Thursday, December 17, 2015

Strolling around slopes and valleys in the adaptive landscape

Another article about evolution and the attainment of perfection has appeared. This one was published by Nathaniel Scharping on the Discover website [Could Evolution Ever Yield a ‘Perfect’ Organism?].

The article focuses on a recent paper from Richard Lenski's group at Michigan State University (Lenski et al., 2015). Lenski's group asked a different question. They wanted to know whether there was a limit to the increase in fitness in their evolving E. coli populations in the Long-Term Evolution Experiment (LTEE). It's a different question than whether evolution can select for a "perfect" organism because Lenski and his collaborators understand modern evolutionary theory. They know that mutations causing small fitness increases are beyond the reach of natural selection in their evolving populations and they know that deleterious mutations can be fixed by random genetic drift.

They know that real evolving populations can never reach the summit of an adaptive peak or, if they do, they can never stay there.

But, given these theoretical limitations, can their E. coli cultures reach a limit beyond which further adaptation is not possible because of the limitations of natural selection under their growth conditions? You would think that the answer is "yes." Most of us would imagine a hyperbolic curve of decreasing fitness over time where the cultures approach but do not reach a "perfect" level of adaptation. In other words, we imagine that the cultures will climb slowly toward the top of an adaptive peak but get stuck somewhere below the summit where they reach a steady-state condition of survival at optimum—but not perfect—adaptation.

That's not what the long-term evolution experiment has discovered. The results show that the fitness increases are declining in all of the populations but the results do not fit a hyperbolic curve. Instead, the results are more compatible with a power-law curve that does not have an asymptote.

This paper extends the results to 60,000 generations but it's just confirming the earlier results of Wiser et al. (2013). Here's how they describe the result ...
Wiser et al. [4] challenged the presumption that there must be an upper bound to organismal fitness. They measured the fitness trajectories over 50 000 generations for Escherichia coli populations in the long-term evolution experiment (LTEE). They compared the fit of two simple models—a hyperbolic model and a power-law model—that both predict a decelerating fitness trajectory (i.e. a declining rate of fitness improvement), but only the former has an upper limit, or asymptote. The power-law model, by contrast, predicts that the logarithm of fitness will increase with the logarithm of time, a relationship that has no asymptote. Both models fit the observed fitness trajectories well, but the power-law model fit much better. Moreover, if truncated datasets (e.g. from only the first 20 000 generations) were used to predict the subsequent trajectories, the hyperbolic model consistently underestimated the extent of future improvement, whereas the power-law model accurately predicted the changes seen in later generations. Despite having no upper limit, but owing to its logarithmic dependence on time, the power law did not lead to absurd predictions that would seem to violate physical constraints. Indeed, when the power-law model was extrapolated millions of generations into the future, the predicted fitness levels correspond to growth rates that are within the range that some bacterial species can achieve under optimal conditions.
What's going on? These populations are evolving in a constant environment so why isn't there an optimal limit to adaptation?

Evolution is complicated. One of the remarkable things to come out of the LTEE is that the trajectories of evolution are different for each of the twelve populations. The one that evolved the ability to use citrate isn't included in this study and two others can't be included because they don't grow on the plates used to assay for fitness.

Of the remaining nine populations, you can see that they all differ in relative fitness. That's because they have all followed different trajectories over the past 60,000 generations. This is contingency in action. It doesn't explain the slope of the curve but it does suggest that there is no absolute fitness landscape that applies to all of the cultures.

One of the cultures, Ara+1, has the lowest overall fitness of any population. It also showed the lowest increase in fitness—a result that seems counter-intuitive because it has the most to gain. This population has an unusually active transposon (IS150) that creates an unusual number of mutations by insertion. Possibly because of this active transposon, the authors note that, "... this population has, in some sense, gotten stuck in a genotypic region of the fitness landscape that constrains its evolvability."

