Into the future, of course not. It’s is not possible to predict with any great certainty how all the environmental influences will affect population size thousands of generations into the future.
But nevertheless, population geneticists can still model fixation of neutral alleles under a range of condition.
Yet, If I understand correctly, the data matches the idea that the no: of mutations fixed per generation are the same as the mutation rate.
Yes, but that’s because the RATE of fixation is independent of population size, and thus independent of the TIME to fixation.
A) How many are fixed every generation? This is the rate of fixation.
B) How long does it take for a novel mutation to rise from it’s initial occurrence in one (or a handful of individuals independently) to being present in basically all individuals? This is the time to fixation.
C) Out of all the mutations that occur, how many of them are ultimately fixed? This is the probability of fixation.
These are three different, but related concepts, and should not be confused.
The fixation time should be not be fixed… so the no: of mutations that are fixed should not be constant…
Why not? You seem to be mixing time-to-fixation and rate-of-fixation here.
It’s a mystery to me.
Think of it this way. While in a bigger population it takes more time for a new mutation to spread, because there are also more individuals being born every generation each of which are born with novel mutations, there are therefore more mutations present in the population with the potential to fix, with the result that the overall rate of fixation is unaffected.
I understood this to mean “mu” mutations are fixed per generation irrespective of the population size. i.e in the case of humans, it’s 50 mutations per generation.
1/(2N) is the chance that any single mutation will reach fixation. I don’t think that is the term you are looking for.
The fixation rate is the mutation rate, which is u. 4Ne is the time it takes for a mutation to reach fixation. For one generation, 50 mutations will reach fixation and those mutations came into existence 4Ne generations ago. Since there are new mutations in every generation there are going to be mutations reaching fixation in all future generations, just as a whisky distillery has 18 year old whisky available every year because they make new whisky every year.
No. @T_aquaticus analogy of the whiskey distillery explains it perfectly… only it should tell us why we can’t expect the same no: of mutations per generation.
There must be something averaging out the effect of change in time taken to fix mutations.
As with any model, it is simplified compared to reality. Changes in population, mating patterns, and other processes complicate the picture and will produce results different from the model. This is true of science as a whole. What we can do is see if divergence between species is within shouting distance of our models.
To use another analogy, if I built a model of flipping coins I would say that the probability of getting heads is 0.50. If I flipped a coin ten times, would I get 5 heads every time? No. Does that mean my model is wrong? No.
Exactly, and the reason for why the rate of fixation is independent of population size is that as you increase the size of the population, the probability of fixation of any one neutral mutation decreases, but you also increase the number of mutations, leaving the average rate of fixation unaffected. The effects apparently cancel each other out.
This is ok, provided we are clear what has been simplified and have good validation for it.
Ne is supposed to account for changes in mating patterns (I think).
Changes in population is a variable that might mess things up given the changes are large.
It all depends on what is taken as the mutation rate.For, example, for the human/chimp divergence, the split could have taken place anywhere between 4 mya to 13mya.
Direct measurement of mutation rates from parent to child gives the older split date between humans and chimps. I found this paper useful in outlining some of the issues and the range of predicted mutation rates.
Bill, there are models that relax all the assumptions of the W-F model. I bet you could even read about some of them in Joe Felsenstein’s free textbook that I linked to earlier in the thread.
For those keeping score Behe’s Darwin Devolves has sunk to # 6,742 in Amazon book sales and is still dropping fast. No wonder the DI is so frantic to stir the pot more and get Behe’s name back into the public eye.
I don’t think 1/2E is realistic as it makes too many unrealistic assumptions as we will rarely see a species without any population separation and it does not appear to take large genomes into account as when I have run the simulations with a 1% mutation to normal gene ratio with a population of 100 genes it rarely goes past 10 generations before the mutation is lost. The issue is to get 1/2E probability of fixation you may need more than one of the specific mutations in the population to lengthen the mean time to gene loss. The average time to fixation being 4E or 400 generations in this case.
Again based on this so far drift appears not to have much of a role in what we are observing.
If we imagine a species which has rapidly increased its population followed a period of stasis at which population, then Kimura’s model might give thousands of generations where no mutation is fixed…
I guess it’s limited to ideal applications over long periods of time…
One of the simulators that Josh posted earlier in the op. A bunch of these out there. The key question is the equation i/2E or 1/2E as if it is derived as i/2E it will operate differently at the boarders of elimination.
Rarely is all that is required. Only rarely will a lottery ticket be a winner, yet people win all of the time. For a population of 100, 1 out of every 200 mutations will reach fixation. With a mutation rate of 50, there are 5,000 mutations every generation, of which 25 will reach fixation.
If you don’t have completely connected populations which is the norm not the exception then the time gets so long the theory is unworkable as starting with 10k in order to get fixation you need the mutation to randomly occur in all populations that are not genetically connected since the occurrence of the mutation.
In a population of 10K the chance of a specific mutation occurring in two populations in a human type genome is around 1/10^11. It appears very difficult to get fixation from drift if there is any separation in the population.
Obviously, we are talking about connected populations. If there is no gene flow between populations then they are considered separate species, or at least at the beginning of the speciation process.
It only has to happen once, and then spread from there.
