6 A Third Cooperative Study of " Vespa Vulgaris " 
(4) On the Variability of the Autumn and Spring Queens. 
Table II gives the standard deviations of the absolute measurements and the 
indices, and we see here at once most interesting and important conclusions can be 
drawn. We note in the first place that for absolute measurements the autumn 
queens are on the average 10 to 12 per cent., and for indices 18 to 22 per cent, 
more variable than the spring queens. Now it would seem that there is only one 
interpretation of this result : The reduced variability of the spring queens as 
compared with the autumn queens is the result of selection after the dispersal of 
the nest population. 
There is only one apparent exception to this rule and that is the case of cell b, 
or measurement B*. Even including this case the reduction is still 10 to 12 per 
cent. 
Now two points must be noted here : 
(a) The standard deviations have been markedly reduced without sensibly 
altering the means. 
Hence, if we assume the distributions to be practically Gaussian and suppose 
autumn queens to provide iVo spring queens, the non-differential deathrate 
being neglected, we shall have : Nij{\/2ir<7^) = N 2 l(^2ir<r 2 ), but a- 1 = lllo- 2 say, for 
absolute measurements. 
Hence N 2 = '90^, or 10 °/ Q of the autumn queens are on the average destroyed 
by a differential deathrate in the case of the absolute measurements. 
In the case of the indices we have : iVo/iVi = (r.Ja 1 = 100/120 = '83 say, or 17 °/ 0 
of the autumn queens are on the average removed by a differential deathrate 
depending on the proportions of the wing. In the case of the ratio of the cell b 
to the total length of the wing, i.e. K = BjA, the loss of variability is about 50 °/ D 
or NJNz = 100/152 = 66 °/ 0 , or 34 °/ Q seem to be destroyed by this ratio diverging 
too far from its mean or type value. 
(b) The reduction of variability is considerably greater in the matter of the 
proportioning of the wing than in the case of absolute size. 
Thus the exact fitness for survival of the queen during the period in which she 
is seeking winter quarters, hibernating and starting to form a new colony, seems 
to depend more considerably on the ratio of the parts of her wings than on their 
absolute size. That 34 °/ G of queens should fail to survive, owing to the failure of 
the proportioning of the cell b to the total length of the wing between autumn 
and spring, will perhaps appear less wonderful to many now than it would have 
* In order to test whether this exception arose from personal equation in determining the length of 
the cell b, the spring series were most carefully remeasured for this character with the reading micro- 
scope. There resulted : 
Correlation J. H. and b 
•515 
■557 
•506 
•617 
No argument has been based on differences of this order; and it was some satisfaction to find that in 
this, the most difficult measurement, independent processes agreed so well. 
Cell 6, mean 
S. D. 
C. of V. 
Beading microscope, E. 
wing 
7-856 
•2023 
2-58 
L. 
wing- 
7-866 
•2043 
2-60 
Ocular micrometer, R. 
wing 
7-770 
•2099 
2-70 
L. 
wing 
7-718 
•2026 
2-59 
