CHROMOSOMES AND SEX 395 



of the fragments, indicating the presence of many sex factors located 

 in various portions of the X.*^ 



Comparable with the foregoing conception is the "algebraic-sum" 

 hypothesis of Schrader and Sturtevant (1923), who hold that, although 

 the determination of sex depends upon a preponderance of the genetic 

 effect of the factors for one sex over those of the other sex, a certain 

 threshold degree of preponderance is necessary before there can be clear- 

 cut determination.*'* The case of Habrohracon, in which the monoploid 

 parthenogenetically produced males and the occasional diploid biparental 

 males are similar sexually, appears to require a somewhat different 

 explanation/^ 



The effect of heteroploidy on sex in plants is well illustrated by 

 Rumex and Pellia. In Rumex acetosa, as pointed out in an earlier section, 

 the diploid somatic complement of the female consists of 12 autosomes + 

 XX while that of the male consists of 12 + YXY; hence the X: autosome 

 set ratio is 2 : 2 in the female and 1 : 2 in the male. In a series of hetero- 

 ploid forms the following conditions were observed:'*^ a triploid plant 

 with 18 + XXX (ratio = 3:3) was female; a triploid with 18 + XXYY 

 (ratio = 2:3) was bisexual; a tetraploid with 24 + XXX YY (ratio = 

 3:4) was bisexual; a triploid with 18 + XYYY (ratio = 1:3) was male; 

 a tetraploid with 24 + XXYYY (ratio = 2:4) was male. 



In Pellia Neesiana, a heterothallic liverwort, the female gameto- 

 phyte ordinarily has 8 autosomes + X (ratio = 1:1), while the male has 

 8 + F (ratio = 0:1). A race has been discovered in which the gameto- 

 phyte is diploid (18 chromosomes) and the sporophyte tetraploid (36); 

 moreover, this gametophyte is bisexual.*^ Although the mode of origin 

 and cytological constitution of the original bisexual gametophyte are not 

 certainly known, it is thought probable that it arose from a diploid spore 

 formed after ameiosis in a normal sporophyte (16 + XF). If this is 

 true its X: autosome ratio (1:2) is intermediate between those of mono- 

 ploid males and females. In Sphferocarpos Donnellii, diploid gameto- 

 phytes arising from such unreduced spores (14 + XF) are functionally 

 female but frequently show a male tendency in the structure of their sex 

 organs.*^ Simple doubling of the chromosome set in the monoploid 



■*3 Dobzhansky and Schultz (1931). Other portions appear to be without such 

 genes. See Muller and Altenburg (1928), Muller and Stone (1930), Patterson (1931c), 

 and Muller and Painter (1932). For a discussion of the supposed origin of the sex- 

 chromosome mechanism, see Muller (1932). 



*'* See the discussion by Schrader and Schrader (1931). 



«P. W. Whiting (1921), A. R. Whiting (1927, 1928), Torvik (1931). 



*6 Ono (1928, 1930a6), Ono and Shimotomai (1928), Kihara and Yamamoto 

 (1931), Ono (1932). 



" Showalter (1927c). Also in P. epiphylla (Heitz, 19276). 



*8 Lorbeer, 1927; C. E. Allen, 1932. 



