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  • Self-organization

    I’ve come across a series of fascinating articles which to an extent looks at evolution in a different way, and most certainly looks at the cell and cellular processes in a new way.

    The articles deal with a process familiar to physicists, called “self-organization”.

    Self organization is a process whereby some kind of structure or process pops into existence, doing so thanks to local interactions between components of a system that was initially disordered. Its a spontaneous process, requiring no controlling agent either inside or outside of the system. Crystalization is an example of self organization. Convection patterns in a liquid heated from below is another example. Self-organization is, to use that cliche, “order out of chaos”.

    Two papers in particular make for an interesting read:-

    Self-organization, Natural Selection, and Evolution: Cellular Hardware and Genetic Software

    Self-Organization versus Watchmaker: stochasticity and determinism in molecular and cell biology

    Both papers are quite readable although the second of the two is more global in scope. The first looks at the process of self-organization in the context of evolution, particularly the role of natural selection. The second looks at self-organization in the context of the cell and cellular components and perhaps makes for a more interesting read. This is so because it challenges so much of what we think we know and understand about the cell and the processes which occur inside of it.

    Basically the second paper blames Newton and Descartes for setting us up with a reductionist, mechanistic, clockwork view of the universe. The problem with this has been that once scientists came to grips with the notions of the cell, ribosomes, DNA, and genes, so they interpreted their experiments in the light of this mechanistic clockwork paradigm. And when electron microscopes and other devices were invented such that the cell and its subsystems could be “observed”, so scientists continued to interpret what they saw, using this paradigm. Thus the cell and its various subsystems were seen as mini-factories. Proteins and other molecules moved around thanks to systems of levers and cogs.

    However, the second paper argues, this is really a deception. At the level of the cell and its various components, these mini-factories and systems of levers and cogs simply don’t exist. What is being viewed are molecules and conformations that are continually falling apart and reforming, and its this that allows these subsystems to do work and to evolve, thereby allowing an organism to live and organisms to change over time.

    It’s this kind of work that’s behind the occasional claims that evolutionary biology needs a rework, that the current paradigm is anything from totally inadequate to adequate, but in need of retuning and reconceptualizing at its most fundamental level.

    I found both papers to be a thrill to read.


I am not qualified to judge them to be right or wrong, but I do understand them enough to find their ideas very interesting.


Next time you read a text book on molecular biology, the cell, genetics or evolution, these papers will make you ponder as to what is really happening at the deepest physical level. They will certainly sit in the back of my mind at least.


They remind me a bit of quantum mechanics and its relationship to classical physics. In our world, we see levers, gears, and cogs doing things and moving things. In the world of quantum mechanics, this simply does not happen. Virtual particles pop in and out of existence. Particles can be here and there, lacking a discrete existence.

    And it’s like that here. Proteins might look like levers in some cases, levers that mechanically move along some part of a cellular structure, thanks to the mechanical forces of classical physics as used by engineers. But, say these scientists, that is not what is happening. Rather the proteins continually fall apart and self-organize and because this happens in the context of a surrounding environment, this is what causes the protein to move, as it reassembles itself in part or in total.

    It’s like hopping in a car to drive from Adelaide to Sydney, and the car moves, not because of levers causing wheels to turn, but the car moves because its wheels continually fall apart and reassemble, and in the process moves the car on its journey.

 This movement occurs because, during the reassembly, the components interact with an environment which brings about this motion.

    And they claim to have the experiments to support this new way of looking at life.


Over the next set of posts, I’ll describe that first paper. There are a couple of reasons for this - it’s shorter, deals only with one topic - evolution, and was easier to understand.

    My war in reorganizing the back yard continues, and in a few days I go away on holidays. So there may be breaks in posting.

    To be continued ....

    Last edited by rwatts; 01-08-2015, 03:51 PM.

  • #2
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .


    I do not know, therefore everything is in pencil.


    • #3
      Originally posted by shunyadragon View Post
      Yes. I thought so too.

      Like I said, I'm not really qualified to judge but from the bits of physics and biology I do know, but this came across as [mods keep away ] really bloody [/mods keep away ] interesting.

      I also found myself beginning to understand what dissipative structures are and what order out of chaos is all about.

      All in all I'm finding the papers a bollicking of a good read.


