Elements of Physical Biology

A. Zones of Influence. In general the motion of the individual will be determined by laws too complicated to be readily analyzed, and therefore will be described as random. But there will upon occasion be arather abrupt break away from such random movement, according as a certain feature of the environment lies without or within certain zones. For example, the movements of a fly wandering about on a window pane are, presumably, in all cases physically determinate. But in a homogeneous field (uniform illumination etc.), the motion will assume, on the whole, a random character. We may suppose that, in first approximation at any rate, the migrations of the individual will follow some such law as those developed, for example by Sir Ronald Ross,’ by Pearson and Blakeman,* or by Brownlee’ for random migration. But, bring some particle of food within the field of sensuous observation of the fly, and the law of motion instantly changes from random to more or less clearly directed.

We may, then, construct about each individual a sort of target of zones of influence. The ideal would be to draw this target on a quantitative plan, according as a stimulus of strength s exerts a directing influence d at a distance r. In practice there may be difficulty in constructing these zones, but we may at least conceive them as drawn. We may say that a given organism is “in encounter” with a given point (e.g., a feature of the topographic chart) when that point falls within its field of influence. Similarly we may say that two organisms are in encounter when the one falls in the field of influence of the other. This encounter is mutual or one-sided according as each is within the other’s field, or as only one is in the other’s field, but not conversely, for example if A sees B, but B does not see A; or, to take an example

°K. Pearson and J. Blakeman, Drapers’ Company Research Memoirs, from chess, a bishop may threaten a pawn, though the pawn does not threaten the bishop. Zones of influence may extend over millions of miles, as in the case of a traveller steering his course by the stars. B. Zones of Mobility. We may stake out around each organism a target of zones indicating the distance which it is physically capable of travellingin1,2,. . .munitsoftime. These zones also we shall think of as attached to the organism and carried round with it in its wanderings through the landscape.

It is clear that the fate of the organism, and the history, the evolution of the system as a whole, will depend, first, on the character of the zones of influence and the zones of mobility; and second, on the nature of the correlation, the law of the aimed movements, established through these zones. We may seek to establish analytical expressions for this dependence. Let g be a parameter defining the character or “pattern” of a target of zones of influence or of mobility of the organisms of species S. Thus, for example, g might be parameter, or one of a set of parameters, defining visual acuity, measured on some suitable scale, at a distance of 5,10, 15,. . . feet, under standard conditions, Or, g might be a parameter defining the minimum time required for the organism to reach a point 5,10,15, . . . feet from his actual position, under standard conditions.*®

1. What will be the effect upon the rate of growth of the species if the parameter g is increased by a (small) amount dq? If r is the fractional rate of increase of the species S, can we establish an expres- A glance at the chess analogy will help to make clear the nature of the question thus raised. In chess we might ask: What would be the effect upon the course of the game if, other things equal, we were to modify in some stated particular the rules limiting the permitted moves of a given piece, for instance by allowing a pawn to move two squares, instead of the conventional one?

2. A second enquiry of peculiar interest relates, not to the character (pattern) of the zones of influence and mobility, but to the form of 8 Isochrone charts of essentially this character, relating to travelling facilities, were, according to Darmstaedter, first suggested by K. Richter in 1833 and actually prepared by Sir Francis Galton in 1881 (L. Darmstaedter, Handbuch zur Geschichte der Naturwissenschaften und der Technik, 1908, p. 792). relation established, through these zones, between the action of the organism and his environment. For it is hardly necessary for us to be reminded that two individuals or species with the same visual acuity, for example, may react in very different manner on seeing the same thing.

Here again the chess analogy is helpful. The corresponding enquiry with regard to chess is: What would be the effect upon the course of the game, if, with unchanged rules as to the moves of the pieces, a given change were made in the method, or the ability, of one of the players? To deal with these problems it is desirable to introduce two concepts, that of the Behavior Schedule, and that of Specific Productivity in a given activity. It has been remarked? that ‘‘a living organism is both cause and effect of itself.” Wemay say in somewhat more detailed statement, that the organism goes through a certain routine of motions or activities which are rendered possible by its structure, and which, in turn, are a necessary condition for the continued existence of that structure. These activities in general involve the expenditure of certain quantities of free energy, and a part of the energy so expended necessarily is spent in collecting (earning) a “replacement”? amount equal to the total expenditure, to balance the account, to cover the cost of living. While this phenomenon is, in a general way, characteristic of all mobile forms of life, the particular method followed in this cyclic activity of gathering and spending free energy varies in the most multiform manner from one species or type of organism to another.

