Elements of Physical Biology

On the whole, so far, it must be said that the result of a careful analysis of the principle of Le Chatelier yields negative results, so far as practical application to biological systems is concerned. The chief conclusion is that great caution must be exercised in employing the principle. This result may be somewhat disappointing, but it is for that none the less important. Facts are stubborn things; it seems a pity to demolish the idol of a pretty generalization, but in such things we cannot permit the wish to be father to the thought. And the idol is not wholly demolished—in fact his hitherto doubtful title to certain domains has been established on a clear basis. But his province must be recognized as very definitely bounded.

In view of the limitations in the field of strict applicability of the principle of Le Chatelier, we are in general forced to consider separately each particular case of displacement of equilibrium. How such cases may be treated may be exemplified by the following two instances. Case 1. Displacement of Equilibrium between Food and Feeding Species. Consider a species S, of mass Xz, which requires for its (equilibrium) sustenance of a mass k,X» of food. Let this food be derived exclusively from the slain bodies, of total mass d, Xi, of a species S;. Let a fraction e of all the deaths in S; be those caused by S, feeding upon S;. Then

It is generally in the interest of the species S, to reduce this ratio to a minimum, especially in such a case as that of a domestic species S,, kept by man (S,) to provide him with flesh food. For the species S; itself consumes food, and is thus directly or indirectly a tax upon the system. In fact, the species S; is merely a sort of food factory for S:, and the less of S; is required to produce the requisite amount of food k,X», the more efficient is S; as a food factory.

We may therefore enquire what the formula (2) tells us regarding the efficiency of S; as a food producer. It will be observed that the ratio a = = = = may be reduced in two ways by operating upon the species S; (operating on S2, it might be reduced by diminishing k,; but we will exclude this from consideration) ; an increase in either ¢ or in d; will bring about this result of reducing a. Now e would be increased if the species S, helped to protect S, from its other enemies. This, of course, is one of the obvious expedients employed by man toward his domesticated sources of sustenance.

But the species S, may also operate to reduce the ratio a = a oa where N, is the number of the population of Si, m; the mass per head of this living population, m;’ the mass per head of the individ- ; i m uals slain by S2, and j is a factor, namely or Evidently d,j is the death rate per head in the population Si; to simplify matters we may assume that 7 is (nearly) unity, so that d, represents directly the death rate per head in S. It is evidently possible to increase di, the death rate per head in Si, without disturbing the equilibrium, provided that the birth rate 6, is increased in equal amount. There are several ways of accomplishing this. The most obvious is systematic breeding. We may briefly consider the analysis of an ideally simple case in point.

Let b; be the natural birth rate per head and d, the death rate per head, in a population of N, individuals of a food species Si. Of the total deaths, let pN, occur through various other causes, while gNiN2 are due to the destruction of S; by the species S, that feeds upon Sy. Furthermore, let the species S:, when in equilibrium, consume tN, individuals of species Ni, so that ; qd Now let S. “cultivate” the species S1, so that the birth rate of the

latter is raised from b; to b; + oNz. The conditions for equilibrium now are The effect of this cultivation, then has been, in this case, to leave the population of S;, the food species, unchanged. But the feeding This result could hardly have been foreseen by the aid of the principle of Le Chatelier. In this argument it has been supposed, as a first approximation, that q is a constant. In point of fact ¢ will no doubt be somewhat modified when the species S; is “cultivated” by S2. The effect of such modification of g would then be superimposed upon the effect derived in the argument set forth above.

