116 PARASITES OF GIPSY AND BROWN-TAIL MOTHS. 



been present in the spring the insect could never, by any possibility, 

 increase beyond the abundance then prevailing. If the increase each 

 year was 6 egg masses for each 1 of the year before', it was merely 

 necessary to destroy 5 out of every 6 in order to maintain the status 

 quo. If the increase was tenfold, the destruction of 9 out of every 10 

 egg masses would be required, etc. The same would obtain if 5 out 

 of every 6 or 9 out of every 10 eggs in each and every mass were 

 similarly destroyed. 



Reduced to percentages, this would be equivalent to the destruction 

 of 83.33 per cent or of 90 per cent, respectively, a rate of parasitism 

 which was physically an impossible accomplishment for the egg 

 parasites alone. Additional parasitism of the caterpillars or pupae 

 would be a requisite to success, and such parasitism would of neces- 

 sity be similarly limited in many instances through circumstances as 

 completely beyond our control as the physical inability of Schedius or 

 Anastatus to parasitize more than the uppermost layer of eggs in each 

 mass attacked. Without attempting to go into any of the details 

 of the processes by which conclusions were reached, it was finally 

 determined, beyond any doubts arising through arguments which 

 have been presented up to the present time, that an aggregate parasit- 

 ism of 83.33 per cent would be absolutely necessary if a sixfold 

 increase was to be met, but that it made no difference whether this 

 was brought about by one species or two or a dozen, or whether they 

 attacked the egg, the caterpillar, or the pupa?. It was also deter- 

 mined that the aggregate percentage necessary could not be secured 

 by simply adding together the figures representing the parasitism 

 resulting through attack by each of two or more species. It was 

 going to be necessary to combine these * several aggregates in a dif- 

 ferent manner. To illustrate : A 50 per cent .parasitism of the eggs, 

 if it could possibly be secured, followed by another 50 per cent parasit- 

 ism of the caterpillars, could not by any possibility be considered as 

 resulting in 100 per cent parasitism or complete extinction, but only in 

 50 per cent parasitism added to 50 per cent of what remained, which 

 amounted, in effect, to 25 per cent of the whole. In this manner an 

 aggregate of 75 per cent only is secured. 



As is illustrated by the table on page III, it requires the combina- 

 tion of an imposing array of figures representing relatively small per- 

 centages of parasitism in each instance to acquire a sufficiently large 

 aggregate. 



It was further determined that any specific amount of parasitism, 

 as 20 per cent of the eggs, was neither more nor less, but exactly as 

 effective as 20 per cent parasitism of the caterpillars or pupae, in so far 

 as its value in constructing the final aggregate was concerned. 



It can not be denied that when the validity of these conclusions 

 became established and when in addition the possibility that a much 



