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     Allow me to add a further note to my discussion 
of treatment of the equilibrium concept in biology/ 
ecology.  There is another figure in here who had 
a well developed idea of equilibrium, even arguably 
of general equilibrium to some extent, and more 
interestingly of dynamic equilibrium (and still more 
interestingly of dynamic non-equilibria), although 
curiously enough he was largely drawing on physics 
ideas.  This was Alfred J. Lotka, whose magnum 
opus was _Elements of Physical Biology_, 1925, 
Baltimore: Williams and Wilkins (reprinted in 1945 
as _Elements of Mathematical Biology_). 
      Lotka is most famous as the originator of the idea 
of the predator-prey cycle, initially in 1920, but fully 
discussed in his 1925 book.  It was taken up and 
advanced further in 1931 by Volterra and more later 
by Kolmogorov, with both Richard Goodwin and Paul 
Samuelson applying it to economics in 1967.  Samuelson 
was very heavily influenced by Lotka in his analysis 
of the relationship between statics and dynamics using 
the Correspondence Principle, and cites Lotka in his 
_Foundations of Economic Analysis_. 
       Lotka was aware of different concepts of equilibrium. 
Thus, in Chap. 9 he drew on Pareto as well as Le Chatelier 
and Maxwell and Poincare for his discussion of static 
equilibrium.  He then distinguished moving equilibria 
from stationary states (and analyzed their local stability). 
He noted a "kinematic" equilibrium" in which "velocities 
vanish," also a "dynamic" equilibrium in which "forces 
are balanced and the resultant force vanishes," an 
"energetic" concept in "virtual work done in any small 
displacement compatible with constraints vanishes," 
which is a minimization of potential energy concept. 
Furthermore he saw evolution as an irreversible 
process driven by the Second Law of Thermodynamics 
and he labeled as "quasi-equilibria" states maintained 
by a "dissipation or degradation of available energy." 
He also consciously used combined human-animal 
examples (mosquitos and humans, for example) and 
said that he was analyzing "the biological basis for 
economics." 
      I note that he studied most of the kinds of dynamic 
patterns of fluctuations that we now know of with the 
major exception of chaotic dynamics.  He well understood 
the important concept of the bifurcation of dynamic 
equilibria, which he got from Poincare.  His work was 
enormously influential on another physicist who went 
into ecology, Robert May, whose 1976 article in Nature 
was the first to consciously suggest the application of 
chaos theory to economics, although some others had 
observed such patterns in economic models without 
understanding what they were observing (Strotz et al, 1953). 
 
References: 
 
Alfred J. Lotka, 1920. "Analytical Notes on Certain Rhythmic 
Relations in Organic Systems," Proceedings of the National 
Academy of Sciences of the United States, 6, 410-415. 
 
Alfred J. Lotka, 1925. Elements of Physical Biology. Baltimore: 
Williams and Wilkns (reprinted in 1945 as Elements of 
Mathematical Biology) 
 
Robert H. Strotz, J.C. McAnulty, and Joseph B. Naines, Jr. 
1953. "Goodwin's Nonlinear Theory of the Business Cycle: 
An Electro-Analog Solution," Econometrica, 21, 390-411. 
[speaking of engineering approaches] 
 
Richard M. Goodwin, 1967. "A Growth Cycle," in C.H. Feinstein, ed. 
Socialism, Capitalism and Economic Growth. Cambridge: Cambridge University 
Press. 
 
Paul A. Samuelson, 1967. "A Universal Cycle?" in R. Henn, ed. Methods of 
Operations Research III. Muhlgasse: Verlag Anton Hain. 
 
Robert M. May, 1976. "Simple mathematical models with 
very complicated dynamics," Nature, 269, 471-477. 
 
Barkley Rosser 
 
 
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