34. Natural selection and evolution: a mass misconception

The first person to use ‘mass’ in a recognizably modern and dynamical way was Kepler when trying to explain the motions of the planets. He proposed that bodies resist transitions from rest to motion in a manner proportional to their densities. Galileo had already recognized this distinction between a gravitationally caused weight and a natural resistance to motion, but he had not yet clearly articulated it. Christiaan Huygens drew similar conclusions based on his work with pendulums (Bynum et al, 1983). Our concern is to determine: is there a similar distinction, within biology and ecology, analogous to that between ‘weight’ as a specific form of the presentation of inertia, in this case to gravity; and any other form of inertia, as with all other kinds of motion? If, for example, natural selection is a kind of inexorable ‘weight’ on all biological organisms in the manner meant by Darwin, then is that ‘weight’ or activity distinguishable from all other forms of biological activity?

With Kepler’s suggestion accepted, Newton then argued that it was necessary to distinguish the quantitas materiae or quantity of matter in a body from its gravitational weight. He insisted that the former was invariable. But since the earth was not a perfect sphere, the latter varied with location—which he then demonstrated and carefully calculated.

Newton was certainly pointing at mass as a concept, but his definition of ‘quantity of matter’ was unfortunately circular. He could not break from the practice of defining it as a body’s volume multiplied by its density. But although he failed to properly clarify this ‘quantity of matter’, his alternative conception of quantitas motus or ‘quantity of motion’ was far more easily indicated … and ushered in the modern era in science by proving to be wonderfully receptive to mathematical treatment. Newton defined this quantity of motion with his Definition II by saying:

The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.

The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple (Newton, 1686).

Newton’s overall success was of course important, but he had in fact given a rough definition of what we now call momentum, p. Furthermore, he erred in not regarding it as a vector (Iltis, 1971). He thought of it as scalar, and since he treated momentum as scalar it caused problems because it was clearly not conserved when the direction of motion changed.

The person who carefully distinguished between what he called vis viva, which he regarded as conserved, and what he called vis mortua, which was Newton’s above scalar concept and so clearly was not, was Gottfried Leibniz. He also carefully distinguished between what he called a motive force or motricis potentiae and the above quantity of motion or quantitas motus of Newton. But although Leibniz’s motricis potentiae worked together with his vis viva, he in his turn introduced an error. He did not distinguish—as Newton did—between mass and weight. He therefore tended to refer to what we now call work rather than to force … and he was therefore handling what we now call kinetic energy rather than momentum:

I suppose the same force is requisite to raise a body A of one pound weight, to the height of four yards ; which will raise the body B, of four pounds weight, to the height of one yard. This is granted both by the Cartesians, and other philosophers and mathematicians of our times. And from hence it follows, that the body A, by falling from the height of four yards, acquires exactly the same force, as the body B by falling from the height of one yard (Iltis, 1971).

The person who ultimately gave mass the definition that lasted for over a century in physical theory was Leonhard Euler. In Euler’s hands, mass became an unquestioned, unquestionable, and irreducible ‘given’ of the surrounding material world. It remains the one with which biologists and ecologists are the most familiar for they meet it in Galileo’s inclined planes:

Euler states explicitly that the matter (mass) of a body is not measured by its volume but by the force necessary to impart to it a given motion (acceleration). Here, then, is the earliest expression of the well-known formula “force equals mass times acceleration” and it serves as an accurate definition of mass.

The definition of mass as the ratio of force to acceleration gained wide acceptance … (Jammer, 2010, p. 89).

But although Euler gave mass a most clear definition, it has since been supersceded. And if his concept of mass—present as it is in problems with inclined planes and rolling balls—is now deemed inadequate for physics and for chemistry, then it is hard to see why it is still considered adequate for biology and for ecology. This Newtonian-Eulerian concept of mass and inertia is still so entrenched that there is scant evidence that biologists and ecologists are even aware how much ideas on mass and inertia have changed since Euler’s original proposal. Biologists were at the forefront of the development of the energy concept, yet they have do not seem to have moved on from the above Eulerian definition for mass.