Each type of organism may thus be said to possess a characteristic Behavior Schedule, which may be defined in terms of certain coefficients as follows: Of its total expenditure HZ per unit of time, a representative individual of the population will spend, on an average a fraction \j in a particular activity Aj, which may be defined as the maintaining of a parameter Uj at the value uj. So, for example,!° a human being may expend on an average, per day,

10'The figures in this example are chosen arbitrarily; although an effort has been made to make them reasonably realistic. In view of the wide variations in standards and cost of living in different countries, different social 180 external work (services sold) in maintaining his daily food supage DE ce hy ge a are eae 3,000 cal. 2,500 internal work (physiological work) in maintaining his body temperature abs... Janes cas cm «os 98°F. 130 external work (services sold) in maintaining his house rent at, CLA oe Wee Sa ey oho ce $2.00 60 external work (services sold) in maintaining his daily supply of clothingvatsaemrcct ee acest se $0.75 30 external work (services sold) in maintaining his daily supply of BIOTA telus mente Mien Oath $0.25 100 external work (services sold) in maintaining the rate of increase of the population at.... 1 per cent per annum 3,000 calories—total expenditure and total earnings (Note: 1 calorie = 3086 foot pounds.)

Consider some particular activity A; which results in maintaining a parameter U; (e.g., food capture per head per unit of time) at the value uj, then we will define P;, the Specific Productivity of energy E; spent in activity Aj; by strata, and at different epochs, close figuring, in such an example as this, would be out of place. Numerical data pertinent to this example will be found scattered widely in various sources, of which the following may here be mentioned: J. Amar, Le Moteur Humain, 1914, p. 254; R. Hutchison, Food and Dietetics, 1902, p. 37:46; J. LeFévre, La Chaleur Animale, 1911; F. H. Streightoff, The Standard of Living, 1911.

We are now prepared to consider the analytical representation of the influence of changes in the pattern of the zones of influence and the zones of mobility, on the one hand, and, on the other, of a change in the behavior schedule, on the Bee nes rate of increase r of ax This proportional rate of increase, r = Xap 8 ™ general a function of the parameters U (food capture, shelter, etc.), so that we may write Now the specific productivity P; in activity Aj; itself depends upon the character of the zone pattern. For, the more perfectly the individual is apprised of the relevant features of its environment (i.e., the more perfectly developed its zones of influence), the better, other things, equal, will it be able to direct its activities to the ends defined by the parameters U; and a similar remark evidently applies to the zones of mobility. If, then, q is a parameter defining the character of these zones, we may write

Ou; Oq J (8) or, more generally, since a change in q may affect not only a single productivity P;, but also others, Pi, Ps, . . . Pa the summation being extended over all the activities Ai, Ao, . A;, . . . An in so far as they are affected by the parameter g. (It is immaterial whether those not so affected are included in the summation or not, since they will contribute a zero term.) It lends a certain interest to the relation (9) if we observe that such

Or Or partial derivatives as ss » >), Possess a concrete signification, as follows: Consider two small increments Ag: and Aq in two parameters g: and gz. (To make matters concrete, suppose gq; measures visual acuity, g2 auditory acuity.) If Ag: and Aq. are such that then it will be indifferent for the rate of the increase of the species whether visual acuity is increased by Aqi or auditory acuity by Ago. We might say, in this sense, that the increments Aq; and Aq are, in this event, equivalent, or that that they have the same total value (in exchange against each other) for the species. Moreover, from (10) it is evident, on this same understanding, that the partial deriva-

or ; ; tive a measures the value (in exchange) per unit," to the species, of uv: the parameters gi; and aes similarly measures the value (in exchange) per unit of the parameters gz We may symbolize these facts by writing 11 An arbitrary proportionality factor enters, which is conveniently made unity by suitable choice of units. Certain steps in the development set forth above are reminiscent of the hedonistic calculus of Jevons and his school of economists. One is thus naturally led to look for a relation between value (in exchange) as here defined, and economic value in exchange, as conceived by those authors. It should be expressly noted, however, that the reasoning here followed, and the conclusions reached, are quite independent of any economic theory. As for the relation of the present reflections to economic theory, this will become apparent in the paragraphs that follow.