But the real question is whether the fitness landscape is rugged, with large peaks and low valleys, or smooth, with gently rolling hills. Maybe the whole idea of climbing Mount Improbable is flawed from the get-go and real evolution wanders around a changing landscape of gentle slopes and shallow valleys trying lots of adaptive hill climbing but never getting stuck at the top of a steep hill. As the populations diverge by fixing different (mostly neutral) mutations the adaptive landscape also changes so there's never a "perfect" adaptive goal but only transient hilltops that are forever changing.

The Discovery article quotes Michael Wiser who says,
“The reality is that what would be perfection is going to depend on lots and lots of circumstances. So as the populations adapt and you get different mutations arising and sweeping through the population…you’re going to have different sets of things that are beneficial and deleterious at different times along the evolutionary trajectory.”
It's important to recognize that the trajectory, or path, that a population takes over many generations is a feature that's often overlooked. That path is determined by many chance events, including the chance occurrence of particular mutations at a particular point in time (contingency). This is one reason why mutationism deserves more attention and one more reason in support of evolution by accident.

"Palouse hills northeast of Walla Walla" by Lynn Suckow from Walla Walla, WA, USA - Hills, grain elevator, and little yellow plane (really)Uploaded by X-Weinzar. Licensed under CC BY-SA 2.0 via Commons - https://commons.wikimedia.org/wiki/File:Palouse_hills_northeast_of_Walla_Walla.jpg#/media/File:Palouse_hills_northeast_of_Walla_Walla.jpg

Lenski, R.E., Wiser, M.J., Ribeck, N., Blount, Z.D., Nahum, J.R., Morris, J.J., Zaman, L., Turner, C.B., Wade, B.D., Maddamsetti, R., Burmeister, A.R., Baird, E.J., Bundy, J., Grant, N.A., Card, K.J., Rowles, M., Weatherspoon, K., Papoulis, S.E., Sullivan, R., Clark, C., Mulka, J.S., and Hajela, N. (2015) Sustained fitness gains and variability in fitness trajectories in the long-term evolution experiment with Escherichia coli. Proceedings of the Royal Society of London B: Biological Sciences, 282(1821). [doi: 10.1098/rspb.2015.2292]

Wiser, M.J., Ribeck, N., Lenski, R.E. (2013) Long-term dynamics of adaptation in asexual populations. Science 342:1364–1367. [doi: 10.1126/science.1243357]

41 comments :

  1. This sentence is confusing me:

    "They know that mutations causing small fitness increases are beyond the reach of natural selection in their evolving populations and they know that deleterious mutations can be fixed by random genetic drift. "

    Given that fitness is indeed increasing in these populations, in what sense are fitness-increasing mutations "beyond the reach" of natural selection?

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    1. The ability of natural selection to "detect" beneficial mutations depends on the population size (among other things). Some of these beneficial mutations of very small effect may not be selected by natural selection because they are effectively neutral in the experimental conditions used in the LTEE.

      However, if you are calculating a theoretical peak in an adaptive landscape you need to take into account all possible mutations.

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    2. Okay, that makes sense. It sounded (to me) like you were suggesting that essentially all fitness-increasing mutations were "beyond the reach", and that didn't make sense to me either in the context of the LTEE or the rest of your post, but I get it now. Thanks for the clarification.

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    3. The fact that there continue to be beneficial mutations in the LTEE (that selection can detect) points to the population continually being unable to locate the peak (which of course might be moving, even in such a near-constant environment). That there is a mutational load caused by deleterious mutations affects the question of fixation more than it does whether an optimal genotype is ever reached by any individual or not.

      I also think this makes it unlikely, btw, that any mutations ever go to fixation by drift. Genetic draft/hitchhiking yes, but not pure drift. I think the term "genetic drift" is used too loosely, and that it would be preferable to talk about stochasticity - which is always there, even when selection os strong.

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  2. Oh boy!! I get to correct Larry.

    Wasn't that word in the post title supposed to be "landscape"?

