354 INTRODUCTION TO CYTOLOGY 



and male gametes with unusual numbers may not function, especially in 

 competition with normal ones, the megaspores and female gametes are 

 more successful, so that plants with various chromosome numbers appear 

 among the progeny of a triploid. Meiotic irregularity may result in 

 almost complete sexual sterility in some triploid plants; these are often 

 propagated regularly by vegetative means.^ 



The behavior of a pair of Mendelian characters when three homologous 

 chromosomes are present is well illustrated in trisomic maize.^ In Zea 

 the smallest chromosome (number X) of the set carries a factor R for 

 colored aleurone; when the factor is recessive (r), it tends to make the 

 aleurone colorless. In the sporocytes of plants trisomic for this chromo- 

 some there are usually nine bivalents and one trivalent. The distribu- 

 tion of the three members of the trivalent is such that somewhat more 

 than half of the pollen grains carry the normal set of 10 chromosomes, 

 while the remainder (somewhat less than half because of lagging on the 

 part of the extra chromosome) carry 11, including two number X's. 

 However, the 11-chromosome grains do not germinate and develop pollen 

 tubes as rapidly as the competing normal ones, so that the 11-chromosome 

 male gametes tend to be eliminated. From this it follows that the extra 

 chromosome is practically always transmitted to the next generation 

 through the female gamete alone."' 



On the basis of these facts it is possible to calculate the characteristic 

 ratios ^^ of types expected after selfing and back-crossing plants with 

 RRR ("triplex"), RRr ("duplex"), Rrr ("simplex"), and rrr ("nulli- 

 plex"). It is found that the results conform satisfactorily with the 

 expectations. Moreover, since the elimination of male gametes with an 

 extra chromosome is much more complete than that of the corresponding 

 female gametes, the ratios yielded by reciprocal crosses differ. In actual 

 tests the following results were obtained. When pollen from an Rrr 



* E.g., Hyacinthus, Narcissus, Tulipa, Carina, Hemerocallis, and Rosa. 



8H. Hill (1930), McClintock and Hill (1931). 



1" The same is true in strains trisomic for chromosome II, which carries the B-lg 

 linkage group (Besley, 1930). 



11 Blakeslee and Farnham (1923) calculated the ratios for Datura on the basis of a 

 random distribution, two from one, of the three members of the trisome concerned. 

 So calculated, the back-cross ratios for an Rrr maize plant would be IR.lr when the 

 trisomic plant is used as the female parent, and lR.2r when it is used as the male 

 parent. The corresponding ratios for an RRr plant would be 5:1 and 2:1. However, 

 if calculations are made on the basis of the random distribution of six chromatids, the 

 ratios tend to be 7: 8 and 1 : 2 for an Rrr plant, and 4:1 and 2:1 for an RRr plant. The 

 degree of approximation to these latter ratios may be expected to vary with the dis- 

 tance of the genes concerned from the spindle-attachment point, genes near this point 

 tending rather to give the ratios based on the distribution of three whole chromosomes. 

 This is because the chromatids in this region do not segregate at random, and show a 

 relatively low frequency of crossing-over (pp. 302, 323); hence only those genes located 

 far enough away from the spindle-attachment point to escape these restrictions 

 actually give the ratios based on random chromatid distribution. 



