Alfred J. Lotka
CONTRIBUTION TO THE ENERGETICS OF EVOLUTION
Narrated by William Dufris
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It has been pointed out by Boltzmann that the fundamental object of
contention in the life-struggle, in the evolution of the organic world, is
available energy. In accord with this observation is the principle that,
in the struggle for existence, the advantage must go to those organisms
whose energy-capturing devices are most efficient in directing available
energy into channels favorable to the preservation of the species.
The first effect of natural selection thus operating upon competing
species will be to give relative preponderance (in number or mass) to
those most efficient in guiding available energy in the manner indicated.
Primarily the path of the energy flux through the system will be affected.
But the species possessing superior energy-capturing and directing de-
vices may accomplish something more than merely to divert to its own
advantage energy for which others are competing with it. If sources
are presented, capable of supplying available energy in excess of that
actually being tapped by the entire system of living organisms, then an
opportunity is furnished for suitably constituted organisms to enlarge the
total energy flux5 through the system. Whenever such organisms arise,
natural selection will operate to preserve and increase them. The re-
sult, in this case, is not a mere diversion of the energy flux through the
system of organic nature along a new path, but an increase of the total
flux through that system.
Again, so long as sources exist, capable of supplying matter, of a charac-
ter suitable for the compositon of living organisms, in excess of that
actually embodied in the system of organic nature, so long is opportunity
furnished for suitably constituted organisms to enlarge the total mass of
the system of organic nature. Whenever such organisms arise, natural
selection will operate to preserve and increase them, provided always
that there is presented a residue of untapped available energy. The re-
sult will be to increase the total mass of the system, and, with this total
mass, also the total energy flux through the system, since, other things
equal, this energy flux is proportional to the mass of the system.
Where a limit, either constant or slowly changing,6 is imposed upon the
total mass available for the operation of life processes, the available energy
periunit of time (available power) placed at the disposal of the organisms,
for applicption to their life tasks and contests, may be capable of increase
by increasing the rate of turnover of the organic matter through the life
cycle. So, for example, under present conditions,7 the United States
produce annually a crop of primary and secondary food amounting to about 1.37 X 1014 kilogramcalories per annum, enough to support a popula-
tion of about 105 million persons (equivalent to about 88 million adults)
at the present rate of food consumption (4,270 kilogram-calories per adult
per day). Suppose, as a simple, though rather extreme illustration,
that man found means of doubling the rate of growth of crops, and of
growing two crops a year instead of one. Then, without changing the
average crop actually standing on the fields, the land would be capable
of supporting double the present population. If this population were,
attained, the energy flux through the system composed of the human
population and the organisms upon which it is dependent for food, would
also be doubled. This result would be attained, not by doubling the mass
of the system (for the matter locked up in crops, etc., at a given moment
would be, on an average, unchanged) but by increasing the velocity of
circulation of mass through the life cycle in the system. Once more it
is evident that, whenever a group of organisms arises which is so consti-
tuted as to increase the rate of circulation of matter through the system
in the manner.exemplified, natural selection will operate to preserve and
increase such a group, provided always that there is presented a residue
of untapped available energy-, and, where circumstances, require it, also a
residue of mass suitable for the composition of living lhatter.
To recapitulate: In every instance considered, natural selection will
so operate as to increase the total mass of the organic system, to increase
the rate of circulation of matter through the system, and to increase the
total energy flux through the system, so long as there is presented an un-
utilized residue of matter and available energy.
This may be expressed by saying that natural selection tends to make the
energy flux through the system a maximum, so far as compatible with the
constraints to which the system is subject.
It is not lawful to infer immediately that evolution tends thus to make
this energy flux a maximum. For in evolution two kinds of influences are
at work: selecting influences, and generating influences. The former
select, the latter furnish the material for selection.
If the material furnished for selection is strictly limited, as in the case
of a simple chemical reaction, which gives rise to a finite number of prod-
ucts, the range of operation of the selective influences is equally limited.
