A Second Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]

Nutters.org ^ | 28-Jul-2000 | Brett Watson

[Southack]

This is part two of the famous "Million Monkeys Typing On Keyboards for a Million Years Could Produce The Works of Shakespeare" - Debunked Mathematically.

For the Thread that inadvertently kicked started these mathematical discussions, Click Here

For the Original math thread, Click Here

[edsheppa]

In a fixed sized population each instance of a neutral mutation will be passed on to one offspring on average. I'm pretty sure this is what Dan meant. It is intuitively obvious to me. If you reflect on it I bet you will get it. If not I can explain.

[Southack]

"In a fixed sized population each instance of a neutral mutation will be passed on to one offspring on average. I'm pretty sure this is what Dan meant. It is intuitively obvious to me. If you reflect on it I bet you will get it. If not I can explain."

You do realize that even what you say above is not a 100% mathematical expected success rate, don't you?

Dan said 100%. That's his claim. He's added later qualifiers to his claim in an attempt to distance himself from that position, but no matter how much spinning or word-smithing is done, you still don't expect 100% of all mutations (neutral or not) to be successfully passed to subsequent generations.

[Nebullis]

In experiments using statistics, outcomes are presented as expected values vs. observed or actual values. Transmission of a gene or mutation from one generation to the next is expected to be 100%. The actual rate differs from this, due to sampling error.

[Nebullis]

Sampling error in the transmission, that is, not the experiment.

[edsheppa]

Yes, I'm quite aware of it. Further, as I previously posted, I don't think that's what Dan meant. Perhaps he can shed some light.

I take it you agree with what I posted as you did not dispute it.

And what did you mean by my "claim of mutation-proliferation?"

[Nebullis]

I think you're trying to read something into Dan's post that isn't there. As far as I have read, he's talking about transmission fidelity in evolution. You seem to be turning this into a discussion of allele segregation of diploid organisms or something along those lines. It's hard to know where to start when such things are not stated.

[Southack]

"In experiments using statistics, outcomes are presented as expected values vs. observed or actual values. Transmission of a gene or mutation from one generation to the next is expected to be 100%. The actual rate differs from this, due to sampling error." - Nebullis

No, that's not accurate. You might be able to support a claim such as "the expected rate for the transmission of established genes approaches 100% in an ideal environment", but in no way, shape, or form can you claim that mutations bat 1,000 in the propagation ballgame.

For one thing, no species has ever batted 1,000 for their propagation success. Not everybody lives to propagate.

For another, many mutations are caused by "errors" in context, not data. Context is not replicated. It is the data in DNA that is replicated, but the same data might produce different results (read: mutations) based upon context during replication and processing. Even a benficial mutation, if caused by an error in context rather than in the data of the sequenced bases themselves, will NOT propagate to offspring (simply because that error in context/environment is highly unlikely to present itself at the precise time/place required to cause the DNA code to reproduce that mutation again).

Then there is the replication process itself, which is not 100% perfect by the very definition of Evolutionary theory. You can't have a 100% success ratio of passing on mutations if the replication process itself isn't even that effective.

So for these three major reasons as well as scores more, the "expected rate" or mutation propagation is never 100%. Mutations do not bat 1,000 in the game of life. Two-headed snakes, even when forcefully bred in the lab, aren't going to always produce two-headed offspring.

[Nebullis]

Expected rate refers to ideal conditions.

[Southack]

Even in an ideal environment, the successful transmission of mutations won't hit 100%. The very replication of genes isn't even perfect itself. Make enough copies of copies of copies, and you'll get an error. To have a 100% expectation that mutations will be successfully passed on, your copying process would first have to be flawless.

It isn't flawless.

[Nebullis]

It isn't flawless.

Right. (That's one of the reasons we see evolution.)

[Southack]

So now you are finally agreeing that we do not see a 100% expected rate of the propagation of mutations, after dancing around claiming otherwise for a small number of posts.

