294. VARIATION, DISTRIBUTION, AND EVOLUTION OF THE GENUS PARTULA. 
supposition is made, namely, that the observations are reliable as they stand, then 
the figures mean that a great secular change in the direction of lighter color is 
taking place in the whole colony. The former assumption seems to be more war- 
ranted by all of the facts in the case. 
(4) In undertaking the analysis of heredity in the case of the banded and 
bandless characters, the point of departure is the approximate similarity in the 
numerical relations of the two respective classes in the embryonic and adult series. 
In the next place, heredity is alternative, so far as the facts are observed. As the 
material to be analyzed, we have the exclusively dextral collections of 1906 and 
1907, taken from closely contiguous areas; that of 1909 is to be disregarded on 
account of intrinsic difficulties, specifically, the small proportion of banded shells 
and the complication introduced by the presence of sinistral members that presum- 
ably do not freely interbreed with the dextral snails. 
In the general adult population, the plain shells amount to 66.71 per cent (to be 
taken as two-thirds) and the banded shells to 33.28 per cent or one-third. The 
assumption is made that the unbanded pattern is dominant to the banded character, 
for which a partial justification is provided by Lang’s results with Helix, where such 
is the case. 
When, now, the gravid adults are classified according to their contents, they 
are as follows: 
(1) Plain adults: plain young only, 95; both types, 7; banded young only, 24=126 
(2) Banded adults: plain young only, 18; both types, 7; banded young only, 41=66 
Assuming the banded adults to be RR, their mates would have been RR in 
one-third of the cases, or 22. Actually, however, there are 41, so that the difference 
of 19 is to be transferred to the middle class in (2). But as # of the third class 
really belong to the middle one, and fail to display both types of young on account of 
the small average numbers, there is the same correction to be made in the number of 
the first class. Transferring § of 18 to the middle group, the formula becomes: 
(3) Banded adults: plain young, 10; both types, 34; banded young, 22 =66 
Thus we find the relative numbers of DD and DR snails in the unbanded group. 
Testing these results by comparing expectation and the actual figures in the 
independent series of plain parents of (1), the first step is to combine the second and 
third classes, because the latter comprises DR individuals mated with DR and RR. 
These fail to produce both kinds of young only because the offspring are so few. 
The next step is to correct the figure of the first class by subtracting #4, our only 
basis for procedure, and assigning the same number to the middle class, when the 
empirical result becomes: 
(4) Plain adults: plain young, 51; both types, 75=126 
In expectation, 29 of those adults would be DD, and whatever their mates 
would have been their young would be plain. Of the other 97, the expected matings 
and results would be as follows: 
DR XDD in 10/66, or 14.7, plain young only. 
DRX DR in 34/66, or 49.9, both types of young. 
DRXRR in 22/66, or 32.3, both types of young. 
