Comments on: Dawkins on Kin Selection: A Correction

By: David B

David B — Fri, 23 Sep 2005 10:54:05 +0000

Michael: Thanks. You had me worried! No need to apologise. These things are very tricky, and I am always willing (if not exactly happy!) to be corrected.

By: michael vassar

michael vassar — Fri, 23 Sep 2005 09:41:01 +0000

Dave B: My apologies, your analysis is correct. The female gets 3/4K-1/2 fitness points from each incestuous offspring, the male gets 3/4K-1/4 points.
The cost to the female is 2X the cost to the male, but both gain the same benefit.
Of course, paternal investment issues make incest an even worse deal.
Actually, I'm glad this issue has arisen. It makes me wonder about how genders are maintained in R-strategy organisms, and suggests to me that the information input via evolution into the structure of such organisms is greater than I had assumed.

By: David B

David B — Fri, 23 Sep 2005 03:21:05 +0000

…when I say ‘worthwhile for a male’ (or for a female) I mean of course worthwhile for the gene in question.

By: David B

David B — Fri, 23 Sep 2005 03:18:08 +0000

Michael: I don’t get your result.

Consider a gene in a female. Assume an outbred mating produces 2 offspring. The female’s expected number of ibd genes from outbred mating is 2×1/2 (the female’s own offspring) + 2×1/4 (her brother’s ofspring).

Now suppose she mates with her brother and has 2K offspring (where K is a fraction between 0 and 1 representing the cost of inbreeding). Her brother also has 2 outbred offspring. The female’s expected number of ibd genes passed on is 2Kx3/4 + 2×1/4 (since the brother’s outbred offspring are unaffected). The ‘gain’ from inbreeding is therefore [2Kx3/4 + 2x1/4] – [2x1/2 + 2x1/4] = 2[Kx3/4 - 1/2]. This will be positive if [Kx3/4 - 1/2] is greater than 0, which is satisfied if K is greater than 2/3.

Doing the equivalent calculation for a gene in the male, I get a break-even value for K of 1/3. So inbreeding is worthwhile for a male if the fitness cost is twice the breakeven level for a female.

Have I gone wrong somewhere?

By: Michael Vassar

Michael Vassar — Thu, 22 Sep 2005 19:27:32 +0000

That is what I’m saying, and it’s not a double count.
I knew the average IQ cost was 32 pts, so half being retarded is no surprise. Also, health problems of other sorts.
The costs have to be pretty obvious for every culture to notice, which is pretty much the case.

By: Darth Quixote

Darth Quixote — Thu, 22 Sep 2005 17:31:35 +0000

The cost of inbreeding is exceptionally high in humans. About half the offspring of father-daughter and brother-sister matings are mentally retarded. That is a lot more than I would have expected.

By: David B

David B — Thu, 22 Sep 2005 12:38:48 +0000

OK, I see your point.

In my post I didn't consider the costs of inbreeding, beyond, obviously, recognising