"However, your mistake is in assuming that the "N" mutations have to happen one after the other without fail, bam-bam-bam." - Dan DayFor the math in this thread, when we are dealing with useful data, the information actually does have to sequence itself one after the other to make the final output.
The sequence may matter, but the order in which the parts of the sequence came into being over time do not. The Maro calculation presumed that it did, even if he did not realize that was implicit in his math.
Whether we are dealing with monkeys accidentally typing a sentence from Shakespeare,
Which, for the reasons given earlier, is an utterly ridiculous and erroneous attempted analogy for evolution, or even abiogenesis...
software programs self-forming on your hard drive after a lightning strike,
This analogy is even worse, on a number of counts.
or DNA bases creating a double-helix structure with the proper codes to create Life,
I'm sorry, you're changing the subject. The "P1*P2*P3..." calculation was specifically in reply to an exchange concerning Maro's question about accumulated mutations by individuals in an already reproducing population.
Your clue, even if you chose not to trace the discussion back, should have been the use of the term "mutations", which only make sense in the context of replicating life. Changes in non-living (or pre-living, if you will) material is not mutation (by definition), it's merely chemical changes.
the sequence really does matter.
The sequence may matter, but that still doesn't make Maro's calculation correct. Even for a non-living string of molecules, the odds of it forming are not "P1*P2*P3*P4...", *unless* one is presuming, preposterously, that it formed all at once (instead of via combination or recombination of other parts or earlier arrangements), that it was the *only* "fish in the sea" (i.e., discounting all of the other chemical reactions occurring all over the world), that it had *one* chance to form (i.e., discounting how many years are available for reactions occurring at a rate of X per second), that it was the *only* suitable result which would have led to the condition being discussed, and so on.
It's the absolutely "worst case" scenario calculation. Of *course* it's preposterously large.
Re-order a few 1's and 0's in a softwre program, re-order a few characters in a sentence, or re-order the bases in a gene and the final desired output will no longer be achieved.
The fact that the sequence matters still does not make Maro's calculation the appropriate one for the situation being discussed. It's not. The end product matters, sure, but Maro's calculation erroneously presumes that it has to happen the very first time any N things hapen to combine, without fail.
It's like declaring that getting a Royal Flush in poker is so rare that it'll never happen, because his calculations presume that there will only be one hand dealt, *ever*, to try to get one, while forgetting that each poker player will on average see thousands of hands dealt, *and* there are millions of poker players playing the game, *AND* you can discard and draw a second round of cards each hand to try to turn a partial Royal Flush into a full one. Gosh, that suddenly improves the odds a hell of a lot, doesn't it?
"Instead, you need to calculate the odds of mutation N1 happening, *at all*, over a huge number of individuals, across a large number of generations. This is, needless to say, much less unlikely. In fact, over sufficient time, it approaches certainty." - Dan Day
Actually, for what you are proposing, you would need to first calculate the odds of mutation N1 happening at all, then second the odds of life-form with mutation N1 surviving, then propagating, then finally of said mutation N1 appearing succesfully in offspring.
Of course. But those are all known quantities. A mutation at a particular site in a gamete destined for reproduction is low (I've seen the figures, but don't have them handy at the moment), but not ridiculously so.
The odds of the organism surviving and propagating are pretty good, few organisms have an insanely high mortality rate, and the few that do balance that out having insanely high reproductive rates, which ironically increases the odds of a given mutation happening in an amount to exactly balance out the mortality rate (i.e., double the rate of offspring production to overcome a halved survival rate, and that doubles the chances for mutation N1 happening during reproduction, which balances the lost genes due to morality).
The odds of the mutation appearing in subsequent offspring? The "expected value" is 100%, in a species that is neither growing significantly in population nor declining, although the actual results can vary from zero offspring carrying the gene, to a large number depending on the fecundity of the species. On average, though, the gene will be passed on to one offspring by each parent that carries it.
There are lots of observable mutations. Two-headed snakes are one such example, for instance, yet how often do two-headed snakes survive, much less propagate, much less have said mutation successfully appear in their offspring?
Try to keep up with the discussion, Maro was specifically trying to calculate the odds for a combination of mutations which, and I quote, "make no functional difference". This is quite a different situation from your cheesy example of two-headed snakes, which are obviously a detrimental mutation which inhibits both survival and reproduction.
A mutation can usually be considered to be a mistake in genetic code copying. Can we see mistakes in said copying after they've occured? Yes.
Not always, no. Again, the Maro discussion concerned "neutral" mutations which did not express as anything.
Is that the same as seeing the mutation/mistake propagate? No.
That's a different topic than the one being discussed.
So for the math that you propose above to be valid, one would to need make Additional calculations than the single equation you alluded to above.
I didn't allude to any calculation, I merely pointed out all the things that the Maro calculation had left out which would have vastly increased the odds of the event being discussed. His was a "worst possible case" calculation, which makes it invalid for calculating how often such a result might *actually* occur.
Although it would usually go without saying, considering the behavior on this thread it is probably worth pointing out that those additional calculations will greatly lower the probability of such events.
It would help if you checked the context of a discussion before you decided to nitpick it, most of your points are moot.
You'll have to explain to me how the "expected value" for the probability of a mutation being passed to offspring is 100% when you admit that mutations such as two-headed snakes WON'T propagate to their offspring.