128 THE STRUGGLE FOR EXISTENCE 



introducing immigration into a homogeneous microcosm we obtain 

 periodic oscillations in the numbers of both species. 



in 



(1) The above given example shows that in Paramecium and 

 Didinium the periodic oscillations in the numbers of the predators 

 and of the prey are not a property of the predator-prey interaction 

 itself, as the mathematicians suspected, but apparently occur as a 

 result of constant interferences from without in the development of 

 this interaction. There is evidence for believing that this is char- 

 acteristic for more than our special case. Jensen ('33) in his mono- 

 graph on periodic fluctuations in size of various stocks of fish con- 

 cluded that he has not found any periodicity identic to those treated 

 by Volterra. The same conclusion was arrived at by S. Severtzov 

 ('33) dealing with vertebrates. There are also plenty of entomologi- 

 cal observations showing the possibility of a complete local extermina- 

 tion of hosts by parasites. We may according to Cockerell ('34) re- 

 call some observations on Coccidae (scale insects) made in New 

 Mexico. Certain species occur on the mesquite and other shrubs 

 which exist in great abundance over many thousands of square miles 

 of country. Yet the coccids are only found in isolated patches here 

 and there. They are destroyed by their natural enemies, but the 

 young larvae can be blown by the wind or carried on the feet of birds, 

 and so start new colonies which flourish until discovered by predators 

 and parasites. This game of hide-and-seek results in frequent local 

 exterminations, but the species are sufficiently widespread to survive 

 in parts of their range, and so continue indefinitely. Such local ex- 

 terminations in grayfish have been recently observed by Duffield 



C33). 



(2) Experimental epidemiology is the one domain where the prob- 

 lems of a direct struggle for existence have already been submitted to 

 an exact analysis in laboratory conditions. Therefore let us consider 

 in brief the results there obtained. If we took a microcosm of any 

 size populated by homogeneous organisms, not allowing any immigra- 

 tion or emigration, and if we caused it to be fatally infected, we should 

 obtain a complete dying out of the organisms (if among them there 

 were no immune ones, and if they were unable to acquire any im- 

 munity). In other terms, we should have before us the well-known 

 elementary interaction of two species. However, the process of dying 



