THE BIOMETRICAL ANALYSIS 



on the variances of F3 families. It overcomes the first difficulty I 

 because it demands no assumption about the distribution of allelo- 

 morphs between the parental lines; but it magnifies the second 

 dirticulty since differences between the effects of the individual genes 

 reduce this estimate of k to an even greater extent than the first one. 

 Both estimates are also reduced by linkage. 



When all these reservations have been made, the estimates ot k 

 are still instructive. Our experience of the fine gradations which 

 continuously varying characters show, would lead us to expect that 

 many genes w^ould be concerned in the polygenic system governing 

 any particular variation. We find, however, that the estimate of k 

 is never large and is commonly as low as 5 or even less. The value 

 given by the Autirrhi}inin data^ using the first method of estimation, 

 is, for example, k = i -9. The reason for this is that k is not truly 

 an estimate of the number of genes, but of a different unit which 

 we may call the effective factor. 



To see what effective factors are, let us consider a hypothetical 

 case when the parental lines differ by a large number of genes, 

 scattered along the length of every chromosome. Genes which do 

 not recombine must always appear as one in segregation. Now the 

 number of chiasmata, upon the formation of which depends recom- 

 bination of genes within a chromosome, is usually no more than 

 one or two per bivalent. Not all the genes, then, will be separated 

 from their neighbours in the chromosome by chiasmata. In fact, 

 one chiasma will break the chromosome into two pieces, the genes 

 within each of which will segregate together. Two chiasmata will 

 give three such segments, and so on. These segments are the physical 

 basis of the effective factors whose number is estimated by k. At 

 most this number cannot exceed the haploid number of chromo- 

 somes plus the mean number of chiasmata in the nucleus. It must 

 generally be less, for some segments will be unmarked by segregating 

 genes. Furthermore any variation, such as we know normally to 

 occur, in the positions in which chiasmata form, will lead to the 

 effective factors varying in their genie content and effect. This, too, 

 as we have already seen, will reduce the estimate of k. 



The effective factors which emerge from the segregation seen in 

 an F2 may be broken down further in an F3 owing to the formation 

 of chiasmata in new positions at meiosis in the Fo individuals. Thus 



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