Sunday, January 18, 2009

More Improbable Pits

The reasoning behind all this is not to attack the Mt Improbable analogy – which is to show that you do not need large-scale jumps to produce adapted forms, but that they are produced through gradualistic processes.

And a good job it does. What I am looking at here, is whether we can formulate an analogy that can be expanded to encompass more of the evolution process, and hence a series of internally consistent descriptions. The Mt Improbable analogy was not formulated to encompass the depth and range of evolutionary processes, and it would be wrong to criticise it on that score.

Close scrutiny of the Mt. Improbable analogy shows that there may be better ways to represent adaptation that can be expanded to other representations of evolution in a consistent way.

Riding Mt Improbable
Adaptive or fitness peaks are a reflection of the current state of allele frequencies. In other words they reflect which allele frequencies are delivering advantages in a particular environment (advantage = greater reproductive success = a higher concentration of alleles). They do not represent the best possible frequency/fitness solution to a particular environment – such a solution would be impossible, or at least constantly changing - influenced as it would be by the environment, the starting point of allele frequencies, and new alleles produced by mutation (and also impossible to achieve as adaptive success would be 'better than everyone else', not the best possible - which is similar to the old joke of two hikers being chased by a bear. Hiker 1 stops to put on a pair of running shoes. Hiker 2 says, "They wont help you outrun the bear”. Hiker 1 says, "I don't need to, all I need to do is outrun you".)

Peaks represent actual frequency/fitness values measured from actual populations/species. Since this is the case, a population/species sits on top of a peak, because the peak is defined by it. In other words the peak represents a particular groups of alleles that produce an advantage and hence are reproductively favoured, and so are concentrated at that point. The greater the concentration here, as opposed to elsewhere in the population, the greater the peak.

Therefore a population always rests on the peak. As the alleles continue to provide an advantage, the concentration of those alleles increases and the peak increases in ‘height’ (or more accurately distance from the fitness plain). Imagine a lava lamp. Once warmed up, a central peak starts to form. As the heat increases, the peak ‘grows’ upward. This is what is happening in the fitness landscape. The population/species sits on the peak and the peak grows underneath it upwards away from the landscape, as the allele concentration increases.

This means that there is no climbing involved. We should be taking about Riding Mt Improbable, not climbing it!

More than adaptation
The next issue we have is how to describe speciation. With the Mt. Improbable analogy this would result in peaks sprouting from peaks like horns, as populations split. The analogy therefore starts to groan under the strain of trying to be consistent. Again I wish to emphasis that the analogy was not meant to do this, and so this is not a criticism, I am pointing out that maybe there is a more consistent analogy we can use.

The other problem is that the peaks are still attached to the fitness landscape, which implies that there is still a route that populations can take to follow in the footsteps (slime trail?) of the new species. In truth, this would not occur, as once the new species has been formed, all connection with the ancestral population are severed. So we would end up with isolated ‘peaks’ suspended above fitness plains, again stretching the Mt. Improbable analogy too far.

"My God, it's full of pits"
So can we establish an analogy that can be expanded to fit into a more encompassing explanation for evolution generally? I think we can.

Firstly we need to explain the fitness landscape. A possible better analogy is one where populations occupy discrete areas, or topographies, of morphospace. Morphospace itself can be considered as an essentially limitless three-dimensional space within which morphospace topographies describe populations.

These topographies can be any shape as there is no “up” or “down”. Populations are described by the current spread of alleles, and so only areas that correspond to current allele frequencies have a topography. No populations, no topography, just empty space. Populations can expand into empty space as allele frequencies shift, or contract to leaving empty space – if they contract far enough, they disappear = extinction. But there is no set landscape that populations occur in. Populations define the extent of the topography.

OK, a population defines a topography that can be any shape. As the alleles in the population shift, the topography shifts. In this analogy, alleles that confer an advantage become concentrated within a sector of the population. This causes the topography to sag. As the advantage continues and resulted in reproductive success, the allele concentration increases, increasing the depth of the pit gradually (though not necessarily constantly). It should be noted that, since the topography could be any shape and orientation, the direction of the pit could be horizontal, vertical or anything in between, as the sagging will be at 90 degrees from the surface topography (which could be at any angle). This does away with the implication (unintended as it is) from other analogies that evolution is directional and upwards.

The pit therefore describes the state of the population in terms of allele frequency, with the bottom of the pit representing the highest concentration of the advantageous alleles and the sides representing decreasing concentrations of the allele. So if people ask how did the population get to be in a pit so deep in one go, to answer, hand them a shovel.

Speciation occurs when the pit separates from the rest of the topography. This does two things. It forms a satellite topography that represents an independent population – a new species – which is free to form it’s own topography, and start the formation of new allele concentrations and eventually new species.

It also causes the topography of the old population to retract away from the new topography as the allele frequencies realign back towards the old population frequency since there has been a significant removal of alleles with the new species.

A word here on genetic drift. The Mt Improbable analogy doesn't cover drift. But in my anaolgy, drift would be represented by a broad shallow pit as the allele becomes incorporated into the population faster that it is at the point of initiation so the pit expands outward through the topography rather than into a pit. Drift is then a ripple in the topography that, once fixed, leaves the topography slightly lower/higher that it was prior to the fixation event.

