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An Attack on Evolution; What am I getting wrong here?

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Hey guys, I just need to preface this by saying that I haven't studied evolution in-depth. I just got a little too bored so I read up a little bit on the specific numbers of mutation rates and all of that. In other words, I'm not really educated on evolution.

So anyway, I'm trying to figure out mathematically how long it would have taken for us to diverge from our closest relative, the chimpanzee. I've tried working it out for myself, but everything I've come up with shows that it should take way longer than it did. Hear me out.

We share 96% of our DNA with chimps, and in there are 6.4 billion base pairs (bp) in the human genome (3.2 billion from each parent). Knowing this, we can figure out how much we share and don't share with chimps:

96% = 0.96

0.96 × 6,400,000,000 = 6,144,00,000 shared bp

6,400,000,000 - 6,144,00,000 = 256,000,000 unshared bp

Now according to this study, the human genomic mutation rate is 1.1 × 10⁻⁸ per bp per generation. So:

(1.1 × 10⁻⁸) × 6,400,000,000 = 70.4 mutations per generation.

256,000,000 unshared bp ÷ 70.4 = 3,636,364 generations worth of mutations needed to diverge humans from chimps.

However, because we get half our genes from each parent, that means that it should be 35.2 mutations (because 70.4 ÷ 2 = 35.2). That also means that the mutations are split into 3,200,000,000 each. At this point, it's important to note that in order for a trait to show, it must either be dominant or have 2 recessive alleles. Generally speaking, any gene that is not 'normal' or 'average' relative to the general population is typically recessive. Basically, both parents should have the exact same mutations for it show. Assuming random mutations, that would mean a 35.2 in 3,200,000,000 chance that the mutations are in favor of the divergence of chimps and humans; this means that out of every 3.2 billion mutations, only 35.2 are likely to have been diverging us from chimps.

3,200,000,000 ÷ 35.2 = 90,909,091.

And in order to account for the likelihood of having the same exact mutations, we use the statistical probability of both A and B being A × B. In other words, this:

(35.2/3,200,000,000) × (35.2/3,200,000,000) = 1,239.04/10,240,000,000,000,000,000.

10,240,000,000,000,000,000 ÷ 1,239.04 = after 8,264,462,809,917,355, 1 generation will have the same mutations on both chromosomes.

Now, knowing that we need 3,636,364 generations in order to diverge from chimps, that means:

8,264,462,809,917,355 × 3,636,364 = 30,052,595,041,322,314,049,586 total generations to diverge from chimps. While the average generation for chimps is 25 years and 30 years for humans, I will assume 20 year generations to speed things up a bit:

30,052,595,041,322,314,049,587 × 20 =

601,051,900,826,446,280,991,736 years needed for humans to diverge from chimps.

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Now clearly, this is way longer than the actual age of the universe. So naturally, I figured I did something wrong. I decided to throw out the whole concept of probability, and assumed that all traits making humans more chimp-like were dominant, assumed that all human-like traits in chimps were also dominant, and also assumed that all mutations that occur were not random and were ONLY meant to diverge humans from chimps:

96% = 0.96

0.96 × 6,400,000,000 = 6,144,00,000 shared bp

6,400,000,000 - 6,144,00,000 = 256,000,000 unshared bp

256,000,000 unshared bp ÷ 70.4 = 3,636,364 generations worth of mutations needed to diverge humans and chimps.

3,636,364 ÷ 2 = 1,818,182 generations from both, chimps and humans in order to get to where we are today. Assuming 20-year generations:

1,818,182 × 20 =

36,363,640 years needed for evolution of humans and chimps.

This is 5 to 6 times the amount of time that the fossil record says. And the thing is, this is STUPIDLY biased in favor of evolution because:

  1. One generation should have been 27.5 years, not 20

  2. This is assuming that any and all mutations that occurred were in favor of delineating the species, which completely goes against evolution since most mutations are random and harmless

  3. It also assumes absolutely no gene flow, which could potentially speed up the evolution process, or (more likely) slow it down.

So, what am I getting wrong here? Did I mess up my math or did I somehow magically show a problem with evolution? What am I missing?

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There are a couple of wrong assumptions regarding genomic differences, but before that, a basic mistake is that your calculation assumes a genomic transition from human to chimpanzee DNA. However, the distance that you should calculate is that from either of them to their common ancestor, which diverged ca. 6 MYA ago. Another fundamental issue is that genome re-arrangements are not based on single nucleotide exchanges alone. Quite a lot of larger scale changes are based on duplications as well as deletions, predominantly in intergenetic regions. You will note that the genome size is actually different and if you align the whole genomes of the two species you will find sizeable gaps in either of them. So depending on how you actually count those gaps (and/or perform the alignment) you will find similarities between human and chimpanzees as low as ca. 80%.

If we focus on actual genes, that shoots up close to 99%.

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7 minutes ago, CharonY said:

the distance that you should calculate is that from either of them to their common ancestor

Well, that's why I had this segment to account for it:

"3,636,364 ÷ 2 = 1,818,182 generations from both, chimps and humans"

Dividing by 2 accounts for the separation of both at the same time. 

9 minutes ago, CharonY said:

If we focus on actual genes, that shoots up close to 99%.

Yeah I remember reading from this as well, but we would have to ignore 18% of chimp DNA and 25% of ours, which I don't think would be academically honest to draw conclusions from. But let's try it anyway:

99% = 0.99

0.99 × 6,400,000,000 = 6,336,000,000 shared bp

6,400,000,000 - 6,336,000,000 = 64,000,000 unshared bp

64,000,000 unshared bp ÷ 70.4 = 909,091 generations worth of mutations needed to diverge humans and chimps

909,091 ÷ 2 = 454,545 generations needed for human-chimp separation

454,545 × 20 = 

9,090,910 years needed

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Now this is much closer than the 36 million estimate I had before. But it's still too slow, and again we still had to exclude much of our DNA and chimp DNA to get there, not to mention it still has the same biases as the other 3 points. 

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Significantly confounding problems with the simplistic approach you've taken include that mutation rates are not uniform between species and across genomes https://www.nature.com/articles/nrg3098 and that the number of observed mutations is proportional not just to mutation rate, but population size also https://www.ncbi.nlm.nih.gov/pubmed/17348929

Usually, to calculate time to most recent common ancestor (TMRCA), you'd use a molecular clock mutation model and a bayesian MCMC analysis to generate posterior probabilities. This article has a really good explanation of methods to calculate TMRCA https://www.genetics.org/content/158/2/897

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