      • #4
        The abstract of the first paper linked to in the OP reads as follows:-

        Originally posted by abstract
        Self-organization is sometimes presented as an alternative to natural selection as the primary mechanism underlying the evolution of function in biological systems. Here we argue that although self-organization is one of selection's fundamental tools, selection itself is the creative force in evolution. The basic relationship between self-organization and natural selection is that the same self-organizing processes we observe in physical systems also do much of the work in biological systems. Consequently, selection does not always construct complex mechanisms from scratch. However, selection does capture, manipulate, and control self-organizing mechanisms, which is challenging because these processes are sensitive to environmental conditions. Nevertheless, the often-inflexible principles of self-organization do strongly constrain the scope of evolutionary change. Thus, incorporating the physics of pattern-formation processes into existing evolutionary theory is a problem significant enough to perhaps warrant a new synthesis, even if it will not overturn the traditional view of natural selection.
        The authors are summarizing their paper as follows:-

        1. Some folk see self-organization as an alternative to natural selection as a generator of new functionality in biological systems as those systems evolve.

        2. The paper argues that selection remains the fundamental creative force in evolution and it uses self-organization as one of its tools.

        3. The self organization of biological systems is exactly the same self-organization seen in physical systems.

        4. “... selection does not always construct complex mechanisms from scratch. However, selection does capture, manipulate, and control self-organizing mechanisms ...”. That is self-organization generates structures which selection then acts on to accept or reject.

        5. Capturing and maintaining these self-organized structures is difficult because such structures are sensitive to environmental conditions. For example, such structures only come into existence within a very narrow range of environmental conditions. And so having them exist in the first place, and then continue to exist so that selection can act on them would seem to be problematical.


6. The often inflexible principles of self-organization actually constrain the scope of evolutionary change. Evolution is limited to what it can and cannot do because of these inflexible principles.

        7. Given points 5 and 6, incorporating the physics of pattern formation into theories of evolution may well bring about a new evolutionary paradigm. Nevertheless, natural selection may well continue to play a central role.

        To be continued ....


        • #5
          Before they discuss self-organization and its relationship to evolution, the paper has three sections - an introduction, a historical preface and a description of evolutionary biology as it is today, focusing mainly on selection.


          Here Johnson and Lam note that a diverse group of people in physics, mathematics and biology have argued that self-organization is at least as important as natural selection in evolution. However, most research into the mechanisms of evolution continue on along traditional lines, ignoring these calls to consider and investigate the role of self-organization.

          Johnson’s and Lam’s paper is another attempt to show the importance of self-organization as a mechanism in evolution, but unlike some, demonstrate that even though it is ubiquitous and creative, it remains used by natural selection, as opposed to being complementary to it, even relegating natural selection to unimportance.

          Their paper is broken into sections which aim to:-

          1) Review of evolutionary theory with an emphasis on those aspects of the theory which are important to their discussion of self-organization.


2) Introduce self-organization and to do so in an intuitive manner.

          3) Discuss the “intersection between natural selection and self-organization”. Here they aim to clear up the misunderstanding that self-organization “competes with natural selection as the organizing force in evolution”. And they intend to show the many ways in which the process affects evolution.

          Evolution to date, has largely been about the gradual evolution of structures and functions and the authors think that the role of (any) “controlled but largely spontaneous” evolution is “the chief unanswered question of today”.

          They note that many folk in the self-organization field deem that a new synthesis might be needed because evolution at the macroscopic level (the morphological level) may in fact be very different to evolution at the molecular level, where self-organization plays out. They suggest “[a]s the first modern synthesis incorporated genetics into natural selection, this new synthesis seeks to incorporate the physics of complex systems”.

          Aside - a background read.

          A name which often appears in these kind of papers is that of Ilya Prigogine. He won the Nobel Prize in 1977 for his work on the thermodynamics of non-equilibrium systems (living organisms are one example of such systems). Prigogine and Isabelle Stengers wrote the following book which was published in 1984:-

          Order Out of Chaos

          To be continued ....

          Last edited by rwatts; 01-10-2015, 03:22 PM.


          • #6
            A brief historical preface

            In a subsection of their introduction with the above mentioned title, the authors describe why there might be a clash of perspectives within the study of evolution.

            Evolution by natural selection is one of biology’s best supported theories. However, the theory was fully formed well before the era of molecular biology. Johnson and Lam make a special note of this because, they argue, the theoretical underpinnings of natural selection were developed using data at the macroscopic level. While the same principles may well apply at the molecular level, and it seems to in many cases, the principles may not universally apply, and molecular biologists may well have a point when they argue that something different is also going on at the molecular level.

