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!