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    1. "Oh boy!! I get to correct Larry."

      Keep dreaming big, Joe ;^)

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    2. Is the spelling "lanscape" some clever pun I missed?

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    3. It's just me making another stupid spelling error.

      Thanks ... but try and move faster so I can fix it before too many people see it. :-)

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    4. I remember that kid in my class. "Excuse me, Doc, but shouldn't that be 'landscape' with a 'd' ?" And I'd make a mental note. "Little Joey, front row, begging for a 'D.' Wish granted."

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  3. Another possibility is that 'perfection' cannot be obtained because organisms are complex as are environments, even under constant conditions. There is always a trade off, slightly better growth rates may be offset by increased waste (I realize waste will continually be removed in a chemostat, but more waste generation means higher levels). Also, if they are assaying fitness on plates but growing the cells in liquid cultures, there is a disconnect as what increases fitness in liquid may very well decrease fitness on solid medium. Now I need to go read the paper, like I didn't have more than enough grading to finish.

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  4. I think that long-term change on adaptive landscapes that themselves change with time has not been overlooked, but rather puzzled about. It is not easy to find a model that seems realistic and at the same time can be analysed. There are many possible models.

    One shorter-term model that leads to insight is by Mark Kirkpatrick in this paper:

    Kirkpatrick, M. 1982. Quantum evolution and punctuated equilibria in continuous genetic characters. American Naturalist 119: 833-843.

    He imagines an adaptive landscape composed of a mixture of two normal-distribution-shaped components, the first component higher than the second. The population comes to sit on top of that peak. But through time, the other peak slowly increases in height, finally surpassing that first peak in height.

    As it gets high enough, the first peak reaches a point where it is no longer a peak, but now just a wrinkle on the side of the second peak. At that point the population suddenly starts moving and climbs the second peak. So within-species individual selection leads to a pattern of punctuated change.

    (Mark also has many other excellent papers on adaptive landscapes that are worth attention).

    But no one yet has proposed long-term multipeak model of a changing adaptive landscape that is persuasively biologically reasonable in its structure and also leads to tractable math.

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  5. We surely have very different views of adaptive landscapes. From my perspective, even considering that there are lots of neutral or nearly neutral mutations the ridges that populations are wandering around on must still be surrounded by deep chasms in many directions. Each knock-out mutation in a survival-critical gene identifies one position at the bottom of such a chasm, plus all the combinations of these mutations.

    One of the problems with contemplating the fitness landscape is of course that is has more dimensions than we can visualise. Given that multi-dimensionality it can be extremely rugged at the same time as containing smooth ridges in five million directions.

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    1. From my perspective, even considering that there are lots of neutral or nearly neutral mutations the ridges that populations are wandering around on must still be surrounded by deep chasms in many directions.

      Why?

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    2. From Alex post above I'd infer the reason to be that there are invariant sites under the near-neutral model. Doesn't seem surprising to me...

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    3. Why? See next sentence. Being inviable due to a deleterious mutation is by definition not being anywhere on the ridge any more, but in many cases it is only 1 mutation away from the ridge. (Many in absolute terms, not in relative terms compared to how many mutations are neutral or near-neutral.)

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  6. Larry, you haven't actually answered why there isn't an optimal limit to adaptation in the LTEE. The fact that the populations are in a near-constant environment would suggest that there should be one. What do we think the reason is?
    1) Something unknown is changing the environment enough for the fitness landscape to have peak-shifts?
    2) Known factors that change the environment could be frequency-dependent effects or... what else?
    3) Does absolute fitness continually decrease in an undetected fashion causing beneficial mutations to reappear?
    4) Do the genomes increase in size allowing new degrees of optimization?
    I don't know (and don't know of Rich et al. can rule out any of these with certainty).

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    1. I don't know the complete answer but some of it has to do with the fact that that the landscape changes with every new mutation that appears in the population. New pathways open up when a new allele rises to appreciable frequency.

