1919] Frost: Mutation in MatthioJa 155 



portions as high as about 1 per cent, and a general mutation coefficient 

 of perhaps 4.5 per cent, while the only Mendelian alternative would 

 seem to be some more complex scheme whose satisfactory formulation 

 might require much more extensive hybridization data. 



To be more specific: (1) these types are not single recessives, since 

 they are not homozygous but split into the mutant and "normal" 

 types; (2) they are not simple cases of multiple recessives, as has 

 been proposed by Heribert-Nilsson (1915) for Oenothera mutations, 

 since what is on that hypothesis the full dominant type reappears with 

 selfing; (3) if these types are single dominants, as they appear to be, 

 they cannot (barring the action of inhibiting factors) arise from the 

 pure recessive "normal" or Snowflake type by segregation, but only 

 by immediate mutation; (4) they are not simple cases of comple- 

 mentary dominant factors, since they occur among the progeny of 

 selfed parents. 



We might assume that a "mutant" type depends on two pairs of 



factors, one homozygous and the other heterozygous, while both pairs 



are heterozygous in the "mutating" Snowflake parent. Thus the 



D Ci 

 crenate type might have the zygotic formula — r , where d is the 



factor for double flowers, C a dominant factor for crenate, and I a 

 dominant inhibitor of C, all three loci being situated in the same 

 chromosome, at distances of, say, 16 and 4 units apart, in the order 

 indicated. A Snowflake parent producing crenate progeny would 



then be , . or ^ ^ , and crossover combinations would produce the 

 dc I del 



apparently mutant crenate progeny. The crenate progeny would 



behave as heterozygous dominants when selfed, and if CC zygotes 



were non-viable would yield constant Snowflake and inconstant 



crenate ; the extracted Snowflake singles, having the composition 



Dei 



-y-^, could ')iot throw crenate individuals except by true mutation of 



c to C. With selfed Snowflake, if we assume 16 per cent and 4 per 

 cent of crossing over in the two positions, and a 60-per-cent selective 

 elimination of crenate zygotes, all CC zygotes being non-viable, sub- 

 stantially the observed percentages of crenate singles and doubles 

 result.-" 



26 See page 125, footnote. This scheme agrees fairly well with the results 

 from crossing, and gives almost exactly the observed proportion of total doubles 

 (a little over 53 per cent) for selfed Snowflake. Its adequate presentation must 

 be reserved for a later paper. 



