The Technium

Adaptive Basins and Strange Peaks


Biologists talk about adaptive landscapes. In these metaphorical places, species climb uphill towards optimal fitness. Going up is a struggle. Climbing takes energy. Optimal peaks can be hard to attain. Many species are distracted by getting stuck on sub-optimal false peaks, or waylaid by the intervening rugged landscape.

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In this standard picture, the form of the peaks is created by the environment – say, the high peaks of fitness needed to survive in a desert. But of course, in real life, optimal fitness is a moving target, or a moving peak so to speak, that is formed in part by other organisms and by variation and behavior of the current organism itself. This is the view of co-evolution. In the new picture, constraints and self-organization can shape peaks, too. Either way, reaching an apex is the key effort.

But on the other side of science, in physics, the landscapes are inverted. Here physicists talk about basins in the landscape of thermodynamics. Strange attractors create deep wells that suck down entities. Getting out of the well is a struggle. Reversing out of the inverted peak is what takes energy. Reaching the bottom is the key effort.

Mscs Energy Landscape

I suggest the at times the same forces which create peaks in evolutionary landscapes can also be thought of as wells, and we might better understand the path of a species in time not as an uphill climb onto an adaptive peak but a downhill fall into an adaptive well. An optimal form may sometimes work like a tractor-beam that pulls in an entity and keeps it there for a duration despite disruptions. Only a severe hit of energy and outside perturbations can dislodge it from a well and move into another form-basin.

This inverted view might illuminate inevitabilities as wells that complex structures fall into.




Comments
  • Woden Kusner

    A high (enough) dimensional euclidean space should satisfy the response surface criteria proposed by Clem Weidenbenner. The response surface is simply a some hyperplane in the variable space, with “fitness” or whatever some function. It should be defined everywhere, so the restriction to some subspace doesn’t seem truly necessary. Then this is indeed finding critical points and the stability thereof.

    Of course, there are some restrictions on the domain (almost every parameter is closed and bounded due to the discrete nature of, well, nature) but it seems odd to think of it as a compact space (with respect to time).

    In regards to the assumption of the existence of set of variables that gives a good approximation (arbitrarily small error) may need to be proven. However, it is reasonable as long as one can make distinct measurements. (could be via known parameters or hidden models)

    As for the actual article, I suppose it exposes one of the problems with ridged conventions in interdisciplinary communication.

  • Michael F. Martin

    Would it be fair to say that the Price equation permits for the the local geography to look different at different points in the plane whereas Hamilton’s equation assumes that the local geography is the same everywhere?

  • Ewout ter Haar

    This doesn’t make sense. The peak metaphor is just a convention. Selection “forces” (another dangerous metaphor) lead species naturally (without struggle or energy expended) to the peaks in the fitness landscape.

    There is a lesson here: metaphors and concepts may not always travel well across disciplines.

  • gabriel bear

    excellent. imho once you eliminate hubris from the set of mapping tools this “well” model conforms to a rather large amount of the landscape.

    and i offer ur captcha mechanism as an example of it: energy being fed into a system without “reward” for the charging of the net; people performing work for machines to conserve the energy of the machines to perform work for people.

  • RobertJ

    I think it’s great that you’r creating a book via blogs, often I wish I could comment on something to the author as I read a book.
    I have to agree with EtH that this dosn’t work, the metaphores are mixed up and misleading.
    If you accept the fitness landscape as a metaphore, then there is no _force_ that kicks a species out of a well, only random mutations. A change in the environment corresponds to a shift or reshaping of the mountains or wells, which could indeed catapult them to a different place on the map, but not out of a comfy well, the well has to go.

    The reason you are able to pretend that there is an attractive force kindof like gravity, is that most mutations create small changes in the animals phenotype, meaning that it explores the near neighbourhood of the point the species currently occupy. Natural selection is then equivalent to a computation determining the gradient at that exact point. The gradient has the same direction as the force of gravity in the second example, this is built into the metaphore in the first place.

    There’s a vast literature on evolutionary algorithms that go into detail on this, but the hillclimbing glosses over a lot of important details in evolution. For instance:
    * Some mutations cause sudden large jumps in the landscape, unlike anything a hillclimber can do. The concept of “nearby” in mutations is nothing like euclidean space.

    * Unlike a hillclimber, the species is blind to the landscape, knowing only the points it visits via mutation.

    * The metaphore isn’t good at visualizing how a mutation in an animal becomes a change in the fitness landscape for another. How could we show an arms race between predator and prey for instance?

    * Noone has actually shown that fitness landscapes look anything like this when you take more than a few phenotype attributes into account. The true fitness parameter space could be an absurd abstract space unheard of outside mathematics departments, for all we know.

    In short, I think the hillclimbing metaphore is too weak to advance the claims you are about to make. But if you could find new and better metaphores in the field of complex systems, computer science or in your own work, that would be a real boon!