Case 2. Change of Circulation through Moving Cycles. Among the moving equilibria in nature an important class are those which arise in systems traversed by matter in cyclic transformations. Consider a very simple example of a cyclic transformation chain, such as that in which, of three components S, S., S83, the first becomes converted into the second, the second into the third and the third returns to the first, after the pattern: where in the most general case g1, gz, gs are each of them a function of Xi, Xe, X3. When a steady state is established, so that the derivatives vanish we have, evidently pas to een (13) Ji gz gs from which it is seen that, in the steady state, that component is most abundant, which has the slowest proportional rate of decomposition, the smallest g. This smaller g acts as a “bottle neck”!2 in the cycle, causing material to accumulate in front of it. It acts

as a brake, as a limiting factor, upon the rate of circulation through the system. 127 am borrowing this term from the language of efficiency engineers, who employ it to denote a point, in a consecutive series in industrial operations, at which the progress of work is arrested by a local “limiting capacity.” If the total mass of S;, S. and S; is in some way fixed, so that we put X, + X. + X; = M = const., we have, evidently, for a steady state The circulation I, i.e., the mass circulating through the system per unit of time, is evidently given by

Hence, to increase the circulation, the best effect, other things equal, is obtained by seeking to increase the smallest g. This result, also, the Le Chatelier’s principle seems incompetent to predict. Some Significant Cases of Instability. It lies in the nature of things that a special interest attaches to stable states and stable systems. They represent the lasting features in the changeful landscape of nature—that is what we mean by stability. They are the survivors in the struggle for existence.

But the class of unstable states and systems is not without a special interest of its own. Departures from stability, so far from forming insignificant exceptions, are found to play an important role both in normal and in pathological life processes. The body does not always react in the direction of a restored equilibrium when exposed to a disturbing influence. The opposite type of reaction is sufficiently frequent to give occupation and means of livelihood to a distinct profession, whose business it is to prevent this adverse type of reaction from proceeding to the point where it sets a limit to life. A particularly pernicious form of this adverse reaction to influence tending to disturb the life equilibrium is that known among medical men as the victous circle. A departure from equilibrium, instead of stimulating a compensating response, provokes a further departure in the same direction, with cumulative effect. If this process goes on only to a certain point and then stops, there may be little or no damage sustained. But conditions may arise which, by their very nature, produce a continued acecumulation of deviations from the stable equilibrium position, until the limits compatible with the continuation of organized life processes are exceeded. So, for example, a person exposed to hardships through adverse economic conditions, suffers from malnutrition ; this lowers his resistance to bacterial infection; he contracts tuberculosis; there is a loss of appetite, and malnutrition not only is accentuated, but may become fixed even if better economic conditions are provided. And now a closed cycle, a “vicious circle,” is established, and the disease grows like an avalanche tumbling down a slope, gathering weight at each revolution of the cycle, on the downhill path to dissolution, thus

8 A condition analogous to that represented by the middle (ascending) limb of the van der Waals’ curve for the relation between pressure and volume of gas. Association of high blood pressure (20 mm. Hg or more above average for age) with ‘“‘over-weight’’ among 6,284 white males* * Statistical Bulletin Metropolitan Life Insurance Company, July, 1923, p. 8 and a forthcoming study by Prof. I. V. Hiscock, Yale University. } Five per cent above or below average weight for age and height.

Cumulative Cycles Simulating Orthogenesis. As another instance of a vicious circle we may perhaps regard certain cases of what has sometimes been termed orthogenesis, or determinate varlation. These are cases in which the evolutionary drift seems to be A group of fishes showing progressive flattening of the body accompanied by thinning out of the tail. Evolution would seem to have been guided, here, rather than by inherent tendency (orthogenesis) than by any utility of the resulting lash-like appendage. But the series may also be interpreted as the

product of a cumulative cycle under the influence of some glandular control of growth, referable, not to extrinsic causes, not to the selecting or other influence of the environment, but to a fatalistic tendency inherent in the organism itself, drawing the race on in a definite direction, for weal or for woe. So, it may be, the extinct races of giant reptiles were swept on upon a tidal wave of unremitting growth, until their cost of living exceeded their earning capacity, until their very strength proved their fatal weakness; unable to gather, in a day’s run, sufficient food to fill their monstrous paunch, they became the victims of their colossal ambition; their carcases remained enshrouded in the rocks, monumental wrecks by the wayside, where the caravan of evolution has passed on. .

