GENETIC FACTORS IN THE ORIGIN OF DIVERSITY 387 



"short chromosome." In the diagram the spermatogonia have been omit- 

 ted, the first stage shown being the primary spermatocyte. The pairs of 

 chromatids are shown in synapsis. In Fig. 17. 5 A they are lined up in such 

 a manner that the paternal pairs of chromatids are on the left in both 

 cases. As a result two kinds of sperm cells are produced in equal num- 

 bers: (1) those containing the maternal "long chromosome" (with gene 

 B) and the maternal "short chromosome" (with gene S); (2) those 

 containing the paternal "long chromosome" (with gene b) and the 

 paternal "short chromosome" (with gene s). 



It is to be noted, however, that the arrangement of chromatid pairs 

 in synapsis is a chance affair. Sometimes they will line up as shown in 

 Fig. 17. 5 A, but they are equally hkely to line up as shown in Fig. 17.5B, 

 with the pair representing the paternal "long chromosome" on the left, the 

 pair representing the paternal "short chromosome" on the right. As a result 

 of this arrangement sperm cells containing one maternal chromosome and 

 one paternal one are formed, with the accompanying Bs and bS combina- 

 tions of genes. 



The two arrangements of chromatid pairs are equally Hkely to occur, 

 hence the four kinds of sperm cells shown in Fig. 17.5 will occur with 

 equal frequency: BS, bs, Bs, and bS. By a somewhat comparable operation 

 of the laws of chance in female meiosis, a doubly heterozygous, black, 

 short-haired female will produce ova of these same four types. 



What offspring will be expected when doubly heterozygous males and 

 females are mated to each other? In other words, what combinations of the 

 four types of sperms with the four types of ova will occur? This is 

 diagrammed in Fig. 17.6 in the form of a "checkerboard" having four 

 squares on a side. Across the top are placed the four types of ova, along 

 the left-hand margin the four types of sperms. Each square in the diagram 

 represents a fertilized ovum; in each case the genetic formula (genotype) 

 is indicated without drawing the enclosing chromosomes. The squares are 

 numbered. At the bottom of the diagram are shown the four expected 

 types of offspring with the numbers of the squares corresponding to each. 

 We note that nine of the sixteen fertilized ova contain at least one B 

 and at least one 5 and so give rise to black, short-haired offspring; while 

 three of the sixteen contain at least one B but are homozygous ss, and 

 hence result in black, long-haired offspring. Similarly, three of the 

 fertilized ova are homozygous bb but have at least one S; they have the 

 phenotype white, short-haired. Finally, one of the sixteen fertilized ova is 

 homozygous bbss and hence gives rise to a white, long-haired individual. 



We may note that this 9:3:3:1 ratio is merely two 3 : 1 ratios multiplied 



