

On the mathematics of evolution - TriinT
http://science.slashdot.org/comments.pl?sid=156877&threshold=0&commentsort=0&mode=thread&cid=13153263

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TriinT
In my opinion, it is rare to find such high-caliber comments on /. these days.
Here's a transcript:

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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 fermentaion). You may as well try to
attack relativity as being "just a theory".

 _sortof like the unprovable assumption of evolution?????_

What unprovable 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 exacly because there is so much evidence that cross checks and cross
validates across so many feilds, both current observations and study of
prehistorical 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 truely 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 CERTAINTY. 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 mutaions. 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 dissappear 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 yeild
useless proteins and enzymes, but the chain of four together may yeild 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.

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