276 



MISCELLANEOUS STUDIES 



exceed the percentage from selfed parents; the expected high pro- 

 portion with series 21, however, might well be realized with adequate 

 numbers and good germination. 



In spite of the small totals, it is very probable that linkage similar 

 to that of the selfed cultures prevails with series 21. Where the 

 crenate type is the pollen parent (series 20) linkage ratios are on our 

 hypothesis impossible, since the eggs are all Snowflake and the sperms 

 all double; the data, however, though statistically inconclusive, sug- 

 gest that the excess of singles with crenate and of doubles with Snow- 

 flake is greatly reduced but not abolished. 



TABLE 33 

 hybridization of the Snow flake and crenate-leaved types. Summary. 



If we may ignore the doubtful correlation just mentioned a fairly 

 adequate complete hypothesis for the selfing ratio is possible. Assume 

 (1) a gametic ratio 19 of 5DC :ldC :1Dc :5dc, or 16% per cent of 

 crossing over; (2) non-viability of homozygous crenate (CC) ; (3) low 

 viability of simplex crenate (G'c), eliminating an average of 60 per 

 cent of this type ; and (4) coupling of D and C in all parents tested. 

 Evidence has already been presented for assumptions (1), (2), and 

 (3), except as to the intensity of linkage, while (4), as will be seen, 

 is not at all improbable. 



Random fertilization under these conditions, excepting (3), would 

 give 26DdCc (crenate single) -(- lOddCc (crenate double) -f- 5Ddcc 

 (Snowflake single) -|- 25ddcc (Snowflake double). The other two 

 classes, 5DdCC and IddCC, would be non-viable pure crenate. Adding 

 assumption (3) gives the following comparison: 



! Representing the singleness and doubleness factors by D and d, and the 

 crenate factor and its "normal" allelomorph by C and c. 



[134] 



