DESTRUCTION OF ONE SPECIES BY ANOTHER 117 



called "innate periodic oscillations," because they depend on the 

 properties of the predator-prey relations themselves, but besides 

 these under the influence of periodic oscillations of external factors 

 there generally arise "induced periodic oscillations" in numbers de- 

 pending on these external causes. The classic example of a system 

 which is subject to innate and induced oscillations is presented by the 

 pendulum. Thus the ideal pendulum the equilibrium of which has 

 been disturbed will oscillate owing to the properties of this system 

 during an indefinitely long time, if its motion is not impeded. But 

 in addition to that we may act upon the pendulum by external forces, 

 and thereby cause induced oscillations of the pendulum. 



If we are asked what proof there is of the fact that the biological 

 system consisting of predator-prey actually possesses "innate" 

 periodic oscillations in numbers of both species, or in other terms that 

 the equation (21a) holds true, we can give but one answer: observa- 

 tions under natural conditions are here of no use, as in the extremely 

 complex natural environment we do not succeed in eliminating "in- 

 duced" oscillations depending on cyclic changes in climatic factors 

 and on other causes. Investigations under constant and exactly 

 controlled laboratory conditions are here indispensable. Therefore, 

 in experimentation with two species of infusoria one of which de- 

 vours the other the following question arose at the very beginning: 

 does this system possess "innate" periodic oscillations in numbers, 

 which are to be expected according to the mathematical theory? 



(4) The first experiments were set up in small test tubes with 

 0.5 cm 3 of oaten medium (see Chapter V). If we take an oaten me- 

 dium without sediment, place in it five individuals of Paramecium 

 caudatum, and after two days introduce three predators Didinium 

 nasutum, we shall have the picture shown in Figure 28. After the 

 predators are put with the Paramecia, the number of the latter 

 begins to decrease, the predators multiply intensely, devouring all 

 the Paramecia, and thereupon perish themselves. This experiment 

 was repeated many times, being sometimes made in a large vessel 

 in which there were many hundreds of thousands of infusoria. The 

 predator was introduced at different moments of the growth of popu- 

 lation of the prey, but nevertheless the same result was always pro- 

 duced. Figure 29 gives the curves of the devouring of Paramecia by 

 Didinium when the latter are introduced at different moments of the 

 growth of the prey population (in 0.5 cm 3 of oaten medium without 