But there is another view which ne account for this chapter in Natural History, as has been pointed out to me by Mr. J. B.S. Haldane in correspondence the gist of which is, briefly, as follows: The large reptiles of the secondary age had large pituitary glands. It was probably the secretion of these that determined their large size. Now a large animal has a high blood pressure—a fact which is exemplified, in a way, in statistics of clinical observations on human material, witness table 32 p. 295. With high blood pressure there would be a tendency for the capillaries to leak. The thing that stops them leaking is pituitrin. Thus selection will tend to increase the pituitary gland in large animals. Unless it is possible for variations to arise increasing the output of pituitrin but not that of the anterior lobe, successive generations will tend to become bigger and bigger, till they ultimately perish of hyperpituitarism.“*

Sometimes, it seems, the trend of evolution by a cumulative cycle may be grotesque rather than pernicious. This might well be the explanation of such singular vagaries as those observed, for example, in a group of fishes related to the shark. This series (fig. 59) (to which my attention was drawn by Mr. J. T. Nichols of the American Museum of Natural History) exhibits progressive flattening of the body accompanied by thinning out of the tail, until the latter is reduced to a mere lash. Here some gland controlling growth may have become increasingly active in response to selection operating on some useful quality, and meanwhile some secondary effect had to be taken into the bargain, regardless of utility.

But cumulative cycles do not always work toward destruction or toward mere caprices devoid of utility. The effect of gathering momentum is equally potent in the constructive sphere. Perhaps the most striking examples of this have occurred in the realm of mental phenomena. The eye and the hand have probably contributed more than any other single circumstance to the evolution of the human mind up to its present level. The possession of an agile member gave opportunity for exercise of the mental faculties, this in turn reacted towards increased development of the tactile sense and manipulative skill of the hand, and so on in a cumulative cycle.

A similar ‘cumulative cycle’ has probably had a large part in developing our faculty of speech. In the present stage of our development, we find it almost indispensable, in thinking, to use language, a vehicle whose primary function would seem to be the transmission of thought from one individual to another, and which would seem wholly superfluous in the traffic of thought within the precincts of one mind, as money currency is needless in the give- and-take within the same household. Which, then came first, thought, or language? Neither, of course, can claim clear precedence. They must have developed together, in mutual stimulation. The habit of communicating thoughts to others must have reacted upon the thinker and made him more perfect, first as a thinker, and then again, in turn, as a communicator of thought, as a speaker; and so, in a species of cycle, not vicious but benign, thought promoted speech and speech furthered thought, in an endless chain of cause and effect, such as that which we witness in the somewhat useless but rather entertaining spectacle of a cat chasing its tail, or (to turn from the fine to the useful arts), in the economically more significant performance of the donkey urged to unwonted productive effort by the hope of catching up with that elusive wisp of hay dangled by the driver before the poor beast’s nose. Cause and effect are so intermingled in a chain of alternations that they have become indistinguishable.

To cite in third place a more modern instance, the mutually fertilizing influence upon each other of pure and applied science falls into the same class of benign cycles. Here also cause and effect are so intermingled that the relative merits of the two not very clearly separated branches of scientific endeavor are hardly a subject for profitable debate. If, as some" bold, “the final justification of science is the power it creates for the use of mankind,” then we must call to remembrance that this “power must be created before it is used.’’!”

The instances cited should be sufficient to demonstrate how effectively resourceful nature makes use, in her economy, of instability, with its cumulative potency, as a progressive force; as well as of stability, the essentially conservative element in evolution. Indeed, we, of the human race, have good reason to be mindful of this fact, for the wholly unparalleled rapidity of our scientific and industrial evolution in past decades is itself the most brilliant example of instability and its cumulative power as a factor in evolution.

16 The writer is not among these, if by final justification is meant the only sufficient justification. No one would think of demanding such justification for art. Why require it of science? Such an attitude towards her is like that of the man who, having received repeated favors from his fellow, begins to acquire the habit, and to look upon such favors as due to him, and as the sole justification for the other’s existence. In dealing with any natural phenomenon—especially one of a vital nature, with all the complexity of living organisms in type and habit—the mathematician has to simplify the conditions until they reach the attenuated character which lies within the power of his analysis.—Karl Pearson.

