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 disappear in a short time under the influences of the parasite. The diminution 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. Experience has shown that it is almost always to the work of parasites that these rapid retrocessions of injurious species must be attributed.
The damage of the Hyponomeutas to fruit trees is almost always stopped at the end of two or three years by Tachinids, or other parasites. 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 pupæ 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 pupæ of the flies, I obtained in the jars in which I had this stubble enclosed, only a
- 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.