The Meaning of Adaptive Landscapes

Massimo Pigliucci and Jonathan Kaplan have written a book on evolutionary theory. Check out Massimo’s description on his blog. But it’s not all masturbatory philosophy — these guys understand the science. Here’s Massimo describing their treatment of adaptive landscapes:

To make the story short (for the longer version you’ll have to read the book), Jonathan and I claim that the idea was fraught with problems and inconsistencies from the beginning, and that it has now been radically modified by the work of a mathematical biologist named Sergey Gavrilets. Sergey actually showed that the mathematical (and biological) properties of realistic (i.e., highly multidimensional) “landscapes” are very different from those of the 2- and 3-dimensional versions usually presented in textbooks and examined in most of the literature. Indeed, these differences are such that some old questions to which biologists have dedicated a large amount of effort ought to be rethought in an entirely different fashion, and may in fact cease to be relevant to our understanding of how evolution works. For example, the classic adaptive landscape problem is how does a population “move” from one adaptive peak to a higher one, i.e. how can evolution re-shape the genetic makeup of populations to increase their average fitness. The problem is that the “peaks” of the classic rendition are separated by maladaptive “valleys,” i.e. by combinations of genes that have lower fitness than the combinations currently present in the population. By definition, natural selection cannot bring a population “down” such a valley to reach a nearby peak, because it (selection) doesn’t have forethought, it cannot sacrifice the immediate advantage for the long-term gain. Several ingenious (but largely unworkable) solutions have been proposed over a course of decades, until Gavrilets demonstrated that if the landscape is highly-dimensional (as must be the case for real organisms with tens of thousands of genes) the problem largely disappears because there are no “peaks” and “valleys,” but rather large continuous multidimensional hyper-planes of high fitness punctuated by occasional “holes” of low fitness (hence the term “holey landscapes” to refer to Gavrilets’ theory). All natural selection has to do is keep the populations from falling into the holes, i.e. to evolve genetic constitutions that would drive the population to extinction.

I put the quote below the fold because it’s so large. I guess you’ve gotta be a philosopher to churn out paragraphs of that impressive length.

Paragraph lengths aside, I find this pretty interesting. I have to admit, however, that my knowledge of classical population genetics theory is less than stellar. I’m more of an empirical population geneticist — if I can’t relate theory to data, the abstract nature of the theory fails to connect for me. That’s why I’m a big fan of the coalescent. But Wilkins thinks this will revolutionize evolutionary theory.


  1. #1 Mike the Mad Biologist
    November 20, 2006

    If ‘holey landscapes’ start to replace adaptive peaks as a common metaphor in pop gen, I think this is actually an important shift (albeit one not necessarily supported by data). What this would mean is that far more of the available landscape space is accesible, and consequently we need to focus a lot more on stabilizing selection, as opposed to directional selection (where far more attention is paid). In other words, why aren’t populations ‘sloshing around’ all the time, since they’re not trapped on fitness peaks.

    Of course, the directional selection experiments are much easier…

  2. #2 chet snicker
    November 20, 2006

    i have checked out gavrilets’ work. can’t follow all the maths, but it seemed interesting. my PI could follow the maths and when i axed him about this he said it’s way ahead of its time in terms of being empirically relevant. told me focus on real empirically driven stuff with baby-math before getting caught up in this, there is something there, but revolutionize? i don’t know. AL are metaphorical heuristics anyway, right? from what i recall provine has shown that wright’s original concept was a bit confused.

  3. #3 chet snicker
    November 20, 2006

    p.s., and why all the hate for philosophy? massimo is a working scientist too, he swings both ways. bitch.

  4. #4 RPM
    November 20, 2006

    No hate for philosophers. At least not those that understand science or are scientists themselves (like Massimo, Kaplan, Wilkins, Dr. Rob).

  5. #5 chet snicker
    November 20, 2006

    scientist, puleez. next you’ll be telling me some of your best friends are philosophers!

    …anyway, i’ll go check out gavrilet’s papers again. mike makes an interesting point re: stabilizing selection, though i am of the opinion in this area attempting to map the quantitative models into works leads to inevitable philosophizing.

  6. #6 chet snicker
    November 20, 2006

    meant “onto words.”

  7. #7 John Wilkins
    November 20, 2006

    Yes I do think Gavrilets’ work is ahead of its time; but what it will do is focus research in more realistic ways than the two-locus/two-allele approach that has dominated thinking for 60 years. But I don’t see why the coalescent is in any conflict with this. Coalescence is about gene trees in populations that have a differing tree topology, sometimes, and is a useful method for working out the latter from the former. Gavrilets’ stuff is about entire genome clusters, and their dynamics in a fitness landscape. They are at right angles to each other.