            And the authors conclude that evolutionary biologists should not be skeptical at the claims of the molecular biologists because “given the history, it would be surprising if a major new approach to evolution were not necessitated by data on life at the molecular level.”.

            Following this, in a section titled:-


Evolutionary biology

            - the authors give a sketch of evolutionary biology, particularly natural selection and those aspects of the process that are most relevant to their discussion.

            I’ll not dwell too much on this section because I want to get onto self-organization, and besides evolution and natural selection are often described by various posters, so much so that even creationists should have a degree of understanding.

            The authors offer an interesting definition of evolution, one that encompasses all the processes they think are relevant to the process. They define it as:-

            The historical process that leads to the formation and change of biological systems.
            Because their interest is in the evolution of function and selection is what gives rise to function they write that natural selection is the consequence of three properties of organisms: 1) variation, 2) differential reproduction, and 3) heritability of traits important for survival or reproduction. And much research focuses on mathematical models of these properties.

            The authors intent however is to briefly discuss three consequences of 
natural selection that have fascinated biologists - adaptation, functional constraint (are all variations of a trait possible, or are variations constrained?), and the nature of evolutionary trajectories (does selection form new adaptations quickly or gradually).

            Johnson and Lam spend a paragraph discussing each of these three points, and if the reader is interested, this discussion can be found at the first link in the OP.

            Then the authors turn their attention to self-organization.

            (Much to my sadness, I shall be absent for the next few weeks. Holidays you see.

            If Jorge was around, I'd ask him to take over in my absence.)

            To be continued ....


            • #7
              Enjoy your vacation
              Glendower: I can call spirits from the vasty deep.
              Hotspur: Why, so can I, or so can any man;
              But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

              go with the flow the river knows . . .


              I do not know, therefore everything is in pencil.


              • #8
                Well, the holidays are over and it’s back to reality. Get your violins out and give me a white handkerchief.

                Having provided a bit of a background and introduction to evolution and the idea of self-organization, Johnson and Lam then describe the process in more detail.


Self Organization

                Systems of self-organization contrast to what they label “conserved systems”. In conserved systems, energy is conserved whereas in self-organizing systems, energy is continually flowing through and being dissipated. 

                Self-organization creates “dissipative structures” which can only persist as long as energy is continually being input and flowing through them. Hence a dissipative structure is not like, say, a salt crystal which persists without any input of energy once the crystal is formed. Rather a dissipative structure is like a hurricane which continually feeds off energy supplied to it by the ocean and which begins to “die” when the hurricane reaches landfall and no longer has that supply of energy. That is, a hurricane is a self-organizing system. It is a dissipative structure.

                We humans are dissipative structures. We require a continual source of energy and once any energy reserves are depleted, we begin to die.

                As the authors write:-

                Originally posted by link at OP
                A dissipative structure is thus not a structure at all, but a metastable pattern
                Our existence is stable only so long as energy is supplied to us.

                They note that we are surrounded by “purely physical self-organization patterns” and in the following section introduce one such pattern, the cell, while noting that self-organization is also important in developmental and other branches of biology.

                Underscoring what has just been described is the following quote by Alvin Toffler in the forward to a book by two particular metastable structures, known as Ilya Prigogine and Isabelle Stengers. They wrote a book, based largely on their work regarding these systems for which Prigogine won the 1977 Nobel Prize in chemistry. (Prigogine’s structure decayed to the point that it could no longer extract energy from the environment to maintain itself and so Prigogine returned to disorder back in 2003. On the other hand, the structure we know as “Isabell Stengers”, remains viable.) Toffler, explaining how the concept of dissipative structures contrasts with Newton’s clockwork, machine view of the universe, writes:-

                Originally posted by Alvin Tofler in a forward to “Order out of Chaos”, Fontana Paperbacks, 1984, p 15

                Summed up and simplified, they [Prigogine and Stingers] hold that while some parts of the universe may operate like [Newton's clockwork] machines, these are closed systems, and closed systems, at best, form only a small part of the physical universe. Most phenomena of interest to us are, in fact, open systems, exchanging energy or matter (and, one might add, information) with their environment. Surely biological and social systems are open, which means that the attempt to understand them in mechanistic terms is doomed to failure.

                This suggests, moreover, that most of reality, instead of being orderly, stable, and equilibrial, is seething and bubbling with change, disorder, and process.

