114 BOTANICAL GAZETTE [FEBRUARY 
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 as1:255. The following objections to a Mendelian 
explanation may be enumerated: 
1. O. 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 tour 
factors, followed by several generations of self-pollination, would 
result in an F, with 6.25 per cent of homozygotes, an F; with 
31.64 per cent, F, with 58.62 per cent, F; with 93.75 per cent, 
F, with 96.87 per cent, F, with 98.44 per cent, Fs with 99.22 per 
cent, F, with 99.61 per cent, Fy. with 99.80 per cent, etc. It would 
be utterly absurd to suggest that out of 8 wild mother plants 
growing far apart, selected at random, 7 were tetrahybrids. 
2. An F, 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 
could exhibit 255:1 segregation in the F;. The other F, hetero- 
zygotes would be hybrids of a lower order. Some would segregate 
in the ratio 63:1, 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, sum- 
marized in tables XII and XIII) that every F, (that is, F, with - 
regard to the wild mother plants from Lexington) plant of which 
seeds were planted either yielded a progeny containing no mum- 
mularia mutations, in which case the number was not large enough 
to be sure of getting this mutation, or else the only Mendelian 
ratio indicated as possible was 255:1. In all, 11 F, 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 F, plants, 9 were selected 
from that one-sixteenth of the culture which was still heterozygous 
for four characters. It may be pointed out that among 142 plants, 
just 9 tetrahybrids might reasonably be expected. The chances 
