THE PROBLEM 9 



unlimited, the time taken up by any process which takes place in a 

 limited space, like the process of multiplication of organisms, cannot 

 be unlimited. It also will have a limit, different for every kind of 

 organisms in accordance with the character of its multiplication. 

 The inevitable consequence of this situation is a limitation of all the 

 parameters which determine the phenomena of multiplication of 

 organisms in the biosphere. 



'Tor every species or race there is a maximal number of individuals 

 which can never be surpassed. This maximal number is reached 

 when the given species occupies entirely the earth's surface, with a 

 maximal density of its occupation. This number which I will hence- 

 forth call the 'stationary number of the homogeneous living matter' 

 is of great significance for the evaluation of the geochemical influence 

 of life. The multiplication of organisms in a given volume or on a 

 given surface must proceed more and more slowly, as the number of 

 the individuals already created approaches the stationary number." 



These general notions on the multiplication of organisms have 

 lately received a rational quantitative expression in the form of the 

 logistic curve discovered by Raymond Pearl and Reed in 1920. The 

 logistic law mathematically expresses the idea that in the conditions 

 of a limited microcosm the potentially possible "geometric increase" 

 of a given group of individuals at every moment of time is realized 

 only up to a certain degree, depending on the unutilized opportunity 

 for growth at this moment. As the number of individuals increases, 

 the unutilized opportunity for the further growth decreases, until 

 finally the greatest possible or saturating population in the given 

 conditions is reached. The logistic law has been proved true as 

 regards populations of different animals experimentally studied in 

 laboratory conditions. We shall have an opportunity to consider all 

 these problems more in detail further on. Let us now only note that 

 the rational quantitative expression of growth of groups consisting 

 of individuals of the same species represents a firm foundation for a 

 further fruitful study of competition between species in mixed popu- 

 lations. 



(10) Apart from a great progress as regards the mathematical 

 expression of the multiplication of organisms, an important advance 

 has taken place in the theory of competition itself. The first step in 

 this direction was made in 1911 by Ronald Ross, who at this time 

 was interested in the propagation of malaria. Considering the 



