FOSSORIAL HYMENOPTERA 
451 
be observed among the Fossors : the family Scoliidce having 
an extraordinarily noiseless flight, often not the slightest 
hum being audible from a much more bulky species than the 
noisy Pompilidce. 
It is common knowledge that every living thing produces 
during its lifetime vastly more offspring than can possibly 
survive : the world since long ages being fully stocked, though 
of course, here and there, a slight change of conditions locally 
may enable one species to increase, at the expense of another. 
Hence great numbers must be destroyed by enemies, disease, 
lack of food, or of space. 
The degree to which this is the case is not realised without 
mathematical consideration. Commenting upon this struggle 
for existence, Wallace 1 takes the example of a pair of birds, 
producing four young at a time, for four seasons. 
In fifteen years the progeny, allowed to multiply unchecked, 
would have reached the appalling number of more than two 
thousand millions ! Wallace goes on to show r that, at a minimal 
estimate, whatever the average number of individuals existing 
in any country, at least twice that number must perish annually. 
In the case of insects, the conditions may be represented clearly 
by an equation. 2 Let the total number of each generation 
be represented by X. Then since all but two will perish, the 
total number destroyed by all causes equals X — 2. Let 
Y = number destroyed by vertebrate enemies, P the number 
destroyed by predaceous insects, and p by parasitic insects, 
and m by micro-organisms of disease. Then — 
X — 2 = V + P p m. 
The number destroyed by vertebrate enemies would be — 
V = (X — 2) — • (P + p + m). 
That is to say, if, as I have claimed for Pompilidce, the number 
destroyed by birds and animals is practically nil, then other 
(invertebrate) enemies must do the work, otherwise Pompilids 
would overrun the world and die of starvation. 
1 Natural Selection and Tropical Nature, 1895, p. 24. 
2 This equation was first stated at the meeting of the British Association 
in 1913. 