      The way I see it, it's not like populations are wandering around in a static landscape. The landscape itself is rising and falling just because the allele frequencies are changing. This can occur even in a static environment.

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    2. How does the landscape (i.e., fitness as a function of genotype) change because of where the population is located in the landscape? Because that is, I believe, equivalent to what you are saying. Frequency-dependence is the only thing I can think of.

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    3. Well there always is frequency-dependence for fitness. In the long run the mean fitness of a population is always ~1, a population with a mean fitness <1 quickly goes extinct, a population with a mean fitness >1 quickly reaches absurd population sizes. A good way to think about this is that a good estimator for the mean fitness over a time period is the number of new organisms divided by the number of deaths. In the long run any organism dies, so these numbers tend to be close to equal for any reasonable time interval and thus the mean fitness is ~1. That does not imply that there is always frequency dependent selection - selection requires !s=0 and s is the log of the quotient of the fitness of carriers and that of non-carriers. I.e. it is a relative rather than an absolute measure and you can easily work out that a constant s implies that the fitness of both carriers and non-carriers changes with frequency given a constant mean fitness of 1.

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  7. My thinking is simply this: Even without frequency dependence or any change in the extrinsic environment, (1) the dimensionality of the adaptive landscape is so vast, and (2) the slopes of many/most potential "late-stage" uphill paths are so shallow (i.e., tiny, but cumulatively meaningful, selection coefficients), that it requires an extraordinarily long time to run out of ways of improving. And to the extent that drift facilitates discovery of higher peaks by wandering into new regions of the landscape and/or crossing of (shallow) valleys, even more so.

    I'd also hasten to add I don't claim the LTEE is "perfect" in terms of eliminating frequency dependence of relative fitness and external changes. However, by design (including the simplicity of the environment and the low population density – by microbial standards – resulting from the low resource input) these complications were minimized. Moreover, I think these complications, to the extent they arise despite my efforts, tend to work *against* our empirical claim that relative fitness keeps rising when measured against a standard, distant competitor. That is, such effects of changing conditions and frequency-dependent selection might promote on-going adaptation, but they would not be expected to show up (on average) as increases in performance relative to the distant ancestor.

    One reader also wondered whether we did the LTEE proper in liquid, but the competitions on plates. The answer is no -- both the LTEE and competition assays are done in liquid. The plating is only used to observe (measure) changes in the relative abundance of the competitors in liquid. But for some populations that have evolved along certain paths, they no longer make colonies that we can reliably observe (count) in the assays.

    -- Richard Lenski

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    1. I just noticed this wonderful quotation on the sidebar from Doug Futuyma: "It is naïve to think that if a species' environment changes the species must adapt or else become extinct ... Just as a changed environment need not set in motion selection for new adaptations, new adaptations may evolve in an unchanging environment if new mutations arise that are superior to any pre-existing variations"

      The latter part -- "new adaptations may evolve in an unchanging environment if new mutations arise that are superior to any pre-existing variations" -- is, in essence, what we study in the LTEE. And our finding is that these improvements can go on for a very long time, with no end in sight, despite the declining overall rate of improvement. (Yes, eventually there must be some physicochemical limit beyond which biology cannot go, but what sets that limit, what the resulting theoretical maximum fitness level will be, and how long it will take to get there are unknowns.)

      As so often with empirical evidence that may seem surprising at first (as it did to me), once one thinks through things more carefully and mathematically -- how many genetic dimensions there are, how many beneficial mutations are lost due to drift while rare and to clonal interference once common (and hence require many "attempts" before they might eventually fix in a population), and how long it takes to fix the many, many improvements that tend to become smaller and smaller as the current fitness level increases -- the surprise factor disappears.

      -- Richard Lenski

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    2. Most people have a naive view of evolution. They imagine that evolution only occurs when the external environment changes.

