INSECTS INJURIOUS TO AGRICULTURE 355 



cloud of parasites which came out during the months of April and 

 May. 



If one would take the trouble to observe, one could multiply similar 

 examples without difficulty. 



It must be remarked that in the case of which we have just spoken, 

 the injurious species are very injurious only from time to time in a 

 rather periodical manner. Several years will occur in a given region 

 when they are not mentioned. Then, under the influences of certain 

 conditions, they multiply for two or three years in an excessive way, 

 giving rise to terrible invasions, until the parasites favored by this 

 great development of the host species become themselves sufficiently 

 multiplied to bring about the retrocession. This repressive and regu- 

 lating action of the parasite, having for its object the limiting of the 

 increasing abundance of the plant-feeding species, moves then in a 

 successive periodical manner, which recalls a little the action of the 

 siphon of an intermittent fountain. This type of injurious species, 

 with great invasions more or less separated and presenting a periodical 

 character, is met with especially with those species which attack plants 

 cultivated upon a very large scale, and corrects an unstable equilibrium 

 which man himself has provoked by the establishment of great homo- 

 geneous cultures. Exception, however, should be made in regard to 

 certain migratory and omnivorous species, such as the grasshoppers 

 and crickets, whose invasions seem to exist during all time and without 

 any correlation with cultural conditions. 



In other cases which more nearly approach the general and primi- 

 tive law of nature, the injurious species maintains always about the 

 same rank, and the fluctuations which it presents are only of secondary 

 importance. The parasites act as a moderating check to the con- 

 tinued increase, and prevent the injurious species from multiplying in 

 an excessive manner. They are themselves present in almost constant 

 number from one year to the other. Their role is not only to bring 

 back an injurious species to a small number of indidivuals when it has 

 passed the mean, but to hold it constantly at a numerical point much 

 below that which it would reach without their presence. 3 



It is very certain, however, that in nature all the intermediate 

 stages between these two types just mentioned are to be found, and 

 these two types themselves, as we admit, are more theoretical than real. 



3 The condition by which the fraction of parasitized insects remains constant 



£ ft 1 



from year to year is represented by the equation : — — ; c represent- 



b a 



ing the number of eggs laid by an individual of the parasitic species, 6 the 

 number of eggs laid by an individual of the plant-feeding species, and \/a the 

 proportion of parasitized insects. (Bellevoye & Laurent, loc. cit.) In other 

 terms, if a quarter of the insects are parasitized, it would be necessary, in order 

 that this proportion should remain constant from year to year, that the fe- 

 cundity of the parasite should be to that of the host as three is to four. 



