Sunday, April 20, 2008

Evolution In A Bucket

When I was a tender lad, the origins argument consisted of two competing narratives roughly equivalent to the partisans in conflict in the old Spencer Tracy movie, "Inherit The Wind." You either believe the dates printed in your Schofield Reference Bible, or you think you're a monkey's nephew.

Later, when in college, I learned that Creationists distinguish between Evolution in the small and Evolution in the large. Specifically, Creationists assert that we have verified proof with things like fruit flies, domesticated animals, or antibiotic-resistant bacteria that selective breeding and mutation can change the morphology of animals. But the evolution we see in the lab, and that we see in nature, is only evolution WITHIN species, not BETWEEN species.

Quite frankly, this distinction between micro and macro evolution seems to have the fossil record going for it. Though we see a lot of different fossils, we don't find a lot of "missing links." If Darwinian evolution explains the presence of millions of distinct species on this planet, then Darwinian evolution posits the existence of many millions more transitional forms between those species. When this complaint was first raised, well over a century ago, the reply was that "we haven't dug them up yet." Time has gone by and the transitional forms remain missing and the reply is twofold: not everything gets fossilized and missing links don't last many generations. The theory is called "punctuated equilibrium." Still it bothers me that there are so many species and so few (any?) transitional fossils. I'm no geologist, I may be wrong, so if there are lots of fossilized missing links out there, I'd like to hear of it.

I am more familiar with mathematical optimization and computer algorithms. Over the last couple decades I've heard of "genetic algorithms" or "evolutionary algorithms" that have been applied in some contexts, but when I'd read more, the details would get fuzzy and I'd lose the thread of what was being described.

However, in a completely different context, I heard a scientist describe an algorithm he called a "simulated anneal" that I could understand quite handily. Let's suppose you have a problem of connecting various things much like the atoms of a metal. Each connection contributes positively or negatively to some objective function. You want to come up with the "global minima" of the objective function. There are too many connections to exhaustively try them all. What to do? One approach is to look at every pair of atoms and make the link that's "best" then connect those pairs of atoms to the pair that's "best" and so on until everything's connected.

This is called a "greedy algorithm" and it often produces a poor result, getting caught in what's called a "local minima" of the objective function. This process is like dropping a marble in a bucket and letting it roll to the lowest point it finds. The trouble is that if the floor of the bucket is shaped inconveniently, say like a mountain range, you may find the marble trapped in a mountain valley whereas had it been dropped elsewhere it would have rolled to the lowland plains.

If this isn't good enough, if you need to get the marble to the bottom of the bucket, you need to dislodge it from its local minima. How do you do this? By shaking the bucket.

In the algorithm I described above, this is analogous to replacing the deterministic rule that I'll make the "best connections" with another rule. I'll add a random variable, analogous to temperature of an annealing vat of metal, to all pair-wise scores and decide whether to link or not on the basis of score+temperature. This biases the solution in the right way, but it doesn't lock it into local minima.

The idea is that over time if you repeatedly perform the process above, the solution (or marble in the bucket) will probabilistically spend more time in better local minimas. By slowly reducing the temperature, you get a solution that's much more likely to be better than you'd get from the greedy algorithm. This process is analogous to the formation of crystal domains in an annealed vat of metal.

Now, there's nothing biological in the last five paragraphs. It's just math and considerations of systems behaving not unlike what you see in soap bubbles or heat-treated metal. I was surprised when someone told me THAT algorithm I just described is also termed an evolutionary algorithm.

Does this mean that any algorithm that includes a random element and an objective function (i.e. fitness) can be termed Evolutionary? This furrows my brow because it makes the notion very expansive. I don't think of soap bubbles settling into minimum energy configurations in this way. I can't think of any Creationist who can have a problem with this sort of mathematics.

Now, could we by selective breeding do the same sort of optimization on successive generations of an animal? Isn't this what the fruit fly experiments demonstrate?

The Bible was written before Carl Linnaeus devised his system of classification. Thus the Creationist must tread lightly. My college Bible classes used the "baramin" which combines two Hebrew words, "bara" and "min." The Hebrew word "min" is translated "kind" but I think this word does NOT mean species in a Linnaeus sense. The phenomena in the Bible is procreation. Those parts of the Bible which speak of animals bringing forth "after their own kind" are places where this Hebrew is employed. Could the word "kind" merely reflect an animal's genotype? That is, does the Bible intend to convey only that the animals delivered their own DNA (with mutations perhaps) to the next generation?

Suppose, for sake of argument that we engage in a program of selective breeding among dogs. So much so that we come up with one breed of dog that cannot successfully mate with another breed. If this occurred, could we claim that speciation had occurred? Would this PROVE the Bible is wrong? I rather doubt it.

I don't know what the Creationist or the Evolutionist would say to this. However, when I've thought in these terms, the lines have tended to blur. No doubt both sides will want to burn me as a heretic.

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