Punctuated Equilibrium and Why it Happens

Okay, first things first: I’m not a biologist and I’m not talking about biological evolution, although this is possibly applicable to it. I’m a computer geek talking about evolutionary algorithms where the mutation rate is encoded on the genome.

This is a note from the front line on my crazy artificial-intelligence project. Well, hopefully not literally crazy, but I haven’t got any realistic chances of getting sanity right on the first try. Sanity can’t exist without consciousness, so it’s a refinement I can’t possibly figure out until I understand why and how the initial system is insane.

Isn’t that reassuring? Well, no really it isn’t. Isn’t it a good thing then that I’m working on “consciousness” instead of “human-level intelligence?” If sanity isn’t expected the first time out, be glad the insane AI is expected to be dumber than a hamster. Still, if you had an insane hamster, how could you tell? Insanity may not even be identifiable to try to debug, until human-level intelligence is reached, and then it may be too late to debug.

But I digress. That’s just the fate of the human race, it’s not relevant to what I’m doing. ‘Look at me still talking when there’s science to do!’

Back to the topic at hand. In evolutionary algorithms with the mutation rate encoded on the genome, punctuated equilibrium in evolution happens because when there is a beneficial mutation it usually happens to an individual that has a higher mutation rate than most. The self-selection effect is at work, as intended. The genes for the higher mutation rate spread along with the genes for the adaptive new trait. This results in more frequent further mutations among individuals with the new trait, and their presence is felicitous because the new trait, if it’s a substantive structural change the way new traits often are, can therefore accumulate further complementary mutations and gross refinements that help further adapt it and exploit it. A ‘cascade’ effect results and successive generations have higher and higher mutation rates.

Given an evolutionary advantage over the vast majority of other individuals around them by the new trait, a higher mutation rate is overall beneficial for the new “species.” They lose more offspring to lethal mutations, but less to competition from other individuals. The higher mutation rate means that further adaptive traits, or gross refinements in the new one, come about faster, so successive generations that find further refinements, also via self-selection, pass along a higher mutation rate.

It is only when some kind of balance is achieved that the rate of loss due to competition becomes greater than the rate of loss due to lethal mutations again. When Yolanda and Zebulon are competing, mutations and recombinations intervening between that moment and the moment when their ancestors Alice and Bob competed give more advantage to one or the other. If the advantages are major and structural, then a higher rate of mutation making Yolanda a member of a new species has been beneficial. If no major winning innovations have intervened, then selection and refinement in the existing gene pool has given Zebulon the edge because less of that selection and refinement has been disrupted by mutations. In that case the lower mutation rate has been beneficial.

This leads to an inversion of the usual technique with AI projects; instead of slowly lowering the mutation rate until the end of the run, we ought to be encoding the mutation rate on the genome and then observing it to discover when the run is over.

I should point out that this applies to Evolutionary Algorithms – ie, where the fitness depends on interaction or teamwork among the whole population – rather than to classical Genetic Algorithms where fitness is considered as the fitness of the most-fit individual. If you code the mutation rate on the genome in a classical genetic algorithm you will rapidly see it drop far below what you want if your goal is the production of a single most-fit individual. With a classical GA, reproduction is “free” in that it doesn’t cost the most-fit individual anything; they can afford to lose hundreds or thousands of offspring to lethal mutations for every one that survives with its new trait intact or possibly improved.

With the Delphic Casino or Prediction Market model, though, reproduction has a cost – the new individual must be given a stake to start gambling with, and it has to come out of the parents’ supply of money. They’re making an investment in the offspring, so it matters, from the point of view of genetic survival, that the offspring are not lethal mutations. This makes the optimal rate of mutation substantially lower in an EA.

The reason why this is potentially applicable to biological evolution is that first, biological evolution works something like EA with a Delphic Casino (which is a tautology since the Delphic Casino is modeled on it even more closely than classical Genetic Algorithms are). Reproduction has costs and an individual’s genetic success is measured across its whole population of descendants rather than by a single most-fit descendant. And second, biological creatures code things on their genomes like gene-repair mechanisms and redundant copies of important structures and functions, which have the effect of moderating their own mutation rate. In fact they code a bunch of different mutation rates applicable to different structures and cell types and moderated by different triggers.

So now this is my theory, which I’m just throwing out as a computer geek who thinks he has some insight into a biological process. Biology isn’t my field so I could easily be wrong. But I think that punctuated equilibrium in biology – where sudden improvements appear and are followed by an unbelievably fast period of evolution compared to most periods – happens for the same reasons why I’m observing them in my EA.

The mutation rates are effectively coded on biological genomes, and higher rates are selected for among a population where a new adaptation alters the cost/benefit of mutation. This is a balance of the cost of lethal mutations against the benefit of occasional improved offspring, in a fitness landscape that offers few threats from competition until the new trait becomes widespread. The mutation rate falls again as the new traits settle out and the cost of competition among creatures that already have the new trait dominates the cost of lethal mutations.

Of course by the time all of us AI scientists are finished, questions about biological evolution may have become irrelevant.

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