136 Dihybrids, Trihybrids, and Polyhybrids 



degree of freedom; therefore line one of the table must be used. 

 For a 9 : 3 : 3 : 1 ratio, or other ratio composed of four terms, 

 there are three degrees of freedom, and the probability is de- 

 termined from the /^ value in the third line of the table. In 

 ordinary ratios encountered in genetics, the number of degrees 

 of freedom is one less than the number of terms in the ratio. 



A cross made by Demerec in maize can be used as an example. 

 A gene, Vs, causes very young seedlings to be yellowish white, 

 and is recessive to the normal green seedlings. These virescent-3 

 seedlings become green very quickly, but the effect of the gene 

 is striking during early stages of the plant's life. Liguleless 

 leaf (Ig) is recessive to normal (Lg). The F2 segregated into 

 769 nonvirescent, liguled : 247 nonvirescent, liguleless : 279 vi- 

 rescent, liguled : 85 virescent, liguleless. The observed and ex- 

 pected frequencies with deviations and x" are: 



(Z - m)2 



The probability that this observed ratio is a true example of 

 a 9 : 3 : 3 : 1 ratio can be determined from Table 3. It is found 

 that with three degrees of freedom and a x" of 2.2042, the prob- 

 ability is between 50 and 70 per cent. This means that if the 

 experiment were repeated a large number of times, as great a 

 deviation as this or a greater would be found in 50 to 70 per 

 cent of the number of times the cross was repeated. The devi- 

 ation found here was undoubtedly the result merely of chance. 

 If x^ was of such value that this deviation would occur in less 

 than 5 per cent of the reported trials, it would generally be 

 considered that it did not fit and that something other than 

 chance was causing the deviation. 



Trihybrids 



If two plants or animals differ with respect to three pairs of 

 genes in three pairs of autosomes, the Fo ratios are fairly com- 



