

 have previously been selected to their limits in opposite directions. Inbred lines that 

 have not been selected for the character under study are therefore of very little use for 

 this purpose. The second condition is easily satisfied, and will be automatically satisfied 

 if the first condition is met. The third condition is probably not very important, 

 because even if all the genes were fully dominant, the error would not be very great 

 compared with the other sources of error. The fourth condition (absence of linkage) 

 is unlikely to be fulfilled unless there are very few genes. Linkage sets an upper limit 

 to the estimate that it is possible to obtain for the number of genes. There cannot be 

 more genes estimated than there are independently segregating segments of chromo- 

 some. The last condition has already been discussed. It is not so much a condition 

 as a definition of the meaning of the number of genes. The consequence of any of 

 these four conditions not being fulfilled is that the estimate obtained will be lower than 

 the estimate that would have been obtained if the condition had been fulfilled. This 

 is the only comforting feature of the situation because it means that we can be sure that 

 the real number of genes is greater than our estimate. 



