March 27, 2006

Survival of the Fittest

The debate about evolution has raged in the comments below for several days. And it keeps returning to "survival of the fittest" and whether the concept is a tautology or not. And if not, whether it can produce falsifiable predictions. And finally, whether the answer to this has any bearing on whether evolution is a "scientific" theory.

I'll try to address at least the first two below.... The first part is a bit tricky. "Survival of the fittest" is a tautology in one sense because it is the logical consequence of a set of assumptions. But I'll argue that that's not relevant to how it's used in evolution. So.... here's my personal interpretation of "survival of the fittest" or selection (natural or artificial, ecological or sexual). Bear with me as I set up the assumptions:

  1. Imagine a replicator r that exists in an environment A
  2. The replicator will cease to operate (i.e. die) after some average period of time
  3. This replicator will replicate with some probability that is dependent on A such that the expected number of copies (i.e. offspring) is Er(A). (You might model this as Poisson reproduction and death processes, with λ's as functions of A, but it's not required.)
  4. The replicator has components (call them traits) that affect Er(A) and that are independently copied with a zero error rate to the "offspring"
  5. There is an arbitrarily large population of replicators with some variation in traits that deliver different Er(A)
Given this situation, it follows that for a constant A, replicators with traits that create a higher expected number of offspring will tend to increase as a proportion of the population. That's just what the math says (although, given the size of the margins, I'll leave the proof to others). And that, I believe, is all that natural selection, or "survival of the fittest", says.

So does it produce falsifiable predictions? Not really, not any more than the fact that "the circumference of a circle is equal to π times the diameter of the circle". If you find a "circle" that doesn't meet that condition, it means that your shape is not a circle or you mismeasured something — it doesn't mean you falsified the formula. (Note that the fact that the formula for the circumference is tautological is far from saying that knowing this relationship is useless.) Likewise natural selection tells us what will happen if our assumptions are true, and in fact it gives us a way to test if our assumptions are true.

And it turns out that, while the assumptions are remarkably close to the truth (especially given that DNA and molecular genetics were unknown in Darwin's time) and we can see selection take place over and over in experiments we run, the assumptions are not exactly true. Examining the assumptions that aren't true and when they are not true has helped us learn about other mechanism that affect genetic variation in populations. So what turned out not to be true?

  • The copying turned out not to be "error-free". Mutations happen. The rate is low enough in most cases to allow selection to occur (and it turns out to be important, which I'll return to below).
  • The "traits" are not independently copied. There are various kinds of linkage that cause alleles to be copied together.
  • The populations are not arbitrarily large. This is crucially important and was underappreciated in early evolutionary theory. The fact that populations are sometimes quite small means that genetic drift can play a major role, including the founder's effect. In small populations, even adaptive traits that increase Er(A) can, through the random walk of the stochastic process, vanish (or likewise for maladaptive traits, dominate) such that the population fixates.
  • The environment, A, is not fixed. In fact, it's changing constantly (though generally slowly compared to the rates of reproduction and death of individual replicators). Moreover, it changes because of the very replicators (and their traits) that we're talking about. And so we have things like evolutionary arms races.
There are others.... (And note that I've ignored sexual reproduction for the time being because it is, perforce, secondary to asexual and because in the view of some theorists (like Richard Dawkins) it is the "selfish gene" that should be considered the replicator, not the sexually-reproducing individual – but enough on that for now).

Regardless, natural selection is useful as a model of how this stuff works and helps us fine-tune our model of replication.

So finally, what's the big deal about natural selection and evolution. Not, I contend, that selection exists – because we see it all around us and can replicate it in controlled experiments whenever we wish. And not the way it specifies the assumptions of our model of replication – while novel in its time, this has been proven much more thoroughly by our modern understanding of molecular biology and genetics. So, what?

To me, the two big ideas of evolution are that:

  1. If you have mechanisms that increase and decrease trait variation in populations, you can account for the diversity of life we see on earth, and
  2. If natural selection is a non-trivial component of the mechanisms that decrease variation, you can account for how it all can look so well-designed.
The first point is critical because any theory has to be able to explain how we ended up with so many wondrous species. With mutation, recombination, gene transfer, and gene flow, you have mechanisms to increase variation in populations. With genetic drift and natural selection, you have mechanisms to decrease it. That, combined with various forms of isolation (e.g. geographic, reproductive), will give rise to diverse species.

But the second is equally important because any theory also needs to explain why everything looks so good at what it does. If there existed completely random mechanisms to increase and decrease variation in populations, you could still achieve some diversity, but it's unlikely that resulting species (assuming they didn't go extinct) would appear adapted to their surroundings. Evolution needs a mechanism to reduce variation – natural selection is one that makes things work better rather than worse.

Anyway, I don't know how clearly I've laid out my understanding. Or how convincing it is. Or how many holes in logic it currently has – it's my first time to write this stuff down, and the impedance mismatch between brain and paper is often higher than it appears. So please, comment away...

Posted by richard at March 27, 2006 11:59 PM


I saw the words "Poisson reproduction" and I panicked and hit the "Hide" button. Somebody will have to explain this to me in monosyllables later.

Posted by: Phutatorius at March 28, 2006 10:09 AM

This is a very interesting post. I'm still mulling over it. But in case that I never have time to give it the full reply it deserves let me make a few remarks.

1. The circle is a formal definition. It is simple,elegant and tautologically true. Many other useful properties can be derived from its definition. Your version of the formal theory of evolution is not nearly as simple and elegant as the definition of a circle. It's an odd comparison, because so much of evolution is *empirical* in nature. And obviously there aren't very many applied math guys studying how circles operate in the wild. Still, I need to spend some more time thinking about this analogy.

2. The entire set up seems to equate evolution with genetics. That's interesting because I do find a lot of merit in genetic theory. I just have a hard time understanding the logical link from that theory to "survival of the fittest." Perhaps part of my discomfort is in your acknowledgement that if the traits and environment can change exogenously, then essentially any observed set of facts can fit the model. So the survival of the fittest part is unfalsifiable.

3. I find your two conclusions about the importance of evolution to be unsatisfying. What if humans nuked the planet and killed all life? Would that disprove evolution (e.g., because there would be no genetic variation left at all)? In the end, I think evolution can describe the wondrous amount of variation we see just as an historian chronicles the civil war. But it really can't explain why there isn't more (or less) variation than we actually see. It just fits what variation we do see to its model.

So, I've refined but not really changed my positions (1) genetics qualifies as a theory, (2) evolution does not and (3) genetics and evolution are not the same thing.

Have I made in progress in convincing you in my absurd belief? I feel like we still aren't at that sweet resolution when either we agree or we understand the exact assumptions that we choose to disagree.

Posted by: pseudonymious at April 5, 2006 04:00 AM