Can "random" have a direction in evolution?

Post of the Month: March 2013

by

Subject:    | A better example of design?
Date:       | 26 Mar 2013
Message-ID: | 6bs4l8dk7h38gjvg4l2qq1ui89tmh2t5r7@4ax.com

>> I also don't see how you got a trend from the idea that there are more ways
>> to be extreme. In this case, when a threshold is passed survivors "jump" to
>> the survival value at the relevant site even though all sites continued their
>> random permutation. Jump processes are common, but they don't imply that
>> there isn't a random walk.

>> This is simplistic, but even with a small set of attributes there are a lot
>> of choices available. If foxes get faster, rabbits can get faster, sneakier,
>> get a better sense of smell, or become nocturnal. Both got more extreme to
>> stay even.

> And this gets to the heart of the question of whether observed trends in
> evolution are simply the result of a random walk. I disagree with John
> Harshman on this - I think they are more a result of changes in size,
> intelligence, etc. opening up niches that did not previously exist. The
> question is how to differentiate between the hypotheses. Do rabbits get faster
> through selective pressure or random walk (e.g. they could also get better at
> avoiding foxes through getting a better sense of smell)? Any thoughts on how
> to differentiate between the competing hypotheses would be greatly
> appreciated.

In this large thread (almost 100 posts) there seems to be a certain level of misunderstand and arguing at cross purposes about several issues: complexity and organization, random processes, random walks, evolution,... I am not responding specifically to you, William, but simply using your comment and seeming disagreement with John as a trigger finally pushing me to comment.

First, there are different notions of "random". Some people use it only if the probabilities of all outcomes of a process are equal. That is not how mathematicians or systems theorists use randomness or random processes: those processes involve a probability distribution that by no means need be uniform and, in fact, seldom is. Flipping a highly biased coin produces a random sequence. Rolling a pair of dice produces a random outcome that is not uniformly distributed.

A simplistic notion of evolution involves two notions: mutation and selection (whether natural, artificial, sexual...). Generally it is considered that mutation is random whereas selection is not. We add genetic drift which is random. However reality is rather more complicated. Selection is not wholly deterministic. I may have drastically lower fitness than you but the lion happened to be on your side of the tree, not mine, so I escape to have lots of kids and you do not. So selection turns out to be a form of random process, also.

To look at the details consider the notion of a random walk, a repeated random process where the results are cumulative: the starting point for step n+1 is the result of step n. In mathematics (or system theory or whatever fancy mathematical theory you want to name), the probability distribution for each successive step does NOT have to have zero mean. If it does not then there is a very distinct systematic trend in the walk. Think of moving the tokens on a Monopoly game board. Each step is taken by rolling the dice. The movement of the pieces (except for going to jail) is a random walk but there is a distinct trend as each player travels systematically clockwise around the board. To get technical (and remaining simplistic about biology) the combination of genetic drift plus selection is exactly this kind of random walk: a walk where selection induces a non-zero mean to the direction of the step. A terribly confusing point is that mathematicians call the systematic part of such a process, the trend, "drift" whereas biologists call the "random" part of the process "drift" and call the trend part "selection". Drift means exactly opposite things in the two contexts.

In particular, when most people think of selection they think purely of what biologists call "directional selection" (there are other forms). Most examples produced here demonstrating that evolution is most decidedly NOT random involves very strong directional selection. That is the argument William presents above: evolution decidedly moves in a particular way and does not meander about aimlessly. However it still is a random process albeit the systematic trend may overwhelm the erratic steps: it is a very directional random process. That is the "hill climbing on the fitness landscape" picture of evolution.

Another complicating factor is that a particular biological community involves a large number of populations all interacting with each other and co-evolving: changes to one influence other members producing closed loops of interaction allowing positive feedback in the selection process driving systems to extremes. This is the kind of example usually produced to show that evolution is distinctly non-random. (Here, I fear, jonathan or marc is likely to jump in yelling "complexity theory". Yes, these feedback cycles can be described in terms of complexity theory but population geneticists and population ecologists have done very nicely with classical mathematics of sets of differential equations (sometimes partial differentials) without invoking complexity or chaos. Complexity theory can put on the icing but is not the cake.)

Mutation is a rather complex issue to put into the context of the random walk because, although random, it is random in a very different context, a very different universe of discourse. A population reproducing is a random walk because random mating within the gene pool of a small population produces only a small sample size of genotypes in the next generation that may differ from the expected ratio (genetic drift) and because a variety of "random" extraneous factors besides fitness determines survival and reproduction. Mutation, on the other hand, is a random walk on the genotype space introducing completely new alleles into the population. However it is generally agreed that mutation, although not random in the ordinary language sense that every nucleotide substitution and every locus has exactly the same probability of occurring as every other substitution, the changes do not seem show any preference caused by fitness. That is, changing 'A' to 'T' here may result in a change in fitness but it is decidedly NOT the case that the reason that 'A' changed to 'T' is because that produced an increase in fitness. It IS decidedly the case that the frequency of 'T's in that location grows with time provided you start with a non-zero value so that eventually ALL the 'A's become 'T's because of the preference of fitness (selection) but selection is totally distinct from mutation. On the other hand, selection and genetic drift are just different aspects of reproduction in finite size populations subject to vagaries of environmental variability.

As described above, most people think of evolution as highly directional. When molecular biologists look at variations in nucleotide sequences, on the other hand, what is invariably found is that the randomness is overwhelming. That, no doubt, results from the fact that virtually all of the changes are as far as we can tell quite neutral. That means there is no natural selection. Put differently, it means that the "steps" in the random walk have zero mean. Considering that evolution is defined technically as a change in the genetic composition of a population, it really does turn out most evolutionary change is entirely "random" in the ordinary language sense of being totally non-directional. So evolution is mostly non-random but evolution is also mostly random.

There is a completely different argument to be made about the lack of directionality in evolution. The simple fact is that the vast majority of life on earth is microbial. That seems to be true whether you measure biomass, count cells, or count "organisms" (there is some debate about biomass). Arguing about coevolution of rabbits and foxes is really just a tiny and, from the perspective of the monera, a completely insignificant part of "real" biology – the study of ALL living things.

The classic arguments about systematic increases in complexity and organization and `information content' (whatever that might mean) are based on the well known properties of random walks with a barrier. You start at or near the barrier (yes, the barrier might move, marc – that doesn't change anything). We happen to be at an extreme point. We naturally think of evolution in terms of evolution of H. sapiens - mammals - animals so we see an inexorable trend from simple to complex. Most living things are at or near the barrier, just what you expect from a random walk with repeated trials. In random walk theory the expected distance from the starting point does grow with time – there is "systematic increase" in that variable. The problem is that for random walks without mathematical drift, the walks are randomly distributed in direction from the origin albeit growing increasingly far away. If the walk is one dimensional with the origin near that barrier, then an increase in one direction is expected purely "randomly". Furthermore, there will be extreme values reached in the random walk process and these extrema will invariably increase with time. Hence the "most complex" organisms will become even "more and more complex" with time. That does not mean selection, it is expected from random walk theory in walks without selection, without trend, without what mathematicians call "drift".

Still, what we actually find in the real world is that almost every living thing we can find, if we only look carefully and without size bias, is that it is all crammed down there right near that barrier. There does not seem to be any general trend for everything to get complex. There does seem to be a general trend for one carefully selected line of organisms to get complex but that is cherry picking the data to reach your foregone conclusion.