Ou; ena where pj = 57 Cefines what we may term the marginal productivity of energy expended upon the parameter U;. This marginal productivity pj; will, in general, differ from the total productivity P; defined by equation (1). It is, however, desirable, to express the relation between r and the behavior schedule in another way, with the following considerations in mind. Rigid or Automaton Type and Elastic Type of Behavior Schedule. The apparatus by which the coefficients \ defining the behavior pattern are determined varies widely in different species of organisms. At one extreme we may suppose that we have an organism with a rigid, inelastic behavior schedule, the coefficients being determined explicitly, once for all, by the properties of the individual. The extreme case of this kind is to be found, presumably, in plants, where, for example, the amount of energy expended in anabolism to replace wear and tear (e.g., annual leaf-fall) may be taken as a comparatively simple function of the leaf area. Many of the lowest forms of animals, actuated by simple tropisms, no doubt also approximate closely to such a rigid behavior schedule, what might be termed the automaton type of behavior schedule.

But in the higher animals, and most particularly in man, we have an elastic behavior-schedule. Here the \’s are not fixed in simple explicit manner by the physical character of the organism. We encounter here the phenomenon which we experience in ourselves subjectively as free choice between alternative courses of action, alternative values of the \’s open to us to choose from. This cannot mean, of course, that the \’s are wholly arbitrary, or physically indeterminate. Some action is and must be taken. But the natural principle which operates in the determination of the )’s, of the behavior schedule, is not immediately obvious.

The avenue of approach which seems to give most promise of lending us an insight into the relations here involved, is the following: The elastic type of behavior schedule, the free-choice schedule, as distinguished from the automaton type, is essentially a characteristic of the more highly organized among the mobile (animal) organisms. This fact is so prominently displayed to us in our own selves, that the adaptive superiority of the elastic type over the automaton type is commonly (and perhaps in a measure unjustly) taken for granted. If this assumption of such superiority be true, then the principle which operates in determining the coefficients \’s must be that they tend, on the whole, to be adjusted, in the operation of free choice, toward values favorable to the growth of the species. In the ideal case of perfect adaptation the ’s would, according to this view, be such as make 7, the proportional rate of increase of the species, a maximum. Let us see what this would imply.

In reacting upon its environment to influence the parameter Uj, the organism itself necessarily undergoes some modification, since it gives up energy Hj, (subjectively this modification is commonly felt as fatigue). In other words, if the state of the individual is defined by the values of certain terial} parameters fi, fz. - - , then the expenditure of an element of energy 6 H; by the indeed if not accompanied by other effects, is accompanied by a change 5 fi, 6fo. . . in the parameters f. At the same time the (external) parameter U; is modified by 6u;.

where, for brevity, the contracted notation has been employed copa Or Ofte Of OF; nm Ofc 08; If r is to be a maximum, (6r) must vanish for any arbitrary small value of 6 Hj, so that we must have for every subscript j, according to (16) Relation between Ideal and Actual Organism. We have thus far considered an ideal type of organism of the free choice type of behavior schedule, constructed on the principle that the ’s shall be so chosen as to make the proportional rate of increase r a maximum.

It remains to consider the relation between this ideal type of organism and the actual organism. The actual organism is not consciously guided by any consideration of the effect of his actions upon the rate of increase of his species. At least the instances in which such considerations are operative are so exceptional that we may well leave them out of account. What guides a human being, for example, in the selection of his activities, are his tastes, his desires, his pleasures and pains, actual or prospective. This is true, at least, of some of his actions, those which are embraced in his free-choice type of behavior schedule. That the human behavior schedule” also contains an element of the non-elastic (automaton) type may be admitted in deference to those who have leveled their destructive criticism at the hedonistic account of human behavior. We may, however, restrict our discussion here to that portion or phase of conduct which is determined by hedonistic influences. In this case, then, we are dealing with an organism which seeks to make, not r, but Q, its total pleasure (“ophelimity” in Pareto’s terminology) a maximum. Argument precisely similar to that developed above here leads to the condition.

In a modern civilized community we cannot very well speak of one typical behavior schedule of the individual, owing to the division of labor, with specialization of individuals in different pursuits. This matter will be found discussed more particularly, in Chapter XXVIII dealing with the adjustors. It is immediately seen that (18) and (20) will lead to the same adjustment of the activities of the individual if, and only if the : i, een marginal ophelimities Ju, ote proportional to the corresponding

We see then, that an organism actuated by pleasure and pain will so distribute its activities as to make r a maximum, if, and only if, its Hing ophelimities are proportional to the corresponding deriva- Effect of Small Departure from Perfect Adjustment. If we look upon the sense of pleasure and pain as an adjunct serving the express purpose of directing the activities of the organism towards ends beneficial to the growth of the species, then a species for which condition (21) were satisfied would represent perfect adaptation in this respect.