Little has been said, so far, of the parameters P employed to define the state of the systems under consideration. In the earlier chapters these parameters have, in fact, been largely eliminated from discussion by restricting the treatment to the case of evolution under constant parameters P; subsequently the special cases of evolution with slowly changing P’s, and the influence upon equilibrium alone of changes of unrestricted kind in the P’s have been discussed; but all of this from a general standpoint, without giving much thought to the particular nature and properties of these parameters. It is desirable now to give some attention to this hitherto neglected phase of the subject.

The simplest, and in many respects a very illuminating example of the nature and function of the parameters P is furnished in the thermodynamic treatment of physical systems. Here we are accustomed to the use of such parameters as pressure, temperature, surface tension, etc., to define the state of the systems under consideration. Topographic Parameters. Obviously there is much latitude in the choice of such parameters; for if any parameter P can be employed to define the state of a given system, any single-valued function F (P) of that parameter will also serve, though certain selections of parameters may be found much more advantageous in practice than others. In particular, it is found, in systems amenable to thermodynamic treatment, that P’s can be so selected that they appear as the intensity factors of an energy.! This selection has actually been made in the example cited above. OF, alternatively, any one of the P’s so selected, can be replaced by

the extensity factor of an energy. So, in place of the pressure p we can introduce the vclume v, these two parameters being connected by a functional relation of the form. The parameter v (volume) is almost the simplest type imaginable of a topographic parameter. In many systems commonly considered in physical chemistry the only way in which the topography of the system plays any appreciable réle in the processes going on therein is through the volume defined by the boundaries of the system. Even the shape of the boundary is in most cases immaterial. In the systems in which organic evolution is proceeding, the situation is very different. In one respect the topographic parameters are often, in this case, even simpler than in the physicochemical example, namely in this, that living organisms (except aquatic species) make their excursions, extend their activities, essentially in a space of two dimensions—the earth’s surface, or at least a rather thin shell near that surface. Hence we are interested in areas rather than volumes; in place of a parameter v, volume, we may expect to find figuring in the discussion a parameter a, area. But aside from this slight simplification (which does not always apply), the influence of topography in systems in the course of organic evolution is immeasurably more complex than in the simple physico-chemical systems that form the chief subjects of study in the laboratory and in theory. Indeed, the conditions presented in nature are so complex that we can hardly hope to construct any systematic mathematical analysis of this phase of the subject, except by the expedient of dealing in somewhat radical abstractions, such as evolution “in a uniform environment” or, perhaps, in an environment reproducing in very greatly simplified form some of those principal geographic features that are typical of our globe. There is something unsatisfactory in such abstractions that seem rather far remote from conditions actually met in nature.

But it must be remembered that such abstractions are a necessary, and, as experience has abundantly shown, a very effective aid to our limited mental powers, which are incompetent to deal directly with unexpurgated nature in all its complexity. Neither should it be forgotten that the worker in the laboratory, though he may seem to be nearer to nature, himself is dealing essentially in abstractions. When the physical chemist investigates a chemical reaction in a constant temperature bath, he is not copying nature, where constant temperature is an exception, but is deliberately establishing an “unnatural” situation. He does this in order to separate the influence of one factor upon the course of events from that of a multitude of others; feeling confident that when he has gained an insight into the workings of such a simplified and, in a sense, unnatural system, he will be the better equipped to understand, or at least to make a further study of more complicated systems, approaching more and more nearly those occurring in nature. It is precisely the same principle which justifies us, in “substituting an ideal, upon which it is possible to operate, for intractable reality,’ when we essay the systematic treatment of natural processes by mathematical analysis. So, for example, Karl Pearson in his memoir on Random Migration treats among others the case in which ‘breeding grounds and food supply are supposed to have an average uniform distribution over the district under consideration;’’* and the simple case of “migration into a cleared rectangular area,” etc. Somewhat similar topographic simplicity is assumed as the basis of studies of Brownlee on the Mathematical Theory of Random Migration and Epidemic Distribution. We shall have occasion to refer to these studies again in another connection. It is not intended to follow up this phase of the subject here.

