Double Chiasmata 211 



single crossover gametes; there would be no noncrossover 

 gametes and no double crossover gametes. Reciprocal and com- 

 plementary types taken together are known as compensating. 



When one of the four chromatids is involved in the forma- 

 tion of both chiasmata and one is involved in neither, the type 

 is known as noncompensating , diagonal, or disparate. There are 

 two such types. If the two chromatids from one chromosome 

 are designated a and b, and the two chromatids of the other 

 chromosome are c and d, and if chromatids b and c exchange seg- 

 ments at the first chiasma, one of the two diagonal types would 

 arise if a and c formed the second chiasma ; the other type would 

 arise if the second chiasma were formed by an exchange be- 

 tween b and d. In each type of diagonal chiasmata, one non- 

 crossover chromatid, two single crossovers, and one double cross- 

 over would be produced, but they would be different chromatids 

 in the two types. As observed cytologically, these two types 

 show no difference, but if one chromosome contained a number 

 of dominant genes and the other chromosome their recessive 

 alleles, the two types would produce very different results 

 genetically. 



An examination of these four types will show why crossing 

 over cannot exceed 50 per cent. If we assume that 2 given non- 

 sister chromatids form the first chiasma and that a second 

 chiasma can be formed at random between any 2 nonsister chro- 

 matids entirely independently of the first chiasma, the four 

 types will occur with equal frequency. When the 16 possible 

 chromatids are tabulated, 4 are found to be noncrossovers, 4 are 

 double crossovers, and 8 are single crossovers. Since the two 

 chiasmata form between the two genes, the noncrossovers and 

 the double crossovers will appear as parental types whereas all 

 the single crossovers will be recombinations. Thus only 8 out 

 of 16 chromatids will be crossover types, and crossing over will 

 be 50 per cent (Fig. 67). 



It might be interesting to consider the effect of three chiasmata 

 on the percentage of crossing over. If each chiasma may be 

 formed at random between any 2 nonsister chromatids, and if 

 the first is formed between 2 given ones, there are sixteen pos- 

 sible arrangements of chiasmata and 64 possible chromatids. Of 

 these, 8 will be noncrossovers, 24 will be double crossovers, 24 



