Evolution of the Eye: Nilsson & Pelger and Lens Evolution

In the last post we looked at the development of pinhole cameras which, forming an aperture, reduce the number of photons which hit the retina, and consequently improves the image, whilst, conversely, the image is dimmed somewhat due to the reduction of photons. We then looked at the emergence of lenses and observed the vitreous mass “lenses” of various sea creatures. In this post, following from where we left off on the climb up the slopes of Mount Improbable, we look at Dan Nilsson and Susanne Pelger’s computer simulation of lens evolution, which is, by the way, fascinating, and demonstrates the power and existence of evolutionary convergence.

Nilsson and Pelger postulated there being three types of tissue of which the eye was comprised: an opaque shield which covered the back of the eye; photocells; and a transparent film or substance (an example of this would be the vitreous mass which we looked at in the previous post.) An eye endowed with the previous constitution formed the basis from which their evolutionary simulation would begin (Phase One, below. (This and the following diagram (Phase Eight, below) from Nilsson and Pelger’s simulation taken from Figure 5.14, Climbing Mount Improbable.)) In other words, this eye rests at the foot of Mount Improbable.

Phase One

From this primary form we can begin the ascent up the long (though, as we shall see, in one sense, surprisingly short, at least geologically) gentle meandering paths of Mount Improbable, incrementally gaining altitude, drawing ever closer to our evolutionary pinnacle: a complex fish eye (Phase 8, below).

Phase Eight

So, how did N&L intend their computer eyes to evolve? Well, they treated a genetic computer mutation as a percentage change in a certain part of the eye, for example, a decrease in the thickness of the transparent layer. A mutation would affect the size of part of the eye, or the functional quality of a part of the eye, such as the refractive index (which we will come to later). And, importantly, the simulation was not programmed to progress in ever-improving stages, as if the whole evolutionary progression was pre-programmed and they simply divided the one long evolutionary phase into lots of small phases, chopping up a pre-selected evolutionary progression into small quantifiable, arbitrary units. Instead, they allowed mutation from which would be selected the variations (mutations) which improved the computer eye – true natural selection.

Before we carry on we need to have a quick look at the afore-mentioned refractive index. Refractive index is the speed at which light travels in a certain substance and the refractive index will determine the quality of the lens and the convergence of light rays. I wrote briefly about refraction in the previous post, and what I wrote about there is basically what I am writing about now. By allowing mutation in the refractive index of the computer eye, and thus allowing variation which selection could then act upon. The single criterion which selection solicited was improved eyesight. If this criterion was met, however fractionally, selection would harness it and further “act” upon it.

An ideal lens would gradate smoothly, with a continuously varying refractive index. Such a lens is difficult, though not impossible, to manufacture artificially, but biologically things are much, much simpler, because a biological lens is not assembled from discrete pre-made constituent pieces, but forms and grows over time. N&L did not predispose, or pre-programme, their simulation to produce such an ideal graded index lens, but rather simply by letting “natural selection” act upon the eyes which mutations threw up, their simulation spawned just such a fine graded index lens. This affirms the power of non-random selection over random mutation.

Nilsson and Pelger's complete eye evolution simulation

So, N&L’s simulation demonstrated the physical evolution of a complex fish eye, equipped with a sophisticated lens, but it also demonstrated the temporal evolution of such an eye. Their simulation took 1,829 steps to evolve the eye when a change in the magnitude of something (such as the refractive index, or in the thickness of the transparent layer) equalled 1%. When a change in the order of magnitude equalled 0.005% the simulation took 363,992 steps. The step numbers are arbitrary; there needs to be some definite quantifiable unit of magnitude, and that meant looking to real genetic change.

N&L postulated that for every 101 animals who possessed the improved eye 100 without the improved eye would survive. Selection pressures vary, though it may be difficult to assign numerical figures to real situations, but for this simulation where N&L selected the selection pressures they could choose to be as “optimistic” (choosing a low survival rate for those without the improved eye, thus shortening the evolutionary timescale) or as “pessimistic” (a higher survival rate for those without the mutation, meaning a longer evolutionary timescale) as they liked, and they configured their simulatory ecology with a very low selective pressure for developing a better eye. If you have a 99.009901% chance of survival without the eye, it is not that worth “developing it.” We can assume, therefore, that in reality their temporal estimate would be too long! As Dawkins writes, “they were bending over backwards to bias their estimate of rate of evolution towards being, if anything, too slow.”

The remaining factors which had to be addressed were the “coefficient of variation” (the measure of a population’s variation) and “heritability” (the measure of heritability of a population’s variation). If heritability is low then much of the variation is environmentally induced, whereas a high heritability means the opposite. Standard heritability is typically ≥50%, so N&L settled for the “pessimistic” heritability figure of 50%. They really were “bending over backwards to bias their…rate of evolution towards being…too slow.”

So, how long would it take, then, to evolve a fish’s complex camera eye? Nilsson and Pelger’s final estimate came to 364,000 generations. And, considering the small marine animals’ (in which this camera eye would evolve) generation length of (≈) 1 year, the eye would take but, roughly, 364,000 years – less than half-a-million years. This simulation spawned a surprisingly short timescale for the evolution of a complex eye, and demonstrates that it is well within natural selection’s reach to evolve such an eye.

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Dawkins, R. (1996). Climbing Mount Improbable. (Viking: London).

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© Francis Smallwood 2010

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