Neither will any attempt be made to sketch here even in outline the empirical side of the subject, our observational knowledge regarding the dependence of life in its various forms upon the parameters of state. There is a ripe and extensive literature available on this special phase of biology, which it is unnecessary to duplicate here. It will suffice to refer to standard works on geographical biology and to general ecology.‘ * The following may be mentioned: A. Engler and O. Drude, Die Vegetation der Erde, Sammlung pflanzengeographischer Monographien (a cyclopedic work in many volumes). A. F. W. Schimper, Clarendon Press, 1903, Plant Geography. E. Warming, Clarendon Press, 1909, Oecology of Plants. A. R. Wallace, 1876, The Geographical Distribution of Animals. F. E. Beddard, 1895, Textbook of Zoogeography. H. Gadow, Cambridge University Press, 1913, The Wandering of Animals, E. L. Trouessart, 1922, La Distribution Géographique des Animaux,

In physico-chemical systems the topographic parameter v (volume) is the capacity factor of an energy, as had already been noted; and associated with v is what may be termed a conjugate parameter pi (pressure), which is the intensity factor of the energy in question, Le., that factor which determines the direction of any change in the capacity factor v, according to the scheme zs s 0 according as p; = De (2) where pe is the external pressure.® The Intensity Law in Organic and Economic Systems. Is there anything corresponding to the relation (2), the Intensity Law, as it has been termed, in the case of the topographic parameter a (area) which enters into the definition of the state of a system in the course of organic evolution? This matter has already been referred to, in a way, in discussing the Principle of Le Chatelier. It was there noted that, in the case of human population area and rent are related to each other in accordance with a scheme of the type (2). More generally, supply and demand in economics stand in a relation of this type, and accordingly present a certain analogy to the capacity and intensity factors of an energy—an analogy which, by some writers, has been construed as actual identity in kind, prices having, by these writers, been identified with the intensity factor of an “economic energy.’’ Now energy is a perfectly definite, measurable thing, of definite dimensions. Those who thus speak of a special form of “economic energy” should be prepared to give us at least some indication how this energy is to be measured, in the customary units of energy. No such indication is forthcoming. On

6 The relation (2) is essentially the Helm-Ostwald Intensity Law. Although this law is not as universal as its sponsors would make it appear, yet it has a certain field of utility. For a critique of this law see M. Planck, Hight Lectures on Theoretical Physics, Columbia University Press, 1915, p. 11. The form of the relation (2) may be taken as the definition of a pair of conjugate parameters. However, the definition must be made a little more general to cover certain cases. We shall say that G, g are conjugate parameters if either

the contrary, as we shall see in dealing with the dynamics of evolution, the economic equivalent of a form of energy (which is something quite different from its mechanical equivalent), is not constant but variable—though it tends to approach, or to fluctuate about, a certain value. On the mistaken identification of prices and related economic quantities with the intensity factor of an energy, some authors have sought to build a system of biodynamics (social dynamics).6 The analogy which certain conjugate parameters of the perfectly general kind bear to intensity and capacity factors of an energy present the opportunity for such efforts, which are, in themselves, well worth while. But it must not be forgotten that the result of such efforts can be only a species of quasi-dynamics, something analogous to, but not identical with, the dynamics of physical forces. Just what the relation between such quasi-dynamics and true dynamics may be, is a separate problem, to which we shall have occasion to give some attention in the section devoted specifically to the dynamics of life-bearing systems.

The paying of rent in coin of the realm is, of course, a phenomenon peculiar to the human species. But the peculiarity is one of mode of manifestation rather than of inherent quality. We may speak of the rent per unit area that the representative individual is willing to pay as a measure or at least an index of the “population pressure.’”’ Now this population pressure—this willingness to sacrifice effort for the sake of gaining elbowroom—is present quite independently of our peculiar method of expressing it in terms of rent. It exists also among other species, though we may lack so convenient a gauge for it as we have, in our own case, inrent. We shall see later how at least a quantitative conception of such biophysical (economic) entities as population pressure and the like can be gained on a general basis, which applies to species other than human.