Sir Joseph Thomson, discoverer of the electron, took the first big step forwards towards the more modern and comprehensive understanding of mass and inertia. He showed that an electrically charged sphere had a greater inertia or resistance to having its motion changed than an uncharged one. This demonstration profoundly affected concepts of both mass and energy in physics.

The English physicist Oliver Heaviside then suggested that mass was a property of the electromagnetic field. Max Abraham even suggested that the whole of mechanics could be reduced to electromagnetics.

And … Heaviside’s suggestion has suddenly become singularly important to biology because electrons mediate the chemical and biochemical bonds that biological entities exploit. If Heaviside is correct that mass is a property of a movement or a change in an electromagnetic field, then this immediately means that a biological entity’s inertia—and therefore its mass—changes every time it forms or breaks a biochemical bond. And if an entity’s inertia changes every time it breaks or forms a bond, then its value for inertia is going to differ if it changes a bond because of natural selection, and if it changes a bond for some other reason. So also … a movement horizontally in a gravitational field is by definition not gravitationally affected, although mass is involved. Also by the same token, a biological activity that is not relevant to natural selection will certainly involve energy, but it will make no contribution to the relevant entity’s “movement” “forwards” or “backwards” in evolution. Do such movements exist? And if so, can they be quantified so we can isolate natural selection in the same way movements north-south, east-west, and up-down can be isolated?

It is not surprising that Darwin did not couch his analysis of natural selection and evolution by taking this kind of distinction between mass and energy into account for the concepts were not available. Darwin was born in 1809; Mayer in 1814; Joule in 1818; and Maxwell in 1831. Darwin and Wallace presented their joint paper On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection in 1858; the Maxwell eletromagnetic theory appeared in 1864; and the last of them (Joule) died in 1889. It is therefore not surprising that Darwin should speak, as he famously did, in the following terms about the evolution of the eye:

Organs of extreme perfection and complication.—To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree. When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei, as every philosopher knows, can never be trusted in science. Reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real. How a nerve comes to be sensitive to light, hardly concerns us more than how life itself first originated; but I may remark that several facts make me suspect that nerves sensitive to touch may be rendered sensitive to light, and likewise to those coarser vibrations of the air which produce sound.

In looking for the gradations by which an organ in any species has been perfected, we ought to look exclusively to its lineal ancestors; but this is scarcely ever possible, and we are forced in each case to look to species of the same group, that is to the collateral descendants from the same original parent-form, in order to see what gradations are possible, and for the chance of some gradations having been transmitted from the earlier stages of descent, in an unaltered or little altered condition. Amongst existing Vertebrata, we find but a small amount of gradation in the structure of the eye (though in the fish Amphioxus, the eye is in an extremely simple condition without a lens), and from fossil species we can learn nothing on this head. In this great class we should probably have to descend far beneath the lowest known fossiliferous stratum to discover the earlier stages, by which the eye has been perfected (Darwin, 1861, pp. 205-206).

Darwin’s presentation of this issue may not be surprising, but what surely is, is that discussion on this topic has progressed so little since he wrote. He had already outlined the process he had in mind. He had already indicated that natural selection exists. He had already indicated that it leads to evolution. He stated the mechanism. He had already indicated a general time scale.

One would have thought that by 1967—when Lorus and Margery Milne wrote Patterns of Survival, in which they engaged in a discussion of natural selection, including amongst lampreys—there would have been some forward movement from Darwin’s original analysis, and a recognition of the effects of mass and energy as pertaining to electron behaviour. But when the Milnes discuss lampreys, any such recognition is wholly absent:

During the sweeping transformation that converts an eyeless denizen of the silty bottom into a free-ranging fish of adult form, the lamprey develops a pair of eyes and a heightened awareness of objects in its vicinity. Often its eyes seem so inconsequential by comparison with those of other fishes that they are referred to as degenerate. The lamprey seems condemned to partial blindness as a consequence of its parasitic ways. But it is impossible to prove this correlation. The degeneracy is slight, no greater than in free-living bats. Both types of animals depend to a greater degree upon other senses.

