DESTRUCTION OF ONE SPECIES BY ANOTHER 139 



teria do not fluctuate in numbers when grown by themselves in 

 sterilized soil; they rise to high numbers and remain at approximately 

 a constant level. Their numbers fall, however, as soon as the soil 

 amoebae are introduced, but no constant level is reached; instead 

 there are continuous fluctuations as in normal soils. There is a 

 sharp inverse relationship between the numbers of bacteria and those 

 of active amoebae; when the numbers of amoebae rise, those of 

 bacteria fall." It is hardly possible therefore to avoid the conclusion 

 that Cutler had to deal here (in a complicated form) with classical 

 periodic variations of the Volterra type. 



In conclusion let us note that this final demonstration of the possi- 

 bility of "classical" oscillations showed that very specialized condi- 

 tions are required for their realization, and it is therefore easy to 

 understand why in real biological systems with their typical adapta- 

 tions leading to very intensive attacks of one species on another the 

 so much discussed "relaxation interaction" between the species ap- 

 parently predominates. 



VI 



(1) In Chapter III we have pointed out that the connection be- 

 tween the relative increase of the predator and the number of prey is 

 not a linear one, and that this is of significance for the processes of one 

 species devouring another. We can now be convinced that this 

 connection is actually non-linear. 



Recently Smirnov and Wladimirow ('34) have investigated under 

 laboratory conditions the connection between the density of the hosts 

 Ni (pupae of the fly Phormia groenlandica) and the relative increase 



of the parasite — —^ [the progeny of one pair ( c? + 9 ) of a para- 



i\' 2 dt 



sitic wasp, Mormoniella vitripennis, per generation]. The experi- 

 mental data they obtained are represented in Figure 40. As the 

 density of the hosts increases, the relative increase of the parasite 

 increases also until it reaches the maximal possible or "potential in- 

 crease" (6 2 ) from one pair under given conditions. That the curve 



showing the connection between — —^- and iVi can actually be ex- 



J\ 2 dt 



pressed by the equation [Chapter III, (23)]: 



N 2 at 



