The Mathematics of Evolution

I found a really neat comment on Slashdot about the mathematical justification of evolution:

First two minor points, then I’ll get to the real subject, the math of evolution.

theory is a theory my friend

Every field of science is a theory, my friend. Everything from the theory of the atom to the theory of zymosis (that's fermentation). You may as well try to attack relativity as being “just a theory”.

sort of like the un-provable assumption of evolution?????

What un-provable assumption of evolution? Evolution fundamentally says that if if you have heritable variation and mutations and selection pressures on that variation then you will get evolution over generations. This is trivially observable fact. There is no genuine scientific dispute over biological evolution exactly because there is so much evidence that cross checks and cross validates across so many fields, both current observations and study of prehistoric evidence left behind. Trying to even scratch the surface of this mountain of evidence in this post would be hopeless. If you are questioning the quantity and quality of the evidence, I suggest you either crack open a text book on the subject or at least browse the talkorigins [talkorigins.org] website. It’s all well documented if you actually question the issue. If you don’t truly question the issue and you instead simply reject the entire subject on non-rational grounds, well obviously you’re not going to be swayed by something silly like actual evidence and actual science.

Anyway, the real issue I wanted to address was this one:

the sheer numeric improbability of evolution

Correction, the sheer numeric CERTIANTY. There’s powerful mathematics to evolution, powerful effects going on that you don’t hear about in the common explanations of evolution. The common idea of evolution is as a sequence of individual beneficial mutations, like climbing a ladder. If that’s how evolution actually worked then critics would be right, it would have been mathematically impossible for evolution to produce the incredible complexity we see today.

To show the true mathematical power of evolution I will first abandon that “ladder climbing” of beneficial mutations. In fact lets assume that every single mutation that occurs is either neutral or harmful. I’ll demonstrate that we still get the real and powerful mechanism of evolution, the math of evolution.
A good place to start is with the common complaint of creationists that mutation and evolution “cannot create information”. Well in the initial mutation phase they are right. When a mutation occurs it introduces noise, it tends to degrade information. But look what happens the moment that mutation gets passed on to an offspring. That mutation is now no longer random noise, it now carries a small bit on information. It carries a little tag saying “this is a nonfatal mutation”. The presence of this mutation in the offspring is new and created information, the discovery and living record of a new nonfatal mutation. Over time the population builds up a LIBRARY of nonfatal mutations. This library is a vast accumulation of new information.

That information actually undergoes even more processing and synthesis. Over generations beneficial mutations would obviously multiply, but we’re assuming there are none of those here. However entirely neutral mutations will also tend to accumulate and multiply. Nearly harmless mutations would also accumulate and multiply to a lesser extent. Somewhat harmful mutations will even accumulate, and extremely harmful-but-nonfatal mutations will pop up and disappear at the rarest frequencies. So not only do we build up a library of nonfatal mutations, the mutations get tagged with a tagged with a frequency, the percentage of the population carrying that mutation. Each mutation is tagged with a measurement. Every mutation now carries a cost/benefit information tag at the population level. The best ones have a high percentage representation and the most harmful ones have a near zero representation percentage. Our library now contains far more valuable and sophisticated newly created information.

The individuals in the population are on average going to carry a roughly stable load of harmful mutations, a roughly constant “cost” in harmful mutations. Individuals loaded with more than the average cost are generally going to die and remove a more-than-average load of harm out of the population pushing the average up, and individuals with a less than average load will multiply and pull the population average upwards. The cleansing effect of selection removing “damage” from the gene pool will automatically scale to offset the exact rate that mutation is causing “damage”. Harm/cost/damage will be weeded out by selection at the same rate it is added by mutation. Neutral mutations will steadily accumulate in the library, and negative mutations will remain at a roughly fixed level constantly measured and scaled by the cost of each. Some mutations will disappear while new ones appear.

The real power in evolution is the recombination. Every offspring contains a random mixture of mutations from that library. every offspring is a test case searching for a jackpot beneficial combination of mutations. Lets assume an individual has a million random mutations across its entire code. There are 500,000,000,000 mutation-pairs being simultaneously tested within that individual in parallel. Perhaps one is a mutation creating a toxin and another mutation for mutant skin pores. Either mutation alone may be harmful, but the pairing could be breakthrough protecting against predators.

