A pessimistic estimate of the time required for an eye to evolve
by Dan-E. Nilsson, Susanne Pelger
This paper  is well known and often cited as demonstrating that eyes could have evolved readily. However, there are several failings, notably that their starting point is a patch of light-sensitive cells – so they completely disregard the substantial difficulties that would be involved in evolving the molecular basis for light sensitivity in the first place. I shall look at that elsewhere.
Here I shall focus on two particular flaws relating to their model for the morphological evolution of an eye:
- The fundamental flaw – common to many evolutionary scenarios – is that it whitewashes over the fact that significant new structures would need new genes, and completely ignores the formidable biochemical reasons against new genes arising.
- An emphasis of their paper is what they estimate to be the short time (number of generations) required for an eye to evolve. Yet, although they claim (repeatedly) that this evolution is through the action of natural selection, their calculations relate to changes brought about in the course of intentional selection e.g. domestic breeding, so are completely erroneous and misleading.
1. The unavoidable requirement for new genes
It is deplorable that professional biologists at the end of 20th century, with the benefit of decades of substantial discoveries about the molecular basis of genetics and developmental mechanisms, still present exclusively morphologically-based evolutionary scenarios which are no better than those of the 19th century. All that we’ve learned about how tissues form through the concerted action of many genes, mediated by sophisticated molecular machinery, is completely set aside – perhaps because the authors know that to take the molecular aspects seriously would completely undermine such scenarios. Yet, unfortunately, it seems to be a common failing of current Neo-Darwinism (the need for new genes).
Nilsson & Pelger’s paper has been cited widely, so their model for the evolution of an eye is well known; but in summary it is as follows (and see Figure 1).
Nilsson and Pelger assessed eye performance in terms of visual acuity, i.e. the ability to discriminate between parts of the image, which depends on different light-sensitive cells having different fields of view; and they used this as the basis for selection and hence for directing morphological change.
As mentioned above, their model starts off with a ‘patch of light-sensitive cells, which is backed and surrounded by dark pigment’ (p54).
In terms of making minor changes to an existing structure, visual acuity can be improved most effectively (most benefit for least change) first by the initially flat patch of photoreceptors becoming concave. That is, the authors assume that the patch of photoreceptors is not always flat, but varies in shape, and in at least some individuals it is somewhat concave; because the latter improves performance slightly, organisms having a concave photocell patch survive better and reproduce preferentially.
Then, some of the progeny have patches that are more indented, which survive/reproduce preferentially, and so on – no matter how much morphological change and selection has occurred in the past, the authors assume that more change – in the desired direction – is possible.
Once the indented patch of photocells is as deep as it is wide then, rather than becoming deeper, visual acuity is improved more effectively by constricting the orifice of the depression; and the authors assume that appropriate variations to effect this will arise as required, be inherited, and lead to substantial morphological change. This continues until an optimum is reached: although further constriction would improve visual acuity by narrowing the angle of incident light to each photocell, this is offset by the reduction in light admitted to the photocells.
When this optimum has been attained, further improvement can be achieved only by addition of a lens, and the authors boldly assert that ‘Even the weakest lens is better than no lens at all, so we can be confident that selection for increased resolution [i.e. improved visual acuity] will favour such a development all the way from no lens at all to a lens powerful enough to focus a sharp image on the retina.’ And they assume that this occurs through progressive localised increase of refractive index of the tranparent medium in front of the light sensitive layer.
There are a couple of preliminary things to note about their account:
1. The evolution they envisage is based on genes – otherwise the morphological changes would not be heritable (in their calculations, see below, they assume only 50% of morphological change is heritable i.e. having a genetic basis). Whilst this is obvious, it needs to be recognised explicitly.
2. Again, rather obvious, but they are not explicit:
a) Either the evolution they envisage is based entirely on selection (of genes or gene combinations) from a gene pool already available, (in effect the genes required to produce an eye were already there in the starting organism, all that had to be done was to identify them (and possibly coordinate their action)). This might sound ludicrous, but it’s the model behind their calculations! (See below.) If they considered their model of eye evolution to be solely through segregating pre-existing genes then that would completely undermine the relevance of their study – because it just pushes back the question of how the required genes arose.
b) Or they anticipate that new genes arise in the course of the evolution they modelled. Despite their calculations, I suspect this is the authors’ expectation – rather than merely selecting from existing genes. But perhaps more likely is that they didn’t actually think about it. They just relied (as so many evolutionary scenarios do) on a vague and not-thought-through belief that mutation will produce the constructive genetic variability they require.
