54 
A Second Cooperative Stmhj of " Vespa Vulgaris" 
to lay much stress on the differences between us. In round figures we may say 
that the population of a nest is about half as variable as the general population. 
Now it might well be supposed that the queens who survive the winter would 
be a somewhat highly selected group. Such selection would usually tend to 
reduce variability, or we might expect that the variability of the general popu- 
lation of queens in the autumn would be, if anything, still larger relatively to the 
nest population. Is then the large variation of the general population due to a 
great variability of the nest means resulting from local environmental influence, as 
Dr Warren suggests in the case of termites ? Unfortunately we have in our case 
only one nest worked out, and we have no data on local variability or the effect 
of season. But first we ought to consider whether this difference is really incom- 
patible with the effect of heredity on the single nest. Let us suppose the ancestry 
inbred for n generations, and the ancestral coefficients to diminish in a geometrical 
series : 
thus obeying the ancestral law of heredity. Suppose the coefficient of assortative 
mating to be e, for each generation, the mating being that of a brother and sister. 
Then the correlation of the «th and sth midparent will be obtained by considering 
the correlation of the means of two individuals only. Let these be Hn and Hs, 
then, following the lines and notation of a memoir on the ancestral law*, we have, 
if N be total population of pairs, 
Hn = i {hn + mh'n), H^s^i + mh'g), 
S (HnHs) = Npns^n'^s = i {S (hjis) + mSQiJi's) + mS (hsh'n) + m'S{h'nh's)}, 
or pns tn 2s = i (cr„ agVng + ma-n a-'s Vns' + ma; a-'nTn's + 0">n's')- 
Now, as in that memoir, take m = an/cr's = as/a'n, supposing no secular change. 
Further, note that we have 
and 
whence 
^"•^■=lTe 4 • 
If now we suppose the ancestral influence of drone and queen to be equal, or 
not being equal we take r„_s to represent the mean of the four values, we have 
for the correlation between an ?ith and sth midparent, which may be represented 
by pn-s, for it depends only on the difference, 
2 on s I 
= l/7./3~, 
if we take ry = (1 + e)/2a. 
* B. S. Proc. Vol. 62, p. 388. 
