Why do you assume that there is no existing variation?
How do you think this different assumption would change the outcome of the model?
So, is my figure above how your model works?
If not, where is selection in your model? How are deleterious mutations removed? Are they removed at all? If not, why not? Are you aware deleterious mutations are removed in Behe’s model? Like, all of them, instantly?
How many offspring are produced by each individual, every generation, in your model? How many of these die?
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No it is not but it is reasonably close with the exception that individuals generate two off spring.
The question you need to answer is why adding complexity to the model makes the model more accurate given assignments like selection coefficients and elimination of deleterious mutations are arbitrary.
How do you think it doesn’t? With math.
Models generally don’t have “outcomes.” They either model something usefully or they don’t.
Then your model is outright nonsensical. You need to incorporate selection. Behe does.
The End.
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If you want to start with mutations in the population your just move you starting point from position 1 forward.
This however does not give you the worst case.
Reality starts with variation. Despite the bad writing regarding SARS-CoV-2, they are only mutations when they occur.
How so, mathematically? Bill, this could be your worst performance ever, which is saying a lot.
That’s what I said. Not the same mutation. OK, but to the same gene. I did not specify that.
So, otherwise, did I describe your model correctly? (And, yes, I realize you jusy answered @Rumraket about his version of your model. But maybe you could answer my question, anyway.)
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If you start with generation 2 then mutations already exist in the population.
There is no misunderstanding now but there are some more parameters that Rum has included like offspring per family.
Why would we start with your gen 2? Why would any natural population exist with only one generation’s worth of variation? Engage your brain, Bill!
And again, if you are ever to think about this clearly, mutations are events. If the resulting changes are passed on to offspring, they are no longer mutations. They are existing variants, which in mammals outnumber new mutations by about a million to one!
This is just one of multiple reasons why Behe’s assumptions conflict with directly measurable reality.
I can’t tell whether that is a “Yes” or a “No.” Did I describe your model correctly, other than forgetting to mention that these 20 mutations in a row occur in the same gene?
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We are trying to simply measure how many generations it would take starting from the beginning to accumulate deleterious mutations in the whole population. Your idea is interesting but not relevant to what we are trying to understand.
Behe is trying to understand the amount of time to a known adaption from a duplicated gene being fixed in the population. The model is trying to see if the proposed mechanism (gene duplication and divergence) can account for the adaptions we observe in nature.
Are you claiming that if you start with pre existing variants in the population this will shorten the time to the adaption?
What beginning?
No, he is trying to deceive by pretending that natural populations have zero existing variation. It’s a million-fold error. Even you know that’s a big number, right?
Models do not try to see anything. Behe is trying to pretend that evolution doesn’t act on existing variation in nature. It’s a major tool in his deception.
I’m pointing out that you and Behe are ignoring them. What do you think, mathematically?
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Bill think. Please just think.
We can implement selection by just stipulating that deleterious mutations are outright lethal. That makes it simple enough that we can run it in our heads, no reason to make it more complicated than that.
Here’s where purifying selection, number of offspring, and population size begins to matter for mutation accumulation.
If there’s just 1 individual that has 1 offspring and 1 offspring gets 1 mutation, chances are 50% every generation that a deleterious mutation occurs. It’s unlikely that this will go on indefinitely as the compound probability of no deleterious mutations drops off drops off with more and more generations.
As long as there’s just 1 offspring, population size remains basically irrelevant for any realistic population size. (Technically for an infinitely large population you would expect extremely long chains of luck, but populations aren’t infinite of course.)
So we ditch the infinite population, and we include something more realistic: Parents have multiple offspring, and population sizes are in ranges of hundreds of thousands to many millions.
So if offspring is increased to 2, and population size remains constant at a million, this dramatically changes the odds. You have proven you can’t work out why, so here goes…
We start with a million individuals without mutations, they produce 2 offspring each. Half of those 2 million offspring will get deleterious mutations, we select them away to instant death due to the deleterious mutation being lethal. That leaves 1 million offspring with a neutral mutation. Next generation, each 1 million offspring with a neutral mutation have 2 offspring each. Again, 50% chance of a deleterious mutation, so half of the 2 million offspring die, leaving again 1 million offspring with a new neutral mutation for a total of 2 neutral mutations. Generation 3: repeat. Repeat ad infinitum.
How. How could you not have worked this out yourself?
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Mike is very clear what his model is and is not.
Models are not all inclusive as you know. You can point out lots of things not included. Rum pointed to things not included. The issue is if including a new parameter adds to the accuracy of the model.
Since selection occurs in reality, and since parents have more than 1 offspring, the “new parameters” do in fact add to the accuracy of the model.
To add to the previous explanation, if population size is something as low as 4, say, this is still low enough that even with 2 offspring it’s going to be uncertain enough that we risk deleterious mutations killing off all 8 offspring eventually in a single generation. At a 50% probability of a deleterious mutation with each birth, having only 8 offspring produced each generation would mean there was approximately 0,4% chance, or slightly less than 1 in 200 odds, every generation, that everyone gets a deleterious mutation.
Notice if we increase offspring to 20 pr individual (so for 4 individuals that’s 80 offspring each generation), that would make it extremely unlikely for everyone to get a deleterious mutation. 100(0,580) = ~0,00000000000000000000000827% chance that all 80 individuals gets a deleterious mutation.
So clearly both population size, and number of offspring matters. A lot.
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Because exponentially increasing populations is not a realistic parameter.
I explicitly said population size remains constant. I ensured this by having half the offspring produced die every generation. So, again how could you not have worked this out yourself?
“So if offspring is increased to 2, and population size remains constant at a million” - Me, in the post you quote me from.
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