  • Doug King

    Yes, DNA is an attractor. Once the first strands started replicating the total energy that has been consumed by the continuation of that replication has increased and continues to increase (don’t forget to include all human activity and energy consumption)so you could say energy is being sucked into this attractor.

    I wonder if the increase is exponential? Can that be calculated? If DNA is information based, leverages homeobox / metasystem transions, perhaps it follows Moores law. Or I would suspect Moores law is an echo of the principles that DNA is operating under.

    What is really going on here? Will this burn itself out, or transition again?

  • Stephen Downes

    Have a look at Boltzmann networks, which describe this basic process.

  • Terry Heaton

    Love it, Kevin. Reminds me of the old saying that if you find yourself at the bottom of a well, the first thing necessary to get out is to stop digging.

  • Leo Freund

    What an insight! Your reversal concept would explain how a species can adapt so well to its niche that it cannot escape when dramatic changes occur to its environment.

  • Tom Buckner

    The thought I’m having at this moment is that sometimes the peak can be not metaphor, but an actual peak. I live in North Carolina, a stone’s throw from the highest mountains east of the Mississippi, and we have creatures such as mountain trout (really a relative of Arctic char) stranded here since the last ice age, which live only higher up the mountains. Global warming and development shrink these available islands and highly adapted species may end up with nowhere to go.

  • Alex Tolley

    I am reminded that I once read that computer simulations of maze traversing ants showed that highly “evolved” ants could not unlearn their maze traversing and failed badly to adapt to new mazes.
    Relatively new, more flexible ants were able to learn the new mazes faster.

    Biologists certainly have the concept of highly adapted vs more flexible forms. Humans and rats being examples of the latter.

    We also see the general tendency of evolution to increase complexity, and those most complex, highly adapted species tend to disappear when the environment changes, much like those simulated ants would when the mazes change.

    So your question is, are highly adapted species living in some sort of informational well that is difficult to emerge from. My sense is that you might look into information theory to look for the appropriate metaphor or mechanism.

  • Clem Weidenbenner

    I find myself agreeing with RoberJ to some extent here. Another limitation of the peaks metaphor is that the peaks have an end point. Once you reach the top you have no here else to go. Even at the tip of the highest peak an organism or population would find itself trapped – in a sense forced to wait until other populations (predators or pathogens) catch up to it.
    Now it may be argued that in young mountain ranges the mountains continue to grow. Everest is still getting taller. But this observation still misses the point, because accordint to plate techtonics the mountains are being pushed up from beneath, and on the peak metaphor an evolving entity moves up the peak along a path where the whole fornt is being pushed up (presumably with all aboard make the same progress upward before making any effort of their own). So in the end the peak is still a dead end.
    The Red Queen Hypothesis (to me at least) suggests that a ‘peak’ or dead end on a fitness ladscape would be eventual doom.

  • Clem Weidenbenner

    Sorry about yesterday’s sloppy posting – and apologies to RobertJ for misspelling his name. I’ll try to do better.

    Kevin – I think your surface metaphor works better if you imagine it as a response surface where populations evolve into uncharted space. For instance, measure several attributes of a population – let’s say fecundity, offspring survival rate, life expectancy, and gross body weight at the onset of reproductive maturity. These four variables may not be independent of each other, but they can serve to tease apart aspects of overall fitness. By plotting these factors against some dependent variable(s) (time, habitat richness, average temperature, etc) one generates a response surface. 3D response surfaces frequently resemble a landscape such as the figures in your original message. The important difference is that the surface is not a fixed landscape. As the populations under selective pressures change they change the landscape. And under this metaphor we are able to follow any increase (or decrease) they achieve in fitness relative to their habitat competitors, pests, or predators. The Red Queen might approve.

  • Reader

    Biologists talk about adaptive landscapes. In these metaphorical places, species climb uphill towards optimal fitness. Going up is a struggle. Climbing takes energy. Optimal peaks can be hard to attain.

    I agree with the others here that this is not quite right. Admittedly, I learned this stuff in the context of engineering (nonconvex optimization) and not biology, but my impression was that the problem is that getting to a peak is hard not because “climbing” is hard, but rather because the peaks are simply hard to *find* (especially when the space you’re looking at is not 1- or 2-dimensional but n-dimensional).

  • stephanie gerson

    “This inverted view might illuminate inevitabilities as wells that complex structures fall into.”

    this is precisely what Rupert Sheldrake proposes with his theory of morphic resonance (http://en.wikipedia.org/wiki/Morphic_resonance). considered pseudoscience by some, and rigorous by others. I find the idea Lovely.

    you might also consider borrowing the notion of path-dependence from the social sciences (http://en.wikipedia.org/wiki/Path_dependence).

    it may go without saying, but we see the same patterns of change and evolution at different levels of organization and in different “domains” (for lack of more appropriate words) of reality.