250 



I'laXCII'LES OF AXIM.M. lilOlAUlY 



four times in a vcrtiail row, placing; the formula of the spcrmatozotm 

 under the formula of the ejj;^-. Th(> r(\sult follows (Fip;. 199). 



Fig. 199. — Diagram showing the sixteen possible combinations of Fi eggs and sperma- 

 tozoa, hence the sixteen possib'.f kinds of F2 individuals, in crosses where two independent 

 pairs of characters are involved. * 



The four letters in each group are the hereditary formula of one 

 kind of F2 animal. Whenever at least one B and at least one R are in- 

 cluded in this formula, the animal is black and rough. There are nine 

 of these out of each sixteen. When at least one B is present, with two 

 r's (hence no R), the animal is black and smooth. There are three 

 of these in each sixteen. When at least one R is present, with two 

 6's (hence no B), the animal is albino and rough. There are three of 

 these in each sixteen. When neither B nor R is included in the formula 

 (that is, when two &'s and two r's are present), the animal is albino and 

 smooth. There is one such animal in each sixteen. The ratio 9:3: 

 3 : 1 is the characteristic ratio in F2, when two independent pairs of 

 characters are studied simultaneously. While this ratio, and the propor- 

 tions stated above, are given with mathematical precision, it is nowhere 

 intended to imply that every sixteen animals will be divided exactly this 

 way. One class might easily be wanting entirely in so small a number. 

 Actual results of breeding experiments, however, accord as nearly with 

 the expected proportions as the laws of chance require. 



Linkage. — The two characters studied simultaneoush' in the fore- 

 going case were said to be independent. That is, in its hereditary beha- 

 vior, neither character influenced the other in any way. Such is not 

 always the case, however. Occasionally two characters go together much 

 more frequently than would be expected if they were independent. 

 Such characters are said to be linked. Usually, in an Fi individual which 

 is heterozygous for two characters (like the BbRr in the above example), 