As I mention in Neo-Darwinism, Dawkins is at least explicit about his belief that the evolution of an eye would require mutations and his feeling that mutations needed for the evolution of an eye can be achieved by minor changes to existing embryonic processes. However, as I explain there, this rationale does not work in practice because of the discrete nature of genes (and that genes cannot arise in a gradual manner).
So now let’s look at their scenario a bit more closely.
Morphological novelty – would the modelled changes actually happen?
I’ll begin with the ‘simple’ case of the initial indentation. Simple in the sense that this aspect of their model could perhaps conform with their assumption that ‘the structures necessary for image formation, although there may be several, are all typically quantitative in their nature, and can be treated as local modifications of pre-existing tissues’ (p53, emphasis added).
As indicated above, and outlined in Neo-Darwinism, it seems biologists have been lulled into the idea that biological tissues are plastic, in the sense that they can change in just about all manner of ways, or at least any way a biologist might wish. They seem to forget or overlook that morphological variations require a genetic basis.
But what is the basis for this belief? It seems to me that the only empirical evidence is the substantial – but, importantly, not limitless – morphological change that can be effected by selective breeding, and some examples by natural selection – such as the wide diversity of cichlid fish species . But not only are such changes limited quantitatively (in degree), they are also limited qualitatively i.e. not every feature can be changed.
So in relation to Nilsson & Pelger’s model the question should be asked: would the layer of light-sensitive cells begin to indent in a progressive way? And why should it – what reason is there for thinking that the genes required to effect such an indentation would actually be available? We need not only speculate about this: we could put it – or at least a similar case – to the test. If Nilsson & Pelger’s assumption is correct, then experimenters could define some small (eye-sized) patch on an animal’s epithelium (or an underlying layer if they prefer) and selectively breed for this to indent.
Bear in mind that Nilsson & Pelger are not suggesting that the relevant layer indents because it has a patch of light-sensitive cells. Rather, they believe that variations, such as indentations, will occur all over the animal’s epithelium, and if an indentation occurs of the light-sensitive patch then this will improve optical acuity, which will confer selective advantage, so the indentation will be retained (and progressively increased). So it would be equally applicable to select artificially for such an indent (which is the procedure modelled by their calculations anyway).
And time need not be a problem either. According to Nilsson & Pelger’s calculations it should be possible to ‘evolve’ a measurable indent within a relatively small number of generations.
The naivety of their approach is seen most clearly when it comes to their description of how a lens arises:
Even the weakest lens is better than no lens at all, so we can be confident that selection for increased resolution [i.e. improved visual acuity] will favour such a development all the way from no lens at all to a lens powerful enough to focus a sharp image on the retina.
And they assume that this occurs through progressive increase in optical density of appropriate areas of the transparent region in front of the light-sensitive layer. The only thought they give to the biochemical implications of a lens is to relate increased optical density to increased protein concentration.
But what about reality? There are two major sources of objections to their model:
- the way in which eyes form embryonically, even at a morphological level, and
- the genetic and molecular mechanisms required to effect that embryonic development.
I shall comment on both of these in relation to the embryonic development of vertebrate eyes. Nilsson & Pelger consider their model to be generally applicable to all animal eyes (p58), which certainly includes vertebrate eyes. And the embryonic implications of vertebrate eyes will have their equivalent in other animal groups.
Morphological lens development
1. Formation via a lens vesicle which pinches off from the ectoderm
Whilst Nilsson & Pelger’s model envisages that a lens emerges by progressive increase in protein concentration of part of the tissue in front of the retina, this is not consistent with how the lens develops embryonically. A common evolutionary argument is that part of a structure (eye, wing etc.) is better than none and this sort of thinking is behind Nilsson & Pelger’s reasoning that -
Even the weakest lens is better than no lens at all, so we can be confident that selection … will favour … development all the way from no lens at all to a [fully formed one].
If the lens formed embryonically in a comparable fashion i.e. through merely gradual quantitative development of a tissue, then the argument could be applicable. However because of the way the lens forms – via pinching off of part of the ectoderm – there seems little doubt that a part-formed lens would impair vision rather than improve it. In other words, their supposed gradual evolution of a lens would at some stage require a substantial jump.
(E.g. even if a lens placode were transparent and had some lens-like properties, in the course of pinching off from the ectoderm these properties would be disrupted, and natural selection has no foreknowledge that the end result of a fully formed lens would ultimately be an improvement.)