But you spoil even that intellectual breakthrough by then claiming that seeing mere mutations (which you've already agreed don't always propagate even when beneficial) is the same as seeing evidence of evolution.

You've got to have mutations propagating successfully before a species can evolve.

[Nebullis]

We see a less than 100% actual rate.

[maro]

You poor confused sap. Let's say your lottery involved picking a number from 1 to 6, in an (ordered) sequence of 10, with replacement. The odds of any single 10-tuplet are about 1 in 60 million. That is calculated as 6 raised to the tenth. When you say suggest that the odds are certain that someone will win (actually, not quite certain, because there could be no match, and a rollover of the jackpot), you are implicitly defining the universe of successes as the universe of all 10-tuplets, the probability of which will be 60 million times 1 divided by 60 million, or one. The probability of any one 10-tuplet is still 1 in 60 million. Let's say you wanted to figure the odds that all the winning numbers are even. That's 1/2 raised to the tenth, or 1 in a thousand in rough numbers. Both computations are figured as P1*P2*P3...PN. You can get from the first computation to the second by figuring the number of 10-tuples in which there are only even numbers (3 to the tenth, or about 59,000, and multiplying by the probability of each 10-tuplet. Thus, it is seen that is useful to separate the question of what the probability is of one 10-tuplet from the question of how many are in the set A for which one is determining P(A). One practical reason why this approach makes sense is the difficulty of determining how to count all functional DNA computations. Because we are talking about bitflip mutations, it seems obvious that PN << 1, and we have assumed some significant minimum size of N, so in our case P1*P2*P3...PN is pretty small. As to how dense in our probability space are the functional DNA sequences--by intuition it seems likely to be not dense at all. In logic, well-formed sentences form a small fraction of all sentences. In all programming languages I have been exposed, the fraction of working programs in the space of all possible binary combinations of a certain set size is also small. I would think that if the density of successful DNA combos in DNA space were high, we would irradiating our sperm and ova rather than avoiding high radiation--or at least doing that to our livestock. I think the onus is on the evolutionary camp to show that things are different when it comes to DNA. And by the way, math majors at Harvard don't take "probability" in their freshman year. They take Math 55, or 22, which used to be the advanced calculus classes, which are preparatory to other classes.

[maro]

Can you summarize your model constraints in a post?

[edsheppa]

I could post the c# program if you'd like, but to summarize: the population is maintained within a range (+/- 50% of a "niche size" parameter); reproduction is asexual - individuals die or split with equal probability except to maintain the population in the range; "normal" individuals become "mutants" and "mutants" become "normal" with the same likelihood; parents pass their state to their offspring (which may then mutate/unmutate).

[maro]

That's very interesting, and I believe you got the results you got, since a few simple computations on paper lead to the same result. The simple answer is that as long as you're giving up x% of your "score" and getting x% of the other guy's "score," your score moves up until the two sides are at parity. I think for a 4 state game, equilibirum is reached when all four states are at 25%, and so on, so the long-term probability of a particular mutation existing in a population (assuming no selection) is close to the 1 over the number of possible states for that gene. Of course, for low probability mutations, the drift toward equilibrium is slow. Why don't you pop in a low initial probability into your model (say, 1 in a thousand) and see how long it takes to get to equilibrium?

[Nebullis]

For a diploid population the drift toward equilibrium is either to 1 or 0 for a single allele.

[maro]

That's not the same as the a priori probability of the allele. Here's an excerpt from a book I have never gotten around to reading, "Molecular Evolution" by Wen-Hsiung Li: "We note that a new mutant arising as a single copy in a diploid population of size N has an initial frequency of 1/2N....For a neutral mutation, P [the probability of fixation] = 1/2N." Pp. 47-48.

[Nebullis]

The initial frequency is 1/2. With neutral drift the allele carrying this allele becomes homozygous.

Good book, btw.