Mutations Confirm Common Descent

It would be easiest to consider a model with a single DNA base, I suppose. In a population of size N, with zero mutations for this base, it may to to 1 mutation at rate mu * N per generation.When n individuals have this mutation, it will go to n + 1 with probability p, and to n - 1 with probability 1 - p. For beneficial mutations, p would be greater than 1/2.Numerically, this is east to iterate to find the distribution after a certain number of generations, for fixed p = 1/2 for example. Or draw a random p from a probability distribution, where we use estimates of beneficial mutation, neutral mutation, bad mutation ratios. But it gets complicated fast, as we would need some continuous probability distribution for p values between 0 and 1.

In the equation for neutral fixation the probability of a mutation reaching fixation is just the number of genomes with the mutation compared to the total population of genomes. Since humans are diploid, you would take the population size and multiple by 2 to cover 2 genomes per person. When a mutation first occurs in a population with 1 million individuals the probability of that mutation reaching fixation is 1 in 2 million (1 million people = 2 million genomes).

Well, feel free to join the conversation, I suppose.

That is the correct math for one dimensional random walk between two fixed boundaries. If the data would show different rates outside of the models confidence ranges, we may need to see if near extinction events could explain higher fixation for example, as fixation becomes more likely in smaller populations, with boundaries closer together.

I'm just a member of the peanut gallery munching on snacks and watching the discussion. We do have some questions for you at Message 275 however. I said that you were sensible, so now I and others are going to test you.

In a bottleneck situation you would get a surge in fixed mutations, if memory servers. The dynamics of population size will definitely have an effect.

Equlibrium for different popularion sizes.I made these graphs. The model is for a single "neutral" DNA base, that can be A or B, so two possibilities instead of the usual four.The first graph shows equilibrium distribution for the DNA for different population sizes N, for a "mutation rate" of mu = 10^-7.It appears that when N * mu = 1, the distribution is a flat line.For larger populations, the distribution seems to approximate the normal distribution, as the central limit theory predicts.For the graphs below, each individual in the initial population has base A. Population size is fixed, each step consists of picking one random individual and copying it, with mu probability of a mutation happening for the copy. At the same time, another random individual dies to keep the population size fixed.
N steps counts as 1 generation.The gray lines are for the distribution after 1, 2, 4, 8, 16, etc generations until equilibrium has been reached. 1 2 3 4I tried to plot the average similarity between two random individuals against time. But this requires a lot of computer memory for large populations and too long computation time on my computer.

Can you explain what point you are trying to demonstrate here?

I'm showing the data from the model. We can use it for whatever.One of the things that I see is that under this model, in very large populations, practically none of the "neutral" DNA is fixed (at 0 or 1).The gray lines in the graphs are actually more precisely for generations 1, 3, 7, 15, 31, 63 (2^n - 1).What possible predictions do you think we can make from here?

I'm not seeing any images, sorry. EvC is picky on how it displays images. For most of my posts I use html code which seems to work most of the time. If you see one of my posts with pictures in it you can hit the peek button and see how I did it. What does this have to do with the topic at hand? How does it relate to the opening posts?

OK, good. Well, it's your model, why don't you tell us?

Do you see images or links to images now?I described the model simplifications that I used.Starting from a fixed DNA base, it takes millions of generations to reach equilibrium.Depending on how much of DNA is junk or neutral, comparing DNA of two individuals and finding 99.9% similarity, seems very high, compared to my model for such large population.
Is it because we are still far from equilibrium?

Yes, I see them. I'm still not seeing the relationship between this model and what is presented in the opening posts. What does this have to do with the ratio of transition to transversion mutations?

You are comparing DNA of primates and found that it fits predictions of a common ancestor. So I'm trying to see if other predictions fit as well. Because we don't want to be cherry picking only data that fits our hypothesis now, I suppose.Or do you think it's better to start a new topic?

Yes, and that prediction is the ratio of transition to transversion mutations, along with CpG transitions. If you want to discuss a different prediction then feel free to start a new thread. We also don't want a Gish Gallop. I do think that.