Chapter IV 

 ON THE MECHANISM OF COMPETITION IN YEAST CELLS 



(1) No mathematical theories can be accepted by biologists with- 

 out a most careful experimental verification. We can but agree with 

 the following remarks made in Nature (H.T.H. P. '31) concerning the 

 mathematical theory of the struggle for existence developed by Vito 

 Volterra: "This work is connected with Prof. Volterra's researches 

 on integro-differential equations and their applications to mechanics. 

 In view of the simplifying hypothesis adopted, the results are not 

 likely to be accepted by biologists until they have been confirmed ex- 

 perimentally, but this work has as yet scarcely begun." First of all, 

 very reasonable doubts may arise whether the equations of the 

 struggle for existence given in the preceding chapter express the 

 essence of the processes of competition, or whether they are merely 

 empirical expressions. Everybody remembers the attempt to study 

 from a purely formalistic viewpoint the phenomena of heredity by 

 calculating the likeness between ancestors and descendants. This 

 method did not give the means of penetrating into the mechanism of 

 the corresponding processes and was consequently entirely aban- 

 doned. In order to dissipate these doubts and to show that the 

 above-given equations actually express the mechanism of competi- 

 tion, we shall now turn to an experimental analysis of a comparatively 

 simple case. It has been possible to measure directly the factors 

 regulating the struggle for existence in this case, and thus to verify 

 some of the mathematical theories. 



Generally speaking, biologists usually have to deal with empirical 

 equations. The essence of such equations is admirably expressed in 

 the following words of Raymond Pearl ('30) : "The worker in practi- 

 cally any branch of science is more or less frequently confronted with 

 this sort of problem: he has a series of observations in which there 

 is clear evidence of a certain orderliness, on the one hand, and evident 

 fluctuations from this order, on the other hand. What he obviously 

 wishes to do ... is to emphasize the orderliness and minimize the 



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