Vol. 6, 1920 
BIOLOGY: A. J. LOTKA 
411 
Starting out first from a broad basis, we may consider a system in the 
process of evolution, such a system comprising a variety of species of 
matter Si, 52. . . .5„ of mass Xi, X2. . . The species of matter 5 
may be defined in any suitable way. Some of them may, for example, be 
biological species of organism, others may be components of the "in- 
organic environment." Or, the species of matter 5 may be several com- 
ponents of an inorganic system in the course of chemical transformation. 
We may think of the state of the system at an instant of time as being 
defined by statement of the values of Xi, X2. . . .Xn; of certain para- 
meters Q defining the character of each species (in general, variable with 
time); and of certain other parameters P. The parameters P will, in 
general, define the geometrical constraints of the system, both at the 
boundaries (volume, area, extension in space), and also in its interior 
(structure, topography, geography) ; they will further define such factors 
as temperature and climatic conditions. 
For a very broad class of cases, including those commonly treated in 
chemical dynamics, but extending far beyond the scope of that branch of 
science, the course of events in such a system will be represented by a 
system of differential equations of the form 
(t = 1,2 n) ) 
If we restrict ourselves to the consideration of evolution at constant 
P's and Q's we may write briefly 
= F.-(Xi,X.....X„). (2) 
The writer has elsewhere^ given a somewhat detailed discussion of the 
general case, in which no special assumption is made regarding the form 
of the functions F, that is to say, regarding the mode of physical inter- 
dependence of the several species and their environment. 
We now proceed to consider a simple special case, as follows : 
The system comprises 
1. A species of organism 5i, a plant species, say, deriving its nourish- 
ment from a source presented in such large excess that the mass of the 
source may be considered constant during the period of time with which 
we are concerned. 
2. A species 52, for example a herbivorous animal species, feeding on Si. 
In this case we have the following obvious relations 
[ Other dead 
Mass of 5i or excretory 
destroyed byi matter elimi- 
52 per unit of | nated from 5i 
time per unit of 
I time 
Rate of in- 
crease of Xi 
per unit of 
time 
Mass of newly 
= formed 5i per 
unit of time 
(3) 