In the case of organic evolution the situation is very different. We
have no reason to suppose that there is any finite limit to the number of
possible types of organisms. In the present state of our knowledge, or
rather our ignorance, regarding the generating influences that furnish
material for natural selection, for organic evolution, an element of uncer-
tainty enters here. It appears, however, at least a priori probable that,
among the certainly very large (if not infinite) variety of types presented
for selection, sooner or later those will occur which give the opportunity for selection to operate in the direction indicated, namely so as to increase the
total mass of the system, the rate of circulation of mass through the sys-
tem, and the total energy flux through the system. If this condition is sat-
isfied, the law of selection becomes also the law of evolution:
Evolution, in these circumstances, proceeds in such direction as to make
the total energy flux through the system a maximum compatible with the
We have thus derived, upon a deductive basis, at least a preliminary
answer to a question proposed by the writer in a previous publication.'0
It was there pointed out that the influence of man, as the most successful
species in the competitive struggle, seems to have been to accelerate the
circulation of matter through the life cycle, both by "enlarging the wheel,"
and by causing it to "spin faster." The question was raised whether, in this,
man has been unconsciously fulfilling a law of nature, according to which
some physical quantity in the system tends toward a maximum. This is
now made to appear probable; and it is found that the physical quantity
in question is of the dimensions of power, or energy per unit time, as was
hinted by the writer on an earlier occasion."
It may be renarked that the principle of maximum energy flux here
set forth bears a certain outward resemblance to a principle enunciated
by Ostwald : "Of all possible energy transformations, that one takes
place, which brings about the maximum transformation in a given time."
This principle of Ostwald's, however, is based on entirely different grounds
from those here brought forward. It is not of general applicability, and
in particular, its application to systems. of the kind here considered does
not appear warranted.
Addendum. Since the paragraphs above were penned, the writer has
received from the booksellers a copy of Professor J. Johnstone's book,
"The Mechanism of Life", in which that author
touches on matters closely related to those here discussed. Professor
Johnstone draws, however, a somewhat different conclusion, namely
that "In living processes the increase of entropy is retarded."'3 He points
out that this is true, primarily, of plants; but that among animalsl4 also
natural selection must work toward the weeding out of unnecessary and
wasteful activities, and thus toward the conserving of free energy, or,
what amounts to the same thing, toward retarding energy dissipation.
This is perhaps not wholly convincing, for the first effect of the advent
of animal organisms in a world peopled with a purely vegetable population,
would certainly seem to be an acceleration of the process of dissipation.
It appears, therefore, that at certain stages in the evolution of the system,
at the least, life must have tended to increase rather than decrease dis-
sipation. And even if animals ultimately evolve in the direction of de-
creased dissipative effect, they still remain essentially a dissipative type, as compared with plants, and, to make Professor Johnstone's argument
conclusive, it would seem necessary to show, not merely that the animal
organism evolves in that direction, but that the system of coupled
transformers, plant and animal, as a whole has so evolved.
Professor Johnstone's conclusion is, however, not essentially incompati-
ble with the one developed in this paper.
Where the supply of available
energy is limited, the advantage will go to that organism which is most
efficient, most economical, in applying to preservative uses such energy as
it captures. Where the energy supply is capable of expansion, efficiency
or economy, though still an advantage, is only one way of meeting the sit-
uation, and, so long as there remains an unutilized margin of available
energy, sooner or later the battle, presumably, will be between two groups
or species equally efficient, equally economical, but the one more apt than
the other in tapping previously unutilized sources of available energy.
There is here a problem that will call for further investigation. In par-
ticular, it remains to be established just what is the significance of the
phrase "compatible with the constraints" which, in the presentation here
given, modifies the maximum principle enunciated. The present commu-
nication is intended rather a preliminary than as an attempt to say the
last word on the subject.
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