      In order to hold on to such a view, they must assume that organisms in an unchanging environment must be at the top of an adaptive peak where further evolution (i.e. natural selection) is impossible. They have reached adaptive perfection. This is the only way to justify the argument that populations will quickly adapt to a slight change in the environment.

      Your (Richard Lenski's) experiment demonstrates conclusively that we need to abandon such a naive view of natural selection as a mechanism that only responds to environmental changes.

      The LTEE also proves that there's more to evolution that just natural selection but that's a different kind of naivety.

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    3. Anyway, there's no way to hold the environment constant, since the genetic environment is part of the environment too, and a neutral mutation can alter the fitness surface.

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    4. Thanks! I figured it was something like that, but hadn't had time to go through the paper. Heavy grading time.

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    5. How many more generations in LTEE are needed for bacteria evolve to another species?

      What would be the first evidence that bacteria are evolving into an unknown today (or known) metabolism, energy harvesting system etc..?

      Craig Venter has been working for a while now on introducing some of the foreign components into bacterial cell in order to test and challenge some of the well established ideas about evolution.

      He has also been open to an idea of a synthetic creation of a cell membrane. What are your thoughts on an experimenting in this area? What are your thought on these matters, if any?

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    6. Most people have a naive view of evolution. They imagine that evolution only occurs when the external environment changes.

      I don't believe I know anybody who believes that. In addition, what John Harshman said. Mutations just randomly happen, and every mutation changes the environment.

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    7. I don't think it's an issue of belief, but rather overlooking the importance of mutation in regards to the fitness landscape, and the sorts of assumptions that get tossed around because of not fully internalizing this "rather obvious" component of the equation.

      It's just like with drift. I don't think anybody denies that drift plays a major role in evolution. But it's often so overlooked and forgotten, that sometimes rather silly assumptions and hypotheses get popularized in its absence.

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  8. "One of the cultures, Ara+1, has the lowest overall fitness of any population. It also showed the lowest increase in fitness—a result that seems counter-intuitive because it has the most to gain. This population has an unusually active transposon (IS150) that creates an unusual number of mutations by insertion. Possibly because of this active transposon, the authors note that, "... this population has, in some sense, gotten stuck in a genotypic region of the fitness landscape that constrains its evolvability.""

    Is evolution defined only as populations becoming more fit? If or when a population becomes less fit, isn't that still evolution? And isn't the word "evolvability" an assertion that some populations have an evolutionary direction/goal and that increases in fitness are that direction/goal?

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    1. And isn't the word "evolvability" an assertion that some populations have an evolutionary direction/goal and that increases in fitness are that direction/goal?

      I don't see why that would necessarily be so, as (1) you've just pointed out movement could notionally be in the direction of more or less fitness, and (2) the example you cite shows the paradox that overly frequent mutation can constrain fixation and thus much movement in either the more or the less fit direction.

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    2. "Is evolution defined only as populations becoming more fit? If or when a population becomes less fit, isn't that still evolution?"

      Yes, as you say, evolution includes populations becoming less fit. This happens, for example, in mutation-accumulation experiments where populations are put through severe bottlenecks.

      "And isn't the word "evolvability" an assertion that some populations have an evolutionary direction/goal and that increases in fitness are that direction/goal?"

      Evolvability, as it is often/usually used by evolutionary biologists, refers to changes that tend to promote adaptive evolution. But it certainly can be a confusing concept, and context is (as always) important. Personally, I like to distinguish between two types of evolvability. Some evolutionary changes that promote evolvability operate more globally, at the level of the genetic system -- say, rates of mutation and recombination. Others are more local, hence the idea in the quotation you referred to that the Ara+1 population seems to have gotten "stuck" in a relatively unpromising area of the landscape.

      Importantly, neither implies foresight or goal-directedness -- rather, by virtue of their different evolutionary histories, different populations may have evolved different genetic systems and/or occupy different positions in the landscape that influence their future potential.

      By the way, these are experimentally testable ideas, and we've done some of the tests.