In darkness and turbid water, lampreys show a masterful ability to locate victims and mates by smell and electricity. Each individual swims with creditable directness to the source of an attractive chemical substance diffusing through the water or spread by currents. At close range, it zeroes in on any object whose electrical conductivity differs from that of plain water. Emitting weak pulses of electricity from special generators in its head, the lamprey orients its movements according to the electrical “feel” of its charged environment. This is a common enough ability among fishes, but in lampreys electrical sensitivity is so great that vision becomes less important (Milne, 1967, pp. 255-256).

It is hard to see how a cogent and logical discussion of the evolution of the eye is possible with no acknowledgement that electricity has measurable mass and inertia, and that therefore the biological inertia of an entity must change as its ability to handle the electron flows also changes. There is no discussion of the forces that must be at work as lampreys use their eyes or otherwise; as electrons move; and as the lampreys possibly even evolve while doing so, and if so at what pace.

The situation was unchanged some forty years later when Jerry Coyne decided to write Why Evolution Is True. His discussion shows no substantive change from Darwin’s original:

… is natural selection sufficient to explain a really complex organ, such as the eye? The “camera” eye of vertebrates, (and mollusks like the squid and octopus) was once beloved by creationists. Noting its complex arrangement of the iris, lens, retina, cornea, and so on—all of which must work together to create an image—opponents of natural selection claimed that the eye could not have formed by gradual steps.

A possible sequence of such changes begins with simple eyespots made of light-sensitive pigment, as seen in flatworms. The skin then folds in, forming a cup that protects the eyespot and allows it to better localize the light source. Limpets have eyes like this. … The evolution of a retina, an optic nerve, and so on follows by natural selection. … the complexity of the final eye can be broken down into a series of small, adaptive steps.

Yet we can do even better than just stringing together eyes of existing species in an adaptive sequence. We can, starting with a simple precursor, actually model the evolution of the eye and see whether selection can turn that precursor into a more complex eye in a reasonable amount of time. Dan–Eric Nilsson and Susanne Pelger of Lund University in Sweden made such a mathematical model, starting with a patch of light·sensitive cells backed by a pigment layer (a retina). They then allowed the tissues around this structure to deform themselves randomly, limiting the amount of change to only 1 percent of size or thickness at each step. To mimic natural selection, the model accepted only “mutations’ that improved the visual acuity, and rejected those that degraded it.

Within an amazingly short time, the model yielded a complex eye, going through stages similar to the real animal series described above. The eye folded inward to form a cup, the cup became capped with a transparent surface, and the interior of the cup gelled to form not only a lens, but a lens with dimensions that produced the best possible image.

Beginning with a flatwormlike eyespot, then, the model produced something like the complex eye of vertebrates, all through a series of tiny adaptive steps—l,829 of them, to be exact. But Nilsson and Pelger also calculated how long this process would take. … the eye evolved very quickly: the entire process from rudimentary light·patch to camera eye took fewer than 400,000 years. Since the earliest animals with eyes date back 500 million years ago, there was, according to this model, enough time for complex eyes to have evolved more than fifteen hundred times over. In reality, eyes have evolved independently in at least forty groups of animals. As Nilsson and Pelger noted dryly in their paper, “It is obvious that the eye was never a real threat to Darwin’s theory of evolution” (Coyne, 2009).

Coyne certainly draws some exciting conclusions. But when one examines Nilsson and Pelger’s original paper, A Pessimistic Estimate of the Time Required for an Eye to Evolve, it is hard to see how natural selection is in itself supported in the way Coyne claims.

