6 THE STRUGGLE FOR EXISTENCE 



For the study of the elementary processes of the struggle for exist- 

 ence in animals we can have recourse to experiments of two types. 

 We can pour some nutritive medium into a test tube, introduce into 

 it two species of animals, and then neither add any food nor change 

 the medium. In these conditions there will be a growth of the num- 

 ber of individuals of the first and second species, and a competition 

 will arise between them for the common food. However, at a cer- 

 tain moment the food will have been consumed, or toxic waste prod- 

 ucts will have accumulated, and as a result the growth of the popula- 

 tion will cease. In such an experiment a competition will take place 

 between two species for the utilization of a certain limited amount of 

 energy. The relation between the species we will have found at the 

 moment when growth has ceased, will enable us to establish in what 

 proportion this amount of energy has been distributed between the 

 populations of the competing species. It is also evident that one 

 can add to the species "prey" growing in conditions of a limited 

 amount of energy the species "predator," and trace the process of one 

 species being devoured by the other. Or, in the experiments of the 

 second type, we need not fix the total amount of energy as a determined 

 quantity, and only maintain it at a certain constant level, continually 

 changing the nutritive medium after fixed intervals of time. In such 

 an experiment we approach more closely to what takes place in the 

 conditions of nature, where the inflow of solar energy is maintained 

 at a fixed level, and we can study the process of competition for com- 

 mon food, or that of destruction of one species by another, in the 

 course of time intervals of any duration we may choose. 



(8) Experimental researches will enable us to understand the 

 mechanism of the elementary process of the struggle for existence, 

 and we can proceed to the next step: to express these processes 

 mathematically. As a result we shall obtain coefficients of the 

 struggle for existence which can be exactly measured. The idea of a 

 mathematical approach to the phenomena of competition is not a 

 new one, and as far back as 1874 the botanist and philosopher Nageli 

 attempted to give "a mathematical expression to the suppression of 

 one plant by another," taking for a starting point the annual increase 

 of the number of plants and the duration of their life. But this line 

 of investigation did not find any followers, and the experimental 

 researches on the competition of plants which have appeared lately 