2. Increased, and gradation of, optical density
Similarly, Nilsson & Pelger envisage the lens merely consisting of an increased concentration of proteins within the pre-retinal region i.e. only a quantitative change. But the increased protein concentration needs to be contained by something, i.e. a structure is required, which would involve a qualitative change. Further, the gradation of optical density by means of a gradation of protein concentration implies multiple containers. This is achieved in vertebrate eyes by a central core of high-density primary fibres surrounded by an onion-ring arrangement of secondary fibres with graded optical density. Again, these clearly require new structures.
Not only do such structures constitute qualitative changes – and hence are outwith their premiss that all of the changes they model are only quantitative, but – the main point I am making – these new structures would require new genes – almost invariably at least some new structural genes, and always new control /regulatory genes to ensure that the structural genes are used appropriately.
To gain a sharp image it is clear that whatever layers are in front of the light-sensitive cells need to be transparent. But biological tissues are generally not transparent – they are usually opaque, or at best translucent, because light passing through them is scattered by the many changes of optical density encountered in passing between cells and through their various constituents, especially the many different organelles (nucleus, mitochondria etc.). Nilsson & Pelger’s only comment about transparency is that their starting point includes a transparent protective layer in front of the light-sensitive cells; so the biochemical challenges of transparency are side-stepped (like those of light-sensitivity).
The vertebrate eye has two major transparent tissues – the lens and the cornea – and it is worth noting that their structures are adapted to achieve transparency in different ways; so, yet again, one cannot be merely a quantitative development of the other. Indeed, both entail sophisticated morphological and biochemical specialisations.
Specialisations of the lens to maximise transparency include:
- The high optical density (refractive index) of the lens fibres is achieved by high concentrations of crystallin proteins which are capable of adopting a glass-like configuration which allows relatively uninterrupted transmission of light.
- A particularly notable specialisation is the dissolution of cell organelles, including the nucleus, from the lens fibres. We do not yet know how this is effected, but one group of investigators comment
- Scattering at the cell borders is minimized by the close apposition of lens fibre cells facilitated by a plethora of adhesive proteins, some expressed only in the lens.
- And, whilst the developing lens requires a blood supply, as the lens matures the blood vessels regress and are completely absent from the postnatal lens, so there is no scattering by them or absorption of light by haemoglobin.
Whilst some of these crystallins have other biochemical functions, it should be noted that they are organised within the lens using what are called beaded filaments which use at least two proteins, CP49 and filensin, which are unique to the lens.
Any model of this process has to account for how the myriad individual components of the various organelle systems are rapidly degraded while the cytoplasm (most notably the assembly of crystallin proteins), the membrane, and critical components of the lens fibre cytoskeleton (including actin and the beaded filament proteins CP49 and filensin) are spared. 
Together, these structural adaptations serve to minimize light scatter and enable this living, cellular structure to function as ‘biological glass’. 
There can be no doubt whatever that these adaptations would require significant new genes, both structural and regulatory. It really is time that biologists stopped proposing evolutionary scenarios that completely ignore genetic and biochemical implications. They have got to be taken seriously. A blind faith in the power of opportunistic genetic variability just will not do.
Genetic aspects of lens development
So, even from just a straightforward consideration of the morphology of eyes and how they form embryonically, it is abundantly clear that it is hopelessly naïve to think that they could evolve simply by quantitative changes of a primitive light-sensitive patch. On the contrary, it is inescapable that the evolution of an eye would involve qualitative changes which require new genes e.g. for new structural proteins, and new regulatory genes to ensure that the structural proteins are used correctly.
And we do not need to speculate about this. Even before Nilsson & Pelger’s paper we were well aware of some of the genetic mechanisms involved in the embryonic formation of eyes. And, of course, ongoing research continues to discover many more, which underlines the fact that evolutionary scenarios that consider only the morphological level are anachronistic and of little if any value.
An interesting aspect of embryonic development is induction - where cells from one tissue stimulate a response in another by means of a chemical messenger. Induction mechanisms that have been identified in the embryonic formation of a vertebrate eye are illustrated in Figure 4.
Of particular note is that on one hand the optic vesicle induces the lens ectoderm to develop into the lens placode (on its way to become a lens), and on the other there is a reciprocal mechanism such that further development of the optic vesicle is dependent on induction from the nascent lens: If a barrier is placed between the lens vesicle and ectoderm, not only does the lens placode not form, but development of the optic vesicle ceases and, not only is there no optic cup, but also no retina formed. This is but one example of the complex interplay of genetic and molecular mechanisms involved in embryonic development.