If we return to the debate between Newton and Leibniz and hypothesize a difference in biology between mass and weight, momentum and kinetic energy, and force and energy, then nowhere in Nilsson and Pelger’s paper is there a mention of the force or the energy or the momentum needed for an eye to evolve in terms of some such quantitative measure that is directly attributable to a natural selection force. Nor does anything in their paper make any such thing calculable (Nilsson and Pelger, 1994). There is in other words no understanding, as is again common throughout the literature, of a strictly biological mass, a biological inertia, or a biological force, and particularly in terms of the energetic movements of electrons:

The calculated number of 1% changes required between each of the stages … was plotted against the optical performance of each stage, which was calculated as the number of resolvable image points within the eye’s visual field …. The graph shows that spatial resolution improves almost linearly with morphological change (Nilsson and Pelger, 1994).

Nilsson and Pelger’s analysis does not state the “cost” of such changes. It does not give a path value or an action in clear and rigorous terms, and as used in other areas of science:

True to our pessimistic approach … we deliberately … assumed that all 1829 steps of 1% change occur in series. This is equivalent to a single structure becoming 1.011829 or 80 129 540 times longer. In terms of morphological modification, the evolution of an eye can thus be compared to the lengthening of a structure, say a finger, from a modest 10 cm to 8000 km, of a fifth of the Earth’s circumference (Nilsson and Pelger, 1994).

The deficiency in metrological reference is surely only highlighted by this comparison they make to illustrate the scale of evolutionary changes elucidated in their mathematical model. That comparison does not allow for suitable calculations nor for determinations of the magnitude of natural selection. It is still simply descriptive. Or … are they proposing that all evidence for natural selection should from now on be presented in reference to the Earth’s circumference … and which is therefore now a standard of measure?

There is, from our perspective, a singular virtue of Nilsson and Pelger’s paper. Unlike most others—and certainly unlike the Milnes and their lampreys—they present their analysis as Darwin intended. Although they fail to specify quite how long one of their generations is, their time scales for natural selection and evolution are per the generation. However … any appreciation for this aspect of their work must be tempered by the fact that it occupies a scant 220 words, just over 3%, out of their 7,000-word paper … with over half that 220 being devoted to listing the terms and variables they use in R = h2iσ and R = h2iVm where their R is what they call “the observable change in each generation”. They claim that it measures “variations” and the heritability thereof, but they give no indication of how those variations impact on natural selection per se, and in terms of some force applicable solely and only to that natural selection. It is therefore difficult to see how natural selection has been quantified, and how it has been discussed in anything other than the terms Darwin originally proposed.

The various discussions we have noted since Darwin originally wrote have all been rather like saying that if we wait a sufficiently long period of time and watch a moving ball, then we will see the ball move … and without giving any indication of the ball’s mass, the forces making it move, or anything else of pertinence to improving comprehension. Nilsson and Pelger’s mathematical model is certainly interesting; and it was of course helpful in indicating how rapidly natural selection could act under certain given conditions. But that is not the real issue for this mathematical model has done nothing more than confirm what Darwin stated in the first place: that natural selection and evolution will certainly occur over a sufficiently long period of time. This was never doubted by any serious scientist. What is needed is a clear and unambiguous way of delineating natural selection; clearly measuring its effects; and isolating it from all other biological effects so its intensity—or otherwise—in any given situation can be stated and observed … and best of all, predicted.

Abraham’s proposal suggesting that mechamics could be reduced to electromagnetics proved erroneous because unfortunately for physical theory, only the electron would succumb. Although that specific project had to be abandoned, electrochemical and electromagnetic energy had nevertheless made its mark on all discussions regarding mass and inertia. With energy firmly in hand, various efforts were later made by Dirac, Heisenberg, Pauli, Feynman and others to account for mass in quantum electrodynamics, but there were many unresolved issues. Einstein’s special relativity eventually equated mass, inertia and energy through mc2; while his general relativity demonstrated that the long puzzling equivalence between inertial and gravitational mass was a natural consequence of his four-dimensional Minkowski space-time.

