31 



111 rlit' following cxauiples the tigures arc iiiuigiiuiry for the 

 sake of convenienc, and should be considered as proportions 

 ratlier than individuals; but the original observations and de- 

 ductions that led to them were made on a genus of Delphacidae 

 {Perkinsiella) during four years' observations, extending over 

 the Western and Southern Pacific. My own observations, added 

 to those of Messrs. Perkins and Koebele, have shown that the 

 main death factors working upon the genus in China, Java, 

 Borneo, the Moluccas, New Guinea, Australia and Fiji are 

 similar; yet in those regions in which two or more species 

 exist side by side there is often a great difference in the propor- 

 tional numbers of the species. 



As my observations have been confined to tropical countries, 

 where insects breed during the whole year, I have left out of 

 consideration the effect of climate. Hyperparasitism has been 

 left out of consideration, as it only complicates the ultimate re- 

 sults and shifts the question back a stage; fungus and other 

 diseases have also been ignored, as they only retard, l)ut do not 

 alter, the final results. 



'^Constant" Number. 



One of the facts upon which Natural Selection is l)ased is 

 the constant numl^er of a species within a certain period and 

 area. During the period the number may rise and fall, but 

 eventually returns to the normal. The period between the two 

 minimum points may .comprise only one generation ; in this 

 case the eggs are the most numerous, the larvae less numerous, 

 the pupae still less and the fertile imagoes least of all. Or the 

 period between the minimum points may embrace several gen- 

 erations, in which case the host will increase until it appears 

 likely to become a pest, then it suddenly drops off. 



in Diagram I, I have shown the results of an imaginary 

 case in which the numbers are kept low for convenience. The 

 curve A represents the increase of a host-insect that produces 

 four young, the sexes being in equal numbers. At the eighth 

 generation, if nothing interferes, it will number 512 individ- 

 uals. Curve B represents the increase of a parasite which also 

 lays four eggs, the sexes being in equal proportion, and each 

 young causes the death of one immature host ; it will therefore 

 have a curve similar to A. We will consider that it appears 

 upon the scene at the fourth generation of the host; curve C 