Also, significantly, because development of the retina is dependent on the nascent lens, - i.e. the lens is not a later addition to the retina - it indicates that Nilsson & Pelger’s model of eye evolution is not applicable to the vertebrate eye.
Finally, note that here I have considered only the lens. Similar genetic and biochemical implications apply to every part of the eye's structure.
2. The time required for an eye to evolve
As just outlined, the most fundamental failing of Nilsson & Pelger’s model for the evolution of an eye is that it fails to take seriously the need for new genes. This failing completely undermines their model and conclusions.
However, their failings do not stop there. Given that the focus of their paper is the time required for an eye to evolve, directed by natural selection, so presumably they intended their conclusions to be taken seriously, it beggars belief that their calculation relates not to the operation of natural selection – even though they repeatedly say that it is through natural selection – but due to domestic breeding! Here is what Nilsson & Pelger say about how they calculated the time required for an eye to evolve (p57, underlining added).
4. THE NUMBER OF GENERATIONS REQUIRED
Having quantified the changes needed for a lens eye to evolve, we continue by estimating how many generations such a process would require. When natural selection acts on a quantitative character, a gradual increase or decrease of the mean value, m, will be obtained over the generations. The response, R, which is the observable change in each generation is given by the equation
R = h2iσp or R = h2iVm,
where h2 is the heritability, i.e. the genetically determined proportion of the phenotypic variance, i is the intensity of selection, V is the coefficient of variation, which measures the ratio between the standard deviation, σp, and the mean, m, in a population (Falconer 1989). For our estimate we have chosen h2 = 0.50, which is a common value for heritability, while deliberately low values were chosen for both i (0.01) and V (0.01) (see Lande 1980; Futuyama 1986; Barton & Turelli 1989; Falconer 1989; Smith 1989). The response obtained in each generation would then be R = 0.00005m, which means that the small variation and weak selection cause a change of only 0.0005% per generation. The number of generations, n, for the whole sequence is then given by 1.00005n = 80129540, which implies that n = 363992 generations would be sufficient for a lens eye to evolve by natural selection.
The reference for the equation they use is Introduction to quantitative genetics by Falconer, D.S., 3rd edition (1989) . The above equation is taken from chapter 11 ‘Selection: I. The response and its prediction’; and one wonders whether Nilsson & Pelger bothered to read beyond the chapter’s title, because the first sentence of that chapter is:
Up to this point the treatment of metric characters [i.e. continuously varying, rather than discrete] has been mainly concerned with the description of the genetic properties of a population as it exists under random mating, with no influences tending to change its properties; now we have to consider the changes brought about by the action of a breeder or experimenter. (p187, emphasis added)
The whole of the chapter, including the equation used by Nilsson & Pelger, is about intentional breeding, not natural selection. Indeed, in leading up to the equation used by Nilsson & Pelger, Falconer stipulates that
we must add the further condition that there should be no natural selection: that is to say, that fertility and viability are not correlated with the phenotypic value of the character under study. (p189, emphasis added)
Clearly Nilsson & Pelger were either incompetent (because they hadn’t understood the equation they were using, despite it being plainly presented) or disingenuous (because they understood it was inappropriate but used it anyway) when they wrote their paper. The fact that the equation they used relates to intentional breeding and not natural selection means that their calculations are completely irrelevant and misleading. But it is instructive to look a bit further.
By way of a reminder – heritability is the proportion of the variance (in the phenotypic character of interest) of a population due to genes and hence heritable (recognising that many characteristics will vary somewhat due to the individual’s environment e.g. nutrition may affect size). Nilsson & Pelger chose a value of 0.5 (= h2) for heritability which they consider a ‘common value’, and assume this is applicable throughout their supposed evolution of an eye. But, again, they should have read what Falconer had to say:
The prediction of response is valid, in principle, for only one generation of selection. The response depends on the heritability of the character in the generation from which the parents are selected, so responses in later generations cannot, strictly speaking, be predicted without determining the heritability in each generation. There are two reasons why the heritability is expected to change. First if there is a response the gene frequencies must change, and heritability depends on the gene frequencies. This change is not likely to be apparent for some considerable time because gene frequency changes are small unless only a few loci are involved. Second, the selection of parents reduces the variance and the heritability. This takes place in the early generations. It will be explained briefly later and will be ignored meantime. These expected changes in the heritability are not large, however, and experiments have shown that response is usually maintained with little change over several generations – up to 5, 10 or even more. (p190)
So it was clearly invalid for Nilsson & Pelger to use a constant value for heritability (over 100s of 1000s of generations) – without any regard for the effect of selection on the degree of heritability. As Falconer makes clear (and is well known anyway), the effect of selection is to reduce genetic variability. Which leads back to their main failing – any evolution of the sort Nilsson & Pelger envisage for an eye, would require new constructive genetic variability – specifically, new useful genes.