Figure 32: Biological Mass and Biological Inertia
 Biological Mass and Biological Inertia

And … while all these developments were under way in the hands of the very people responsible for the scientific definition and understanding of inertia, biologists and ecologists have hung on grimly—and blindly—to Euler’s original definition. But Figure 32 should make it clear that the traditional Eulerian definition so unquestioningly accepted by biologists and ecologists is wholly unsatisfactory for any serious scientific work … which is exactly why chemists and physicists have discarded it. If biology and ecology wish to be taken seriously as sciences, then they should surely do the same

As in the first graphic in Figure 32 we suppose a cell with a boundary that defines it as a system. How many other molecules it might contain is of no moment. By some unspecified process, an energy centre within the cell deploys some mechanical chemical energy and draws five molecules of varying masses in from the environment and across the boundary.

There is now an important distinction to be made between the energy expended by this cell simply in acquiring chemical components; and the energy it can now expend in manipulating those components so it can be biological. The former occurs under constant pressure and reckons only the mechanical work of procuring and securing components from the environment. This is the work done against the desire to retain those same components expressed by the environment and in the inertia of those components, which is simply their mechanical and inertial mass. Since that total mass is m; and since the net distance concerned is d; then the work done in acquiring those components is soon calculated. It can then be assigned to the cell and reckoned as joules per unit volume for that cell per each second as those components are retained. And since joules per unit volume is in fact joules per entity, then that energy exhibited in the needed mechanical work would at first seem to be a full and accurate measure of the cell’s biological inertia—i.e. its total energy expended in being biological and in following the biological cycle.

But as the second graphic in Figure 32 shows, biology requires something rather more than simply mechanical inertia. In that second graphic the acquired components are simply “in” the cell. They have not yet been arranged, and nor are they being manipulated, in any meaningful biological way. Thus the cell only has a mechanical mass due to some mechanical components.

The above deficiency is corrected in the third graphic. The cell’s energy has now manipulated and arranged the components in a biologically meaningful way so that biological work can be done, and the biological cycle can continue. The cell has only become biological through its constant volume work, and by exploiting its capacity for nonmechanical energy. With that energy, it can form a variety of biologically relevant biochemical bonds. Not only is this nonmechanical chemical energy a property of that biological cell, but it certainly increases the total inertia of energy displayed by that cell. This is really some very basic science. But … this expenditure of energy upon the chemical bonds certainly adds to the cell’s total biological inertia, and must therefore be reckoned. In other words, simply to refer to mechanical mass is deficient.

Although the cell has exploited some nonmechanical energy, and has therefore added to its total energy signature, its mechanical Newtonian-Eulerian inertia remains unchanged at m, because the cell’s mechanical mass remains constant throughout. There is, therefore, a most important distinction to be drawn between biological inertia—which is the sum of the cell’s mechanical plus nonmechanical energies—and simple mechanical inertia, which is entirely reckoned by Newton and Euler’s F = ma, and which is simply an inventory of the cell’s mechanical chemical energy. This latter reckoning is by itself insufficient for biology and ecology for it is mere mechanical mass, and it pays no regard to the nonmechanical energies that are at all times being expended by the cell, and that are contributing to the net Wallace pressure, P, over the given population. Biological inertia must therefore incorporate not only all the mechanical inertia of all the molecular components, and as measured by simple mechanical chemical energy; but it must also reckon the chemical configuration energy exhibited in the nonmechanical energy evidenced in all the chemical bonds and chemical activities of the given reactions and their potentials.

The need to properly reckon a biological inertia is made even clearer in the fourth graphic. The biological inertia has further increased as the molecular components adopt a more intense energy arrangement with additional selections of bonds. Once again, the Newtonian-Eulerian mechanical mass remains constant. It holds the same value it had with respect to those components before they first entered the cell. But the total energy being expended by the cell, to maintain its biological nature, is again very different, and so must certainly be taken into account. We cannot hope to tame either natural selection or evolution without doing so.