Separate topographies = no allele transfer = species. It is possible that the old population has retained enough of the advantageous alleles that the separate populations grow back together. But that would need to happen very quickly, before the frequencies become to divergent (as in populations that are geographically isolated but can still share alleles if brought together).

So a cluster of interconnected topographies, and some closely aligned but separate topographies, denote a species. This is the highest magnification. Ratchet the magnification back a notch, and clusters of closely positioned topographies become Genera. Ratchet back again and clusters of genera topographies become Families, etc. The closeness of topographies between separate species, genera , etc can make the decision as to which topographies go where, difficult - as in real life.

Ratchet the magnification back far enough and we can see the all of current life on Earth represented.

But, it would show relationships as they are today, with groups occupying discrete areas of morphospace, separated from each other. It cannot show the connectedness of life because we are viewing it as it is today, after 3.5 billion years of evolution. To show the connections, the evolutionary relationships, we need the 4th dimension – time.

What we can do is run a time sequence backwards, that would show morphological topographies coalescing, firstly species recombining backwards into founder species, then genera, etc, until we see the major groups contracting back together, metazoan topographies coalescing back into single celled topographies, eukaryote topographies coalescing back into prokaryote topographies etc.

Running the sequence forwards we would see the reverse. For example, it could show the origin of the dinosaur topographies from other reptile topographies. Such topographies would increase in number and morphospace coverage, and then start to shrink back over time, but one group of topographies produces a flurry of new topographies that expands and continues to develop and produce new offshoots, even as the main dinosaur topographies reduce in number and finally disappear. This new group of topographies would be the birds.

The pit analogy would then, connect with a more internally consistent consistent group of analogenic (is there such a word?) descriptions of evolution.

It’s pit’s all the way down!


  1. The point of the Mt. Improbable metaphor is to provide an easily grasped, easily visualized model to demonstrate how gradualistic processes can produce large changes. Your new metaphor may incorporate more of evolutions processes, but I have to tell you, I am having a very hard time visualizing it. Maybe it would be easier if you had some illustrations. But I suspect that if you tried making some you would discover that the Pit metaphor actually doesn't translate well. Maybe I am wrong.

  2. We’re getting closer… I think that I may have “read into” your initial Improbable post a little too deeply… To me, this update seems somewhat of a turnaround from the first in that it moves away from the literary argument of a Mt. Improbable as “bad analogy” and instead states “And a good job it does.” I find it much more agreeable. Furthermore, it now seems more apparent that the “pit” analogy is designed so that “we can formulate an analogy that can be expanded to encompass more of the evolution process.”

    Since we agree that Mt. Improbable is a good analogy for its intended purpose, I’ll move on.

    Viewing the two blog post here, as well as the two comments you were kind enough to provide to the “rebuttals” at my site, I think that, broadly speaking, there are a couple of assumptions or implications being made that are fundamentally false – false, based on my understanding.

    1. You describe Natural Selection as acquiring beneficial alleles through a “random process.” This is incorrect; NS is a non-random cumulative process.

    2. You imply that genetic drift contributes to fitness when, in fact, drift is a random process that is entirely disconnected from fitness. (Big point)

    3. Through descriptions of lateral jumps between peaks, distances between pits and by suggesting that new “groups” can arise by “breaking through new fitness landscapes,” you’re implying that a Genus, Class or Family can erupt from a Species. This is false. Species rise from “speciation” at the species level. There is no jumping between points – only steps - a continuous gradation

    4. You imply that “Generalist” and “Specialist” are definitive forms by saying that one has survival value over the other. These are relative terms. You may view/classify a particular insectivorous mammal as a specialist because its diet is limited to only insects – I could counter by saying that it’s a generalist because it eats a wide variety of insects as oppose to limiting its consumption to termites. Without knowing the type and extent of a theoretical catastrophe – there is absolutely no way to predict what niches will remain intact or the rate to which any event survivors will rebound.

    5. You create a false dichotomy between peaks and pits; both are landscapes and as the term “landscape” suggests, both represent a varied ever changing state complete with valleys, ridges, prairies, bumps, holes – they are one in the same –metaphors for change.

    6. You imply that organisms adapt or imbed themselves into a static environment, when in fact static environments don’t exist. Ecology is a balancing act, therefore so is adaptation.

    7. When comparing short-term success with long-term survival you seem to suggest that evolution is a fundamentally different process following some catastrophe or major ecological shift. This isn’t so; the same processes driving speciation, drift and natural selection today are the very same processes that will drive evolution following an asteroid impact. If adaptation and specialization are what is successful in the here-and-now, they are also going to be successful strategies following a catastrophe.

    8. Describing both Natural Selection and Drift in terms of allele frequency is fine; however keep in mind that NS works with phenotypes as well as genotypes; this builds the link to fitness. Drift does not have this link.

    9. The idea that a current level of adaptation exhibited by an organism somehow reflects its future potential or its available genetic plasticity is erroneous.

    However, I do admit, the visual image of a “sag” being created by the weight of an area with increased allele concentration is pretty catchy…

    In closing, I fully admit to being more-or-less a proponent of the adaptationist side of the house and it isn’t my intent to wear out my welcome. Although I express contrary views, I do it only because I feel there is a worthwhile discussion to be had and because you present the “other side” very well.



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