80 THE STRUGGLE FOR EXISTENCE 



coefficients of the struggle for existence. In this we start by assum- 

 ing that the system of equations of competition (see Chap. 3, equa- 

 tions (11) and (12)): 



dNr K, - Qh + aN 2 ) ) 

 -g.-MT, m 



dt 2 2 K 2 



actually describes the experimental data. All the values in these 

 equations except the coefficients of the struggle for existence a and 

 /3, are known to us. To find the latter let us solve this system of 

 two equations with two unknown values in respect to a and /3. We 

 obtain : 



v dNJdt-K, dN 2 /dt-K 2 .. 



a = ni ; * = m 



The values on the right side of both expressions can easily be calcu- 

 lated from experimental data. Thus in the case of the coefficient 

 a: (1) 6i and Ki are known from the curve of separate growth of the 

 first species, (2) JVi and N 2 , or the volumes of the first and second 

 species in a mixed population at a given moment of time (t), can be 

 taken from the graph by measuring the ordinates of the correspond- 

 ing curves of growth, (3) — - 1 represents the rate of growth of the 



dt 



first species in the mixed population, or the increase of volume per 

 unit of time, and can also be easily determined from the graph. It 

 will be sufficient for this to draw a tangent at a given point and to 



measure — - graphically or, better, to use a Richards-Roope ('30) 

 dt 



tangent meter for graphical differentiation. 3 As a result we shall 



obtain the values of the coefficients of the struggle for existence (a 



and /3) for different points of the curve, i.e., for different moments of 



growth: t h t 2 , etc. The values of the coefficients calculated for 



different moments are subject to fluctuations, but by using the middle 



zone of growth sufficiently constant values will be obtained. Thus, 



3 Made by Bausch and Lomb Optical Co. 



