42 THE STRUGGLE FOR EXISTENCE 



certain part (77) of this increase takes up the liberated places, it is 

 evident that a part (1 — 77) will remain unrealized. The mechanism 

 of this "nonrealization" is of course different in different animals. 

 Then as before the intensity of the struggle for existence, or the pro- 

 portion of the unrealized part of the potential increase to the realized 

 part, will be: 



(1 - 7?) bi Ni 1 - V nn n 



77 Oi iVi 77 



(6) We may say that the Verhulst-Pearl logistic curve expresses 

 quantitatively and very simply the struggle for existence which takes 

 place between individuals of a homogeneous group. Further on we 

 shall see how complicated the matter becomes when there is competi- 

 tion between individuals belonging to two different species. But 

 one must not suppose that an intragroup competition is a very simple 

 thing even among unicellular organisms. Though in the majority of 

 cases the symmetrical logistic curve with which we are now concerned 

 expresses satisfactorily the growth of a homogeneous population, 

 certain complicating factors often appear and for some species the 

 curves are asymmetrical, i.e., their concave and convex parts are not 

 similar. Though this does not alter our reasoning, we have to take 

 into account a greater number of variables which complicate the 

 situation. Here we agree completely with the Russian biophysicist 

 P. P. Lasareff ('23) who has expressed on this subject, but in connec- 

 tion with other problems, the following words: "For the development 

 of a theory it is particularly advantageous if experimental methods 

 and observations do not at once furnish data possessing a great degree 

 of accuracy and in this way enable us to ignore a number of secondary 

 accompanying phenomena which make difficult the establishment of 

 simple quantitative laws. In this respect, e.g., the observations of 

 Tycho Brahe which gave to Kepler the materials for formulating his 

 laws, were in their precision just sufficient to characterize the move- 

 ment of the planets round the sun to a first approximation. If on the 

 contrary Kepler had had at his disposal the highly precise observa- 

 tions which we have at present, then certainly his attempt to find an 

 empirical law owing to the complexity of the whole phenomenon 

 could not have led him to simple and sufficiently clear results, and 

 would not have given to Newton the material out of which the theory 

 of universal gravitation has been elaborated. 



