114 BOTANICAL GAZETTE [rEBRUAEV 



is obvious that a Mendelian explanation of the occurrence and 

 frequency of mut. nummularia involves the assumption that each 

 parent plant which gave rise to it was heterozygous with regard to 

 at least four factors. Otherwise no segregate would occur with so 

 low a frequency as i : 255. The following objections to a Mendelian 

 explanation may be enumerated: 



1. 0. pratincola is probably almost invariably self-pollinated 

 in a state of nature, for the anthers burst in contact with the 

 receptive stigma the day before the flowers open. In a very few 

 generations heterozygosis would be eliminated from a strain which 

 had accidentally become crossed. Hybridization involving four 

 factors, followed by several generations of self-pollination, would 

 result in an F2 with 6.25 per cent of homozygotes, an F3 with 

 31.64 per cent, F4 with 58.62 per cent, F5 with 93.75 per cent, 

 Fe with 96.87 per cent, Fj with 98.44 per cent, Fg with 99. 22 per 

 cent, F9 with 99 . 61 per cent, Fio with 99 . 80 per cent, etc. It would 

 be utterly absurd to suggest that out of 8 wUd mother plants 

 growing far apart, selected at random, 7 were tetrahybrids. 



2. An Fi tetrahybrid would invariably show segregation in a 

 255:1 ratio. Out of its F^ progeny, however, only one plant in 

 16 would be a tetrahybrid, and therefore only one F^ plant in 16 

 covdd exhibit 255:1 segregation in the F3. The other F2 hetero- 

 zygotes would be hybrids of a lower order. Some would segregate 

 in the ratio 63 : i, some in the ratio 15:1, and some in the ratio 3:1. 

 It has already been pointed out (see tables III, V, and VII, simi- 

 marized in tables XII and XIII) that every Fi (that is, Fi with 

 regard to the wUd mother plants from Lexington) plant of which 

 seeds were planted either yielded a progeny containing no num- 

 mularia mutations, in which case the number was not large enough 

 to be sure of getting this mutation, or else the only MendeUan 

 ratio indicated as possible was 255:1. In all, 11 F2 progenies were 

 grown, of which only 2 failed to give the mutation. The only 

 uncomplicated Mendelian explanation requires that in picking 11 

 mother plants at random from among 142 Fi plants, 9 were selected 

 from that one-sixteenth of the culture which was stiU heterozygous 

 for four characters. It may be pointed out that among 142 plants, 

 just 9 tetrahybrids might reasonably be expected. The chances 



