Common Ancestry - The Selfish Gene

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SelfishGene
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Common Ancestry - The Selfish Gene

Post by SelfishGene » Tue Mar 16, 2010 6:37 am

I am confused about something I've read in The Selfish Gene by Richard Dawkins. Can you show me where I've gone wrong?

In the quote below, he says that first cousins share 2 common ancestors - a grandmother and a grandfather. Makes sense so far, but he later says that an uncle and his nephew share only 1 common ancestor - the father of the uncle (or the grandfather of the nephew). Don't they also share the mother of the uncle (or the grandmother of the nephew) as a common ancestor as well? If not, why not? Doesn't make sense.

Here is the quote, I have underlined the relevant parts:

From page 91 of The Selfish Gene:
First identify all the common ancestors of A and B. For instance, the common ancestors of a pair of first cousins are their shared grandfather and grandmother. Once you have found a common ancestor, it is of course logically true that all his ancestors are common to A and B as well. However, we ignore all but the most recent common ancestors. In this sense, first cousins have only two common ancestors. If B is a lineal descendant of A, for instance his great grandson, then A himself is the 'common ancestor' we are looking for.

Having located the common ancestor(s) of A and B, count the generation distance as follows. Starting at A, climb up the family tree until you hit a common ancestor, and then climb down again to B. The total number of steps up the tree and then down again is the generation distance. For instance, if A is B's uncle, the generation distance is 3. The common ancestor is A's father (say) and B's grandfather. Starting at A you have to climb up one generation in order to hit the common ancestor. Then to get down to B you have to descend two generations on the other side. Therefore the generation distance is 1 + 2 = 3.

Having found the generation distance between A and B via a particular common ancestor, calculate that part of their relatedness for which that ancestor is responsible. To do this, multiply 1/2 by itself once for each step of the generation distance. If the generation distance is 3, this means calculate 1/2 x 1/2 x 1/2. If the generation distance via a particular ancestor is equal to g steps, the portion of relatedness due to that ancestor is (1/2)^g.

But this is only part of the relatedness between A and B. If they have more than one common ancestor we have to add on the equivalent figure for each ancestor. It is usually the case that the generation distance is the same for all common ancestors of a pair of individuals. Therefore, having worked out the relatedness between A and B due to any one of the ancestors, all you have to do in practice is to multiply by the number of ancestors. First cousins, for instance, have two common ancestors, and the generation distance via each one is 4. Therefore their relatedness is 2 x (1/2)^4 = 1/8.

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Re: Common Ancestry - The Selfish Gene

Post by mamoru » Tue Mar 16, 2010 8:02 am

SelfishGene wrote:In the quote below, he says that first cousins share 2 common ancestors - a grandmother and a grandfather. Makes sense so far, but he later says that an uncle and his nephew share only 1 common ancestor - the father of the uncle (or the grandfather of the nephew). Don't they also share the mother of the uncle (or the grandmother of the nephew) as a common ancestor as well? If not, why not? Doesn't make sense.

You are misunderstanding his intent with the uncle and nephew example. He's not counting common ancestors there; he's counting generational distance. You wouldn't count twice because the grandparents are the same generation.

If you apply the example of calculating relatedness that he uses in the last paragraph to the uncle nephew example, then you should get 2 * (1/2)^3 = 1/4, so an uncle and a nephew have a relatedness value of 1/4.
"Empathise with stupidity, and you're halfway to thinking like an idiot." - Iain M. Banks

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Re: Common Ancestry - The Selfish Gene

Post by SelfishGene » Tue Mar 16, 2010 5:27 pm

If you apply the example of calculating relatedness that he uses in the last paragraph to the uncle nephew example, then you should get 2 * (1/2)^3 = 1/4, so an uncle and a nephew have a relatedness value of 1/4.


Well he says "It is usually the case that the generation distance is the same for all common ancestors ", This works for first cousins, but in the case of the uncle and nephew does not. So are you sure you can simply multiply (1/2)^3 by 2 to get the correct answer?

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Re: Common Ancestry - The Selfish Gene

Post by mamoru » Wed Mar 17, 2010 12:39 am

SelfishGene wrote:
If you apply the example of calculating relatedness that he uses in the last paragraph to the uncle nephew example, then you should get 2 * (1/2)^3 = 1/4, so an uncle and a nephew have a relatedness value of 1/4.


Well he says "It is usually the case that the generation distance is the same for all common ancestors ", This works for first cousins, but in the case of the uncle and nephew does not. So are you sure you can simply multiply (1/2)^3 by 2 to get the correct answer?

Yes. Read the entire paragraph immediately following the paragraphs you quoted (the lower half of pg. 92). The last sentence says the same thing:
Similarly, you are just as likely to 'take after' your uncle (relatedness = 2 x (1/2)^3 = 1/4) as after your grandfather (relatedness = 1 x (1/2)^2 = 1/4).
"Empathise with stupidity, and you're halfway to thinking like an idiot." - Iain M. Banks

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Re: Common Ancestry - The Selfish Gene

Post by SelfishGene » Wed Mar 17, 2010 10:13 pm

Thanks . I probably should've read the rest before posting :P

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