I comparing the rates of mutation over time

[eNathan]

I know this is a long post, but bear with me.. this is what I've got through several days of reserach.

I've always woundered about the mathematical aspects of evolution. I've heard such facts that the mutation rate is fairly consistent and can be used as a biological "clock" to track events in our evolutionary history (when a species diverged, etc). I was recently faced with a creationist asking about the mathematics of evolution and have been studying it. I've made some progress but some things have confused me.. so this is what I got so far:

The first thing I realized was that if the mutation rate is constant, and if I had the dates of the divergence of the ancestor to humans and chimps, and humans and neanderthals (or europeans and africans), I can calculate the percent of mutation change per year and compare the numbers. For the most part, the numbers have some resemblance. I'm not a mathemetician but the equation I came up with for base pair substitutions per year with closely related specices A and species B is: (sorry that I forgot latex formatting)

R = S * D / 2 / T

Which is the size of the genome (S), divided by the DNA Difference of the two species (for humans and chimps this is 4%) (D), divided by 2 (because it's comparing 2 species, so we have to divide that out), divided by how many years have passed since their divergence (T). This should render the number of nucleotide substitutions in the genome of either population per year relavent to the ancestor if I'm thinking correctly. If I'm just totally off, please correct me :)

Now, for humans and chimps the rate of mutation in nucleotide substitutions per year seemed to render 30. With the size of our genome being about the same, a DNA difference of 4%, and an estimated divergence occurring at 4MYA, we get

6*10^9 * 0.004 / 2 / 4000000 = 30.

With Europeans and Africans, we get:

6*10^9 * 0.0015 / 2 / 115000 = 39

I had to to research really hard to find the DNA difference between europeans and africans is 0.15. But 30 and 39 are good enough for me to be explained away by factors not in the equation -- it's consistent. Now I know that the 4 MYA divergence estimate is probably based on an equation similar to this using the biological clock, but I'm sure fossils will generally speak in accordance with it so it can't be considered circular reasoning.

Now what I'm trying to do is figure out these numbers in light of other facts. According to wikipedia, the genometic rate of mutation in humans is ~2.5x10^8 per base per generation. So, given the size of the genome (3 billion base pairs), this is 150 base pair substitutions per generation.

Now, if both of these figures are correct, there needs to be a little reconciliation. This is where I need some help.. to reconcile these numbers, you'd have to say that the average generation was about 5 years (150 / 30 = 5). This doesn't sound right does it?

I had this other idea though. Each "individual" is born with (on average) 150 mutations. An individual's next generational offspring is the result of two parents, so in effect 150*2 mutations would be acquired each generation. With these numbers, 300 / 30, a generation is 10 years, which seems reasonable?

I would definatly appreciate some input on where I'm right and where I'm wrong, and perhaps other mathematical aspects of evolution. I find it quite exiting to understand these things.

Thanks in advance!

 

[Ygggdrasil]

I remember learning about this topic a while back (read: I don't understand it well enough to post anything meaningful now), but a look back through my notes says it may be useful for you to look up the Jukes-Cantor model.

For other mathematical aspects of evolution, it may be worthwhile to look up some papers by Martin Nowak (http://www.ped.fas.harvard.edu/people/faculty/select_list.html ), who has done some nice work modeling evolution mathematically.