## 30 January 2008

### Some probabilistic ramblings on evolution

The Repeater (Olivia Judson, in an NYT blog). The post begins:
Here’s an evolutionist’s dream: 10,000 planet Earths, starting from the same point at the same time, and left to their own devices for four and a half billion years. What would happen? Could you go on safari from one planet to the next seeing an endless procession of wildly different organisms? Or would many of the planets be home to life forms that are broadly similar?

This is the sort of question that's hard to answer a priori. Basically, evolution is made up of a ridiculously large numer of random decisions, each with a very small effect. There are a lot of classes of combinatorial structures for which we can generate members of the class uniformly at random (or according to some other probability distribution; the details don't matter here) and they'll all basically look the same. Why shouldn't evolution be like that? The details will be different every time; but in broad outline one can imagine that a "law of large numbers" and "central limit theorem" could apply to evolution -- if we consider some numerical measure of some evolutionary trait, then if we average that numerical measure over many independent "runs" of evolution we should approach some limit, and the deviations from that average might even be spread out according to a normal distribution.

Of course, this isn't something that has to be true -- the many events that make up a single evolutionary process aren't exactly independent, some of them can only happen if others happen, and so on. And whatever numerical measure I was talking about in the previous paragraph might only exist in some runs and not in others. That would seem to argue against my hypothesis. But on the other hand, evolution isn't just a random walk. There are selection pressures which are the more standard explanation for what's known as "convergent evolution", which is the indepedent evolution of similar traits in evolutionarily distinct populations.

By the way, on the topic of convergent evolution: the eye has evolved something like forty times. This suggests that eyes are very likely to arise via the evolutionary process; things that have only evolved once among all life, like language (although that's open for debate), are given the state of our current knowledge less likely to arise. One might be able to compute something like the "probability" that eyes, language, or some other complex trait evolves by looking at how many times it has arisen independently. But this is the sort of probability that is very hard to interpret -- what would it mean to let evolution happen more than once?

Maria H. Andersen said...

I wonder if you've seen this little exercise in random evolution? Will Wright talks (in this TedTalk) about the soon-to-be-released video game "Spore" which is based on the process of evolution. Can't wait... looks like it's got lots of mathematical underpinnings.

Efrique said...

Basically, evolution is made up of a ridiculously large numer of random decisions, each with a very small effect. There are a lot of classes of combinatorial structures for which we can generate members of the class uniformly at random (or according to some other probability distribution; the details don't matter here) and they'll all basically look the same. Why shouldn't evolution be like that?

Because evolution isn't like that at all.

Evolution is not random.

Evolution is literally descent with modification.

Evolution is not random, because natural selection (the thing that makes evolution "work") is decidely nonrandom.

To an extent the modification part is random -
for example, mutation is random BUT NOT IID - critical genes are much more carefully conserved than ones we can mostly manage if they don't work so well.

Also, sexual reproduction in terms of crossover is random (i.e. in animals, after sperm fertilizes egg there's a random crossover), but at the organism level, it's to a large extent about selection (mate selection, for example) - and the pool of potential reproducers is only going to include the individuals that survive long enough to even try.

That's the modification part (how genes change). But the descent part is all about how important the genes were in contributing to the survival and reproduction of the organisms they came from.

Now it seems that at the molecular level, there is quite a bit of random drift goes on - mostly with minor effects on the phenotype, and this may turn out to be more important than previously understood - but the nonrandomness and importance of selection is quite well established. I can privide links.

It's a bit like noticing the dealer shuffles the cards before dealing a hand of poker, and thereby concluding that the winner at a winner-take-all game will be selected randomly from the participants.