DESTRUCTION OF ONE SPECIES BY ANOTHER 121 



a vast decrease in the size of the individual. The following data give 

 an idea of the diminution in size of Didinium : three normal individ- 

 uals of this species placed in a medium free of Paramecia continue 

 to multiply intensely, and in an interval of 24 hours give on an aver- 

 age 7.1 small individuals able to attack the prey. This vast increase 

 of the "seizing surface" represents, metaphorically speaking, those 

 "tentacles by means of which the predators suck out the prey com- 

 pletely." Translating all this into mathematical language, we can 

 say: the function characterizing the consumption of prey by preda- 

 tors [fi(Ni, N 2 )], as well as the natality and the mortality of predators 

 [F(Ni, N2)],* are apparently more complicated than Lotka and Vol- 

 terra have assumed in the equation (21a), and as a result the corre- 

 sponding process of the struggle for existence has no periodic proper- 

 ties. We shall soon return to a further analysis of this problem along 

 mathematical lines. 



11 



(1) We have but to introduce a slight complication into the condi- 

 tions of the experiment, and all the characteristic properties of our 

 biological system will be altogether changed. In order to somewhat 

 approach natural conditions we have introduced into the microcosm 

 a "refuge" where Paramecia could cover themselves. For this pur- 

 pose a dense oaten medium "with sediment" was taken (see Chapter 

 V). Direct observations have shown that while the Paramecia are 

 covered in this sediment they are safe from the attack of predators. 

 It must be noted that the taxis causing the hiding of Paramecia in this 

 "refuge" manifests itself in a like manner in the presence of the preda- 

 tors as in their absence. - 



We must have a clear idea of the role which a refuge plays in the 

 struggle for existence of the species under observation, as a lack of 

 clearness can lead further on to serious misunderstandings. If 

 Didinium actively pursued a definite Paramecium which escaping 

 from it hid in the refuge, the presence of the refuge would be a definite 

 parameter in every elementary case of one species devouring another. 

 In other words, the nature and the distribution of refuges would 

 constitute an integral part of the expressions fi(Ni, iV 2 ) and F(N h N 2 ) 

 of the corresponding differential equation of the struggle for existence. 



* See Chapter III, equation (21). 