  8. #8 chet snicker
    November 20, 2006

    Yes I do think Gavrilets’ work is ahead of its time; but what it will do is focus research in more realistic ways than the two-locus/two-allele approach that has dominated thinking for 60 years.

    sure. and -omics is going to be hitting the old model from the empirical end.

  9. #9 RPM
    November 20, 2006

    But I don’t see why the coalescent is in any conflict with this.

    I don’t think anyone said there’s conflict. I don’t think I did, at least. But it’s hard to imagine having the data (especially concerning fitness) to be able to apply complex landscapes in an empirical study. I just said one of the reasons I understand the coalescent is that I can apply the theory directly to my data.

  10. #10 chet snicker
    November 20, 2006

    But it’s hard to imagine having the data (especially concerning fitness) to be able to apply complex landscapes in an empirical study.


    then again, some of fisher’s insights in genetical theory are coming to the fore now cuz of genomics. and allozymes resolved the balance vs. classical argument. but this shit is on a whole multiple magnitudes higher in terms of order of complexity.

  11. #11 chet snicker
    November 20, 2006

    btw, gavrilet’s work was in an book sponsored by the santa fe institute. i think that gives people ‘in the know’ a general sense of how far out this area can be. and how ‘complex’ it is. we’re talkin’ stuart kauffman land.

  12. #12 Peter Ellis
    November 21, 2006

    Coming to this fairly much from the outside – is there any attempt to model the effect of the population on the adaptive landscape, rather than vice versa?

    It’s clear how the adaptive landscape drives population genetic changes, but it seems clear to me that there should be (strong?) effects the other way as well.

    At the simplest, if you have a large population of short-necked herbivores eating all the low foliage, that will have the effect of increasing the fitness of long-necked genotypes – i.e. of raising the height of the adaptive landscape in the area corresponding to those genotypes.

    More generally, any population should have the effect of lowering the fitness of its immediate region of the adaptive landscape – any individual’s closest and most effective competitors are the other members of its own species.

    Second question – how are populations treated in the adaptive landscape model? All the pop-science renditions talk of populations as a point on the landscape. Again, fairly obviously, they’re not – no two individuals are identical. The population itself occupies a given hypervolume within the hyperspace. However, when you have random mating, then the offspring of any given individual at the “edge” of the population is likely to end up somewhere nearer the centre of the population – straightforward regression to the mean. This could be analogous to some sort of “gravity” or “surface tension” keeping the population coherent.

    Possible a better visual metaphor, rather than a mountain range with peaks and valleys, would be a set of bubbles trapped under an ice sheet. As the ice sheet moves and warps, the bubbles move one way or another. Speciation would correspond to one bubble splitting into two – rare, but not impossible, depending on the dynamics of the ice sheet and the surface tension holding the bubble together.

  13. #13 RPM
    November 21, 2006

    In response to Peter Ellis:

    1. I doubt the fitness parameters are static in any sophisticated model.

    2. I know that some of the models model individual genotypes. The population is a collection of all the genotypes mapped onto the landscape.

  14. #14 Jonathan Kaplan
    November 21, 2006

    Another (slightly longer) response to Peter Ellis:

    Your points re: the “fitness landscape” changing in response to the behavior of the population is well taken, but modeling it has proven difficult. Lewontin has suggested that one envision the landscape as a flexible sheet that moves / changes shape as the population moves on it. Most of the changes in shape will be locally ‘down’ of course (because populations tend to degrade their own environments), but not all of it, and much of the movement will be unpredictable. It is easy to see how the ‘red queen’ hypothesis / metaphor can be fit into this – climbing a ‘hill’ pushes the hill down and makes other parts of the local landscape go ‘up’, so however fast you climb you can’t reach the top…

    As Chet noted above, there are all kinds of problems with both the original and more contemporary variations of the landscape metaphor; while I disagree with Provine’s particular criticisms, the places he highlights are definitely problems. At the most basic level, the question of what points on a landscape represent is too often glossed over. Some models take points to be individual organisms with particular genotypes (this seems to be what Wright originally intended); populations are then ‘clouds’ of points. Some models take points to be populations with particular allelic frequencies; others take points to be populations with particular genotypic frequencies. The latter two strike me as useless – unexplanatory, inaccurate, and/or intractable.

    I think the best lesson to draw from Gavrilets’ work is that there is NO good visual metaphor for the mathematical models that probably best model speciation. Neither the “landscape” model as traditionally conceived, nor even Gavrilets’ “holey” picture, do justice to the math. They are so over-simplified and misleading in key places that they neither give a good picture of what might be going on, nor suggest likely empirical investigations, nor interesting problems to be tackled. To get those kind of insights, one has to, I think, interrogate the models themselves, not the images…

    I strongly recommend Gavrilets’ book “Fitness Landscapes and the Origin of Species” (2004, Princeton University Press) to anyone interested in these topics. It is very readable (given the topic!) and exceptionally interesting.