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 regulating 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 homogeneous 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 primitive 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 continued 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.
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.
- The condition by which the fraction of parasitized insects remains constant from year to year is represented by the equation: ; c representing the number of eggs laid by an individual of the parasitic species, b the number of eggs laid by an individual of the plant-feeding species, and 1/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 fecundity of the parasite should be to that of the host as three is to four.