This leads us to a somewhat different setting of our problem regarding the influence of a change in the behavior pattern upon the rate of or increase of the species. Instead of enquiring after apy We may seek information regarding the influence, upon r, of a change in the tastes or desires of the species as defined by the derivatives ain An answer can be given at any rate in the neighborhood of the “perfect” adjustment of tastes defined by (21), i.e., for a species whose behavior schedule does not depart materially from that defined by (18). Consider a species for which the ideal (perfect) adjustment is given by

Suppose that this species actually adjusts its activities according to the plan (23) departing slightly (by an “error of valuation” de) from the perfect adjustment, namely a =— vars (vu; pj + vepe) (24) which is the required analytical expression for the influence of a small “error of valuation” upon the rate of increase of the species. The utility which such formulae as here developed may possess must be sought, not so much in their application to numerical examples—data for this are now and may long remain unavailable— as in the light they throw, quantitatively, upon the biological foundations of economics, in the relations which they reveal between certain biological and certain economic quantities. It must be remembered that the mathematical method is concerned, not only, and indeed not primarily, with the calculation of numbers, but also, and more particularly, with establishment of relations between magnitudes."4

Relation of Economic Value to Physical Energy. The behavior schedule has been quantitatively defined in terms of energy. This, if not the only possible definition, is at any rate a convenient one, and has also the advantage of emphasizing the important relation of the organism to the energy sources of his environment. His correlating apparatus is primarily an energy capturing device—its other functions are undoubtedly secondary. Evidence of this is manifold. The close association of the principal sense organs, eyes, ears, nose, taste buds, tactile papillae of the finger tips, with the anterior (head) end of the body, the mouth end, all point the same lesson,’* which is further confirmed by the absence of any well developed sense organs in plants. Exceptions here do indeed prove the rule, for sensitive plants, with a well-defined correlating apparatus, are just those which have departed so far from norm as to consume flesh food. And contrariwise, we ourselves are “blind” toward the one food that is omnipresent and which we consume by

Compare A. Cournot, Researches into the Mathematical Theory of Wealth, English translation by Irving Fisher, 1897, p. 3. ** For a resumé of “plant psychology,” see C. H. Farr, Atlantic Monthly, December, 1922; also Sir Frederick Keehle, The Plant Commonwealth and Its Mode of Government, Nature, 1924, vol. 144, pp. 13, 55. an almost unconscious, vegetative process, namely oxygen. If we seek an insight into the ‘psychology of plants,” it may be well to begin by imagining what our mental state would be if, in all our food quest, we remained as passive and indifferent as in the function of breathing.

The life contest, then is primarily a competition for available energy, as has been pointed out by Boltzmann.!7 Energy in this sense and for this reason has value for the organism—which is a very different thing from saying (as some have said or implied) that economic value is a form of energy. It is true that different kinds of energy are in a certain sense interconvertible into each other at fairly definite rates by exchange upon the market, in a human population. But the conversion factors here involved are of a totally different character from those that enter into the analytical expression of the law of conservation of energy.

This must be immediately apparent from the fact alone that the “mechanical equivalents” of the several forms of energy are absolute constants, whereas the economic conversion factors are somewhat variable, though they have often a species of approximate constancy, a fact which calls for explanation. Economic Conversion Factors of Energy. A simple example may help to clarify the view; the case of the automatic vending machine, the penny-in-the-slot chocolate dispenser, for instance.

1. A definite amount of money brings in exchange a definite amount of commodity (and of energy). 2. The physical process is a typical case of “trigger action,” in which the ratio of energy set free to energy applied is subject to no restricting general law whatever (e.g., a touch of the finger upon a switch may set off tons of dynamite). 3. In contrast with the case of thermodynamic conversion factors, the proportionality factor is here determined by the particular mechanism employed.

Reflection shows that all transformation of money or of economic assets of any kind into energy by exchange upon the market is of this character. It is always a case of trigger action. Somewhere there is a store of available energy, which can be tapped with an expenditure of greater or less effort. The payment of the price sets in motion the requisite machinery for the release of that energy (or for its transfer of ownership, the release being delayed at the discretion of the buyer).