The common belief is that the loss of variability through selection is compensated for by new useful genes arising, generally through mutation. I elaborate on this elsewhere, but the two main reasons for believing that useful new genes arise are:
- belief that evolution is true, this requires new genes to arise, so they must happen some time; and
- mutations do introduce genetic variability by corrupting genes, but there isn’t sufficiently clear thought given to the distinction between constructive and deleterious mutations, so it is thought that at least some times mutations introduce new useful genes (despite the strong case against this happening, and see variations caused by corrupting genes).
Even if 0.5 were a reasonable starting value it certainly cannot be assumed that new genetic material will arise sufficiently frequently (every 5, 10 or so generations) to maintain it at this level. Again, it is so well known that genetic variability decreases with selection – did Nilsson & Pelger think that somehow or other their model would be immune to this? More importantly, what would be required is not just some general 'genetic variability' but appropriate specific genes to effect the specific morphological changes required by their model.
A similar failing is their assumption of a constant value for the coefficient of variance (V, the ratio between the standard deviation, σp, and the mean, m, in a population). As Falconer mentions in the preceding quotation, the effect of selection is to reduce variance (because it decreases the genetic variability), i.e. there is a narrower range of values (or spread) of the character in question.
The consequence of their assumption is that in each generation there is a constant proportionate increase in the (relevant) morphological step. So, whereas we know that in reality the steps that can be achieved with breeding get progressively smaller, their calculations assume they will get progressively larger! This anomaly is so obvious – how could it not alert the authors to the fact that their calculations were erroneous?
In the morphological description of their model they use steps that confer a 1% increase in visual acuity.
This itself seems to be unrealistic, and it would make more sense to describe morphological change of a tissue in terms of its physical size rather than a more derived parameter such as visual acuity.
However, in a sense it does not matter, because they only use this as a means to express the overall morphological evolution of an eye as a linear increase.
But it certainly does matter when they come to estimate the time required for the supposed evolution to take place.
Their calculations are so flawed that, far from demonstrating what they claim, they show that they cannot even be taken seriously.
It is astonishing that two professional biologists could present such a piece of nonsense as this paper by Nilsson & Pelger. Not only is their proposed scenario anachronistic and mere wishful thinking, their calculations are discreditably false. Yet what is even more astonishing – and disturbing – is that they were allowed to get away with it, and have their paper published in the proceedings of the Royal Society. So much for peer review!
That morphological novelties require specific new genes is a common blind spot of Neo-Darwinism; so, although this is the fundamental failing of Nilsson & Pelger's paper, it is perhaps not surprising that this failing was overlooked. But to allow a paper that uses an equation for predicting the response of intentional breeding as a basis for calculations purporting to show the action of natural selection is utterly inexcusable. Presumably the reviewers were so happy with Nilsson & Pelger’s conclusion “the eye was never a real threat to Darwin’s theory of evolution” (p58) that they didn’t bother to scrutinise it properly; or, worse, they did look but did not want to stand in the way of a paper that ostensibly supports such an icon of evolution. It illustrates so plainly that evolution is the prevailing paradigm in biology (see Neo-Darwinism).
And of one thing we can be certain: If a paper that highlighted a deficiency in the theory of evolution were presented for publication, it would be scrutinised exceedingly carefully; and if found to be similarly flawed, not only would it never see the light of day but its author(s) would be pilloried.
Notes display in the main text when the cursor is on the Note number.
1. Dan-E. Nilsson and Susanne Pelger, A pessimistic estimate of the time required for an eye to evolve, Proceedings: Biological Sciences, Vol. 256, No. 1345 (Apr. 22. 1994), 53-58.
2. See Wikipedia article 'Cichlid'.
3. Steven Bassnett, Yanrong Shi and Gijs F. J. M. Vrensen, Biological glass: structural determinants of eye lens transparency, Phil. Trans. R. Soc. B (2011) 366, 1250-1264, p1255.
4. Steven Bassnett, Yanrong Shi and Gijs F. J. M. Vrensen, Biological glass: structural determinants of eye lens transparency, Phil. Trans. R. Soc. B (2011) 366, 1250-1264, p1250.
5. Falconer D.S., Introduction to quantitative genetics, 3rd edition (1989), Longman.
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