                In their next section the authors introduce the cell as a self-organizing system and in the process provide some ideas which, while very new to me, are both interesting, tantalizing and in a general sense, seemingly correct, even if, in a few cases, my mind initially balks at.

                To be continued ...

                Last edited by rwatts; 01-31-2015, 02:46 PM.


                • #9
                  Having described self-organisation, and introduced dissipative structures which, for their maintenance, require a continual flow-though of energy, the authors turn their attention to:-

                  The Cell: The functional unit of biology

                  It’s here that the article begins to get really interesting and provocative. Provocative, not because it necessarily says things that are controversial in the scientific world, but provocative in that I’d never really considered them or thought them through before.

                  Self-organization is, they say, “the fundamental mechanism within the cell”. From there, they claim (and are probably correct) that “the importance of the cell to evolutionary processes is usually downplayed in basic texts on evolution”.

                  To show how important the cell is, or should be, they write that genes don’t make cells. They don’t code for their construction. Cells are units of inheritance from a parent, just like DNA. Furthermore, the cell’s mechanisms are independent of DNA and are enormously complex. (DNA does have an important role to play in cellular mechanisms, but the authors are looking at it from a different perspective. This distinction should become clear shortly.)

                  These two facts have consequences for evolution. 

The cell is inherited and its processes cannot always be constructed from new via genetic instructions. But genes do control and manipulate a cell’s ongoing behaviour. The gene is the cell’s “information-storage device”, but only some information is stored there. Other information is stored within various subsystems of the cell. The basic mechanisms (these cellular subsystems and their interactions) of life are inherited as ongoing, continuous processes. They are not inherited as outcomes of DNA processes. Furthermore, if life evolved as a coupled set of interacting processes between itself and its component parts, then it has remained that way ever since.

                  Given all this, any evolutionary theory which focuses on the “shuffling of genes propagating through time” is necessarily a limited theory because the cell itself as well as its processes are the engines of life and these constitute far more than just the genes and their manipulations of the cell.

                  In short, these self-organization processes pay a large role in cellular dynamics, and that role is, or largely is independent of genes. Genetic processes have one large role to play and self-organization another large role. To be a better theory, evolution needs to consider both aspects.

                  To be continued ...


                  • #10
                    The zygote inherits much more than a mixture of DNA from its parents? I don't see any mechanism for non-DNA inheritance. Or have I really, totally, misunderstood your post?
                    The greater number of laws . . . , the more thieves . . . there will be. ---- Lao-Tzu

                    [T]he truth I’m after and the truth never harmed anyone. What harms us is to persist in self-deceit and ignorance -— Marcus Aurelius, Meditations


                    • #11
                      Originally posted by Truthseeker View Post
                      The zygote inherits much more than a mixture of DNA from its parents? I don't see any mechanism for non-DNA inheritance. Or have I really, totally, misunderstood your post?
                      I'm unsure of what you are trying to ask.

                      The paper is not claiming that the only thing that gets inherited is DNA.


                      • #12
                        Biological examples of self-organization

                        In the section with the above mentioned title, the authors begin with two simple examples of self-organization. The first is the formation of the tobacco mosaic virus and the second is the formation of microtubules.

                        With the tobacco mosaic virus, the parts of the viral coat, under the right conditions, self assemble like a jigsaw puzzle putting itself together. Once the coat is formed, no further energy input is needed. The coat is stable. With microtubules, thin filaments that give a cell support and help it to do work, the filaments self-assemble in a similar way, except that the pieces continually come and go in a dynamic way. Here a continual input of energy is required to maintain the structure, and these kinds of organizations are called “dissipative structures”.

                        More complex examples of self-organization are DNA repair and transcription. Initially it was believed that these processes are undertaken by mini-machines floating around in the cytoplasm. However, when repair to a particular location of damaged DNA is required, the repair mechanism self-organizes from the cytosol. Until then, its subunits are dissolved within the cytosol.

                        The repair work is done and when completed, no further energy input occurs to maintain the structure and so it simply dissolves back into the cytosol.

                        For the repair structure to form spontaneously, an optimum concentration of subunits must be maintained in the solution. The associated molecular crowding helps maintain large numbers of random interactions, an important aspect of the self-organization process. It’s a problem the cell has to overcome, the creation and maintenance of just the right conditions so that self-organization can occur when needed.