      For effect of different mutation rates on fitness trajectories: De Visser, J. A. G. M., C. W. Zeyl, P. J. Gerrish, J. L. Blanchard, and R. E. Lenski. 1999. Diminishing returns from mutation supply rate in asexual populations. Science 283:404-406.

      For effect of different positions in landscape on subsequent evolution: Woods, R. J., J. E. Barrick, T. F. Cooper, U. Shrestha, M. R. Kauth, and R. E. Lenski. 2011. Second-order selection for evolvability in a large Escherichia coli population. Science 331:1433-1436.

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    3. By the way, these are experimentally testable ideas, and we've done some of the tests

      Excuse my ignorance Dr. Lenski. Does this mean that those papers count as evidence that "replaying the tape of life", as Stephen J. Gould would put it, would not produce the same result twice? (or in other words, evolution can't be teleological)

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    1. Those are but analogies Gary. Like your bullshit. You have a simulator of analogies, not a scientific explanation of anything.

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    2. From the article:

      "If evolution can learn from experience, and thus improve its own ability to evolve over time, this can demystify the awesomeness of the designs that evolution produces. Natural selection can accumulate knowledge that enables it to evolve smarter. That's exciting because it explains why biological design appears to be so intelligent."

      Does it make you feel all warm and fuzzy inside to know that "natural selection" can accumulate knowledge that enables it to evolve smarter?

      This leads to a question maybe you or other "evolution" expert can answer: Does natural selection see you when we're sleeping, know when you're awake, and know if you've been bad or good?

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    3. You're right, Gary; this article personifies evolution and it shouldn't. If the article has a good point. it gets lost in the silliness the personification stirs up.

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    4. Gary,

      I doubt that you understood my comment. I didn't say that I liked the article. I said it was but analogy. Nothing else. What made you think that I think of evolution as a sentient being? The imbecile here is you. It's you who makes analogies, metaphors, allegories, "simulations," and then convinces yourself that such analogies, metaphors, and allegories make a scientific theory and blah, blah, blah. So it's you who should be asking yourself if the "Intelligence" you assume for natural processes "sees you when you're sleeping, knows when you're awake, and knows if you've been bad or good." From what I read in your bullshit, you would have to say "yes."

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    5. You're right, Gary; this article personifies evolution and it shouldn't.

      In my opinion trying to keep up with new discoveries using a theory that starts with a "selection" analogy/generalization has led to it becoming difficult to distinguish between "Natural Selection" and "Santa Claus". Along with all else the average person knows it now makes sense why in the mountains of Italy only a Christmas Donkey can climb such a steep fitness landscape.

      The problem stems from reliance on a Victorian Age understanding of a multiple behavior level self-learning system. What is first needed is a good understanding of machine intelligence models from the 1970's by David Heiserman and other vital information from respected cognitive science experts. It's otherwise being guilty of what photosynthesis is now accusing me of. In this case I'm the only one here who starting from decades of searching for what (per Occam's razor) most simply makes things intelligent, while photosynthesis started with what exactly?

      The article and paper is more evidence that evolutionary biologists are still making progress towards what has for years been on Planet Source Code and other places.

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  10. Sorry to be a fanboi about this, but gawd I love being wrong about stuff. For example, yes, I would have assumed populations would eventually find fitness peaks around which they'd tend to move for some time thereafter. And I also hadn't run across the term "clonal interference" before. Cool!

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  11. It is becoming clear that evolutionary trajectories in static correlated fitness landscapes are substantially non-random but the relative contributions of determinism and stochasticity in the evolution of specific phenotypes strongly depend on the specific conditions, particularly the magnitude of the selective pressure and the number of available beneficial mutations.

    From
    http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3509945/

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  12. Since it refers to adaptation, mutation, selection, etc., I suppose that this thread is as good as any to make you all aware of this article:

    http://www.sciencedaily.com/releases/2015/12/151221134204.htm

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