354 POPULAR SCIENCE MONTHLY 



We will have for the first year 300 caterpillars, of which 100 will 

 be parasitized. That will give, as eventually issuing, 200 moths (100 

 females) and 100 parasites (50 females). 



The second year there will be 100 times 100 = 10,000 caterpillars 

 of which 50 times 100 = 5,000 will be parasitized. That will be 5,000 

 issuing moths and 5,000 issuing parasites with 2,500 females of each 

 species. 



The third year the number of caterpillars will be 2,500 times 100 

 = 250,000 and all these will be attacked by parasites so that there 

 will be no moths issuing. 



This theoretical example shows very well how an injurious species, 

 after having increased in threatening progression during several years, 

 immediately after having reached its maximum can suddenly disap- 

 pear in a short time under the influences of the parasite. The diminu- 

 tion of food also contributes to limit the propagation of the plant- 

 feeding species, and may hasten the inevitable triumph of the useful 

 species. Every one who is interested in agricultural entomology 

 knows that incidents like this are frequently observed in nature. 

 When an insect has been very injurious for two or three years, and 

 has multiplied to the point of taking the proportions of a veritable 

 plague, it disappears, usually in a sudden manner at the moment when 

 the alarm which it has provoked has reached its highest degree. Ex- 

 perience has shown that it is almost always to the work of parasites 

 that these rapid retrocessions of injurious species must be attributed. 2 



The damage of the Hyponomeutas to fruit trees is almost always 

 stopped at the end of two or three years by Tachinids, or other para- 

 sites. The same thing occurs with the Bombycids which devastate 

 coniferous forests. 



A remarkable example of the same phenomena is shown with the 

 Cecidomyiids of cereal plants. 



After the destruction caused in Vendee and in Poitou by the 

 Hessian fly and the oat midge, in 1895, these insects disappeared 

 almost completely, and the farmers had no further cause to complain 

 of their presence. 



Now I ascertained that an enormous majority of the pupse which 

 should have been in the grain at the end of 1894, or the beginning 

 of 1895, were parasitized. So much so that it was difficult for me to 

 find specimens with which to carry on certain studies in which I was 

 engaged at that time. Having collected in March, 1895, in the suburbs 

 of Poitiers, some stubble from the harvest of 1894, remaining through 

 the winter and containing an enormous quantity of the pupas of the 

 flies, I obtained in the jars in which I had this stubble enclosed, only a 



2 Aside from parasitic insects, bacterial or fungous epidemics may intervene 

 in a similar manner, but the consideration of these does not fall within the 

 province of this article. 