                        The authors speculate on how the self-organization might be triggered. Rain “instantly” forms in clouds, saturated with water vapour above a certain threshold, providing seed particles exist. This is the principle behind cloud seeding, where large number of artificial seeding nuclei are fed to the cloud. They think something like this may be one mechanism used by the cell. Consider macro-molecules dissolved in the cell’s cytosol. The problem is to get these molecules together so that they can self-assemble. As opposed to evolving a molecule gathering machine, the cell could simply send out seed molecules and achieve the desired result, but with a very low expenditure of energy.

                        They offer another possibility, whereby to transport molecules around the cell, as opposed to transport machines (some of which do exist, for example, vacuoles), a cell could simply tag molecules to be sent, and tag destinations. Molecules with the right tags can be simply fished out of the stream by the destination molecules.

                        The authors conclude the section by pointing out that self-organizing mechanisms are the focus of intense study in biology and they provide the interested reader with the following list of articles in their reference:-


1. Murray AW, Kirschner MW. 1989. Dominoes and clocks: The union of two views of the cell-cycle. Science 246: 614–621.

                        2. Novak B, Tyson JJ. 2003. Modelling the controls of the eukaryotic cell cycle. Biochemical Society Transactions 31: 1526–1529

                        3. Glick BS. 2002. Can the Golgi form de novo?Nature Reviews Molecular Cell Biology 3: 615–619.

                        4. Carazo-Salas RE, Nurse P. 2006. Self-organization of interphase microtubule arrays in fission yeast. Nature Cell Biology 8: 1102–1194.

                        5. Misteli T. 2001. The concept of self-organization in cellular architecture. Journal of Cell Biology 155: 181–185.

                        6. Misteli T. 2007. Beyond the sequence: Cellular organization of genome function. Cell 128: 787–800.

                        7. Kurakin A. 2005. Self-organization versus watchmaker: Stochastic dynamics of cellular organization. Biological Chemistry 386: 247–254.

                        8. Kurakin A. 2007. Self-organization versus watchmaker: Ambiguity of molecular recognition and design charts of cellular circuitry. Journal of Molecular Recognition 20: 205–214.

                        9. Karsenti E. 2008. Self-organization in cell biology: A brief history. Nature Reviews Molecular Cell Biology 9: 255–262.

                        Many of these articles can be found online, providing you Google the title. Often you will find a PDF, or alongside the abstract will be a link to the free text. References 1, 7, and 8 are of this nature.

                        To be continued ....


                        • #13
                          Is self-organization an alternative to natural selection?

                          The authors note that some researchers see self-organization as an alternative to natural selection, thereby driving a very different evolutionary process to that generally envisaged by the mainstream of researchers. 

                          However, they don’t accept this, and their reasons are as follows.

                          There is no doubt that self-organizing systems exist within living organisms. Take the cell. The question to be addressed it this - are these self-organizing mechanisms the product of natural selection or are they simply an intrinsic properties of a cell’s physics and chemistry. If the latter then the role of natural selection is much reduced.

                          The authors don’t accept the latter point of view. They think that self organizing systems evolve and that the mechanisms that sustain them evolve. They describe Bernard convection cells as an example illustrating certain properties which are common to both physical and biological self-organizing systems. Bernard convection cells form rapidly and spontaneously under the right physical conditions. However, they do not form robustly, in that if the physical conditions are altered slightly, then the cells break down or fail to form. These properties appear to exist for all self-organizing processes.

                          Such properties are the basis for the argument that natural selection retains its importance in evolution. A cell has to do a lot of work to set up the conditions and maintain them, for self-organization of any subsystem to occur. Furthermore, finding the right elements to react with each other in a self-organizing process is not a trivial task, given all the possible components genes can make. Hence it would seem from these two points alone, if it self-organization were just an intrinsic property of the cell, then the unique processes we see and the common processes that occur amongst cells simply would not be. It’s as if some kind of “hand” is selecting certain kinds of self-organization to exist.

                          Furthermore, given the non-robustness of self-organizing systems mentioned above, the authors point out that cells have to go to great lengths to maintain the conditions to keep any self-organized system from falling apart as soon as it forms. They write that “Organisms are full of such regulatory procedures for maintaining homeostasis in the face of environmental perturbations, whereas self-organizing processes in isolation have no such ability”.