There are 160,000,000,000,000,000 mutation-triples. Each individual is also testing all of these triples in parallel. One mutation might be for a toxin, a second might might crank up production of that toxin to fatal levels (which would ordinarily a fatal evolutionary dead end), and the third might be a costly and ordinarily useless anti-toxin. The triplet is now a breakthrough, either a powerful defense against predators or a weapon for a predator to use, or even both at once.

Each individual is also testing 40,000,000,000,000,000,000,000,000 mutation quadruples in parallel for free. Maybe those four mutations individually yield useless proteins and enzymes, but the chain of four together may yield a new breakthrough digestive pathway.

Each individual also tests a near infinite number of mutation pentuplets and mutation sextuplets and more. Each individual actually acts as a test of a near infinity number of possibilities and it does this testing in parallel and it does so for free. This is called implicit parallelism. It astronomically multiplies the power of evolution to search for jackpot breakthroughs.

Another point that I raised and haven’t actually applied yet is the fact that each mutation is present with a frequency percentage in the population. The measurement of the cost/benefit of that mutation. When you want the most efficient search pattern you want to minimize wasted effort and minimize your costs and maximize your return-on-investment for your available resources. Well each offspring is an investment of resources, a test effort. When you are investing your effort looking for a payoff you want to expend most of your effort on the mutations that have paid off the best in the past and the least effort on the almost-fatal mutations. You mostly want to test combinations of good stuff with good stuff, and you almost never want to bother testing two nearly fatal mutations that will most likely combine to cause a dead offspring and a wasted investment. However you do still want to make a very rare test of two nearly fatal mutations because it *might* just be a jackpot payoff. In mathematics this exact investment-of-effort and search pattern had already been studied and a mathematical optimization pattern found. And guess what? By an almost staggering coincidence the evolutionary population frequency on each mutation in the population and in the offspring exactly matches and produces the mathematically optimal and most efficient search pattern for the next generation of offspring. You invest lots of effort and lots of offspring on testing the best mutations and groups of the best mutations and you invest exactly the right level of very rare testing of really bad combinations that will probably be fatal but which *might* just find a jackpot payoff. Mutations at all levels are tested proportionally to the measured cost it impose on the host.

So evolution has a nearly infinite multiplier on its search power and it just happens to invest its search effort in the mathematically optimal most efficient search allocation. Two fairly deep and powerful mathematical results that are hardly apparent in the usual way evolution is explained.

A further point is that once some beneficial mutation or combination of mutations is found, evolution then searches that vast library of stored nonfatal mutations. Most new breakthroughs will be extremely crude at whatever it is they do, and they will probably come with harmful side effects. A set of limbs might be mutated into some useful form for getting some new food source, yet be horribly mutated and otherwise dysfunctional. Evolution then searches the library for mutations that combine to further improve that new breakthrough, and it also searches the library for mutations that will repair or offset any harmful side effects of the breakthrough. A search for ways to further improve the mutated limbs for the new purpose, and a search for modifications to repair problems caused by these malformed limbs.

Evolution is very rarely a simple ladder-climb series of beneficial mutations. Evolution is an information processing system building vast database of information and synthesizing complex measurements of that information and doing an incredibly powerful search and mining of that information database to discover and refine improvements.

And this fits in perfectly with punctuated equilibrium. During the quiet phase the library is accumulating new mutation contributions and measuring those mutations into a percentage of the population, and then when there is a breakthrough discovered or there is an environment shift then evolution goes into overdrive. It mines the database for contributions to the new development or to adapt to the new environment. The frequencies of all of the mutations also get re-measured to re-weigh their cost/benefit ratio in light of the new development or in the new environment. Not only can this radically shift the frequency of vast portion of the genes and mutations in the population, it can quite easily trigger the discovery of other independent breakthroughs. If the population underwent heavy selection pressure, if most of the population was exterminated or displaced by this change, then the gene pool gets decimated. Much of that accumulated library gets wiped out along with the losing majority of the population. With a depleted library in the new population you are naturally going to see little change and progress. You see a stable population, equilibrium, until that library can be very slowly rebuilt through accumulation of new mutations.