36 



In Tabic I, A B and C represent three allied species living 

 in the same locality, feeding on the same food-plant and having 

 similar fecundity and length of life. Let 60* represent the 

 aggregate constant number in the locality. If the death factors 

 acting upon each were absolutely identical then the constant 

 number 20 for each species would not vary, but remain the 

 same each generation. Let us suppose that 807o of the eggs 

 are killed by a parasite and 50 7o of the larvae likewise killed 

 by another parasite, of the pupae A has none killed, B 25% 

 and C 50%. Then the number of adults hatching out would 

 be 50, 37.5, and 25 respectively. Predators acting upon these 

 to bring them to the constant number 60 would leave them in 

 the proportion of 26, 20, and 14. At the fourth generation 

 they would stand 37, 17 and 6. Theoretically this would lead 

 to the extermination of C and then B, and it is possible that 

 such has happened at times, but most likely the scarcer species 

 have been able to maintain existence in small, favorable locali- 

 ties. 



Immigraxt Supplaxtixg Exdemic Species. 



The figures in Table I could be used to illustrate this sec- 

 tion but I piefer to present others. Let us take another imagi- 

 nary case of a species D (Table II) whose constant number in 

 a given area is 100, in which the sexes are in equal propor- 

 tion and each female gives birth to one hundred eggs. Let the 

 eggs and larvae be attacked by parasites, each to the extent of 

 50%, and the pupae to the extent of 25%, Under normal con- 

 ditions there will be 837.5 adults for the predators to feed upon, 

 leaving the constant number of 100 to carry on the race. 



Into this area let us introduce an allied species whose fec- 

 imdity, food, life-cycle, and susceptibility to parasites are the 

 same, with the exception of the larva which, for one of the many 

 causes easily imagined, escapes free. Let us imagine that this 

 immigrant succeeded in laying her eggs without otherwise up- 

 setting the balance of life. At the end of the first generation 

 there will be 875 adults for the predators to take, leaving 96.15 

 D and 3.85 E to carry on the two races. In the following gen- 

 eration these proportions will be 92.59 and 7.41, and at the end 

 of the sixth generation the immigrant species will be the pre- 



* Here as elsewhere in this paper the figures should be consid- 

 ered as proportions more than individuals. 