In short, in isolation, a self-organizing process is a product of a given circumstance and when those circumstances change (even slightly), the process breaks down. Such self organization is intrinsic. In biology however, it is different. Amongst all potentialities, only certain self-organizing systems occur, and they have to be maintained in the face of many environmental perturbations. Hence they are not spontaneous in the sense that intrinsic systems or processes are. They write that “selection has to fine-tune and control many parameters to get work out of a self-organization process. Thus, although selection does not need to construct an elaborate plan to generate complexity when self-organization is involved, it does have to drive the evolution of elaborate mechanisms for invoking self-organizing processes and controlling their dynamics. Therefore, selection should play the dominant organizing role even when much of the complexity one observes appears to be spontaneous.”

                          To be continued ...


                          • #14
                            Self-organization, adaptation, and evolutionary trajectories

                            Early in their article, the authors had briefly discussed four consequences of natural selection that are important to an understanding of the evolutionary process. In this section they discuss how an understanding of self-organization can impact these consequences.

                            First they discuss adaptations and evolutionary trajectories or evolutionary pathways.

                            The eye is offered as an example. It’s evolution from a simple to a complex structure can be reasonably understood as a long path of adaptation adding more complexity over time as a result of a gradual process of selection acting on variation. Perhaps a typical understanding of this is illustrated by the following paper:-

                            A Pessimistic Estimate of the Time Required for an Eye to Evolve

                            However, there is another process by which structures form, and this occurs a lot at the molecular level. The Tobacco Mosaic Virus offers an example of this process. Break the virus up into its molecular substructures and given the right conditions, it self-assembles.


Note however, that the conditions have to be just right. And this is the point. It’s hard to see how such a molecular structures could evolve in the same kind of way that eyes and hands do, or that other molecular structures do, namely via a process of variation and selection. In many cases these “self-organizing pattern processes we observe .... happen in their entirety or not at all”.

                            As a result, the authors think that in such cases natural selection discovers a structure that has been built via self-organization, as opposed to generating it via self-organization passing through intermediates, something which seems to be impossible. They speculate how this works. A mutation may trigger a self-organizing process to occur within the cell, causing the formation of a molecule that has some fitness effect on the cell or the organism. Given this, selective pressure occurs for the system to develop some controlling mechanism to bring about this self-organization at the right time and in the right place, namely when the cellular conditions are just right. They write:-

                            Originally posted by link at OP
                            In general, instead of building up from scratch, selection starts with an ill-formed, but functional, adaptation, and then adds increasingly complex organizational controls.
                            Unlike conventional evolution, this kind begins with a qualitative jump in phenotype, namely the sudden appearance of a self-organized molecule which natural selection then builds a controlling mechanism around.

                            Again the authors write:-

                            Originally posted by link at OP
                            Further still, exploring the vast universe of qualitatively different molecular conformations for those that work and then selectively favoring them is probably widespread in molecular evolution and differs from the traditional notion of the gradual construction of adaptations through incremental evolutionary change.


To be continued ....


                            • #15
                              Originally posted by rwatts View Post

                              The eye is offered as an example. It’s evolution from a simple to a complex structure can be reasonably understood as a long path of adaptation adding more complexity over time as a result of a gradual process of selection acting on variation. Perhaps a typical understanding of this is illustrated by the following paper:-

                              A Pessimistic Estimate of the Time Required for an Eye to Evolve

                              Dan-Erik Nilsson and Susanne Pelger's mathematical model on how long it would take for a patch of light sensitive cells to evolve into a lensed eye like that seen in many fish is, if you pardon the pun, a real eye opener. Back in 1994 they found that it would take roughly 364,000 generations -- which equates to less than half a million years.

                              They found that it took roughly 400 steps for the photoreceptor layer and pigment layer to form a retinal pit which continued to deepen until after approximately 1000 steps until it formed into a pin-hole camera eye. After this the lens shape continued evolving and the iris flattened allowing better focusing thereby providing improved optical properties.

                              In the end they found that the complete evolution of an eye like those found in a vertebrate or octopus took less than 2000 steps.

                              And as the title of the paper implies, Nilsson and Pelger bent over backwards deliberately choosing low, conservative numbers in their model -- pessimistic assumptions in their calculations -- so in reality it probably would have taken much less time to take place. For instance, they assumed that for every 101 organisms that got a certain mutation which provided them improved vision that 100 without this improvement also survived. This assumes that you are essentially as well off without the improvement in vision as you are with it which in the real word is extremely unlikely.

                              I'm always still in trouble again

                              "You're by far the worst poster on TWeb" and "TWeb's biggest liar" --starlight (the guy who says Stalin was a right-winger)
                              "Of course, human life begins at fertilization that’s not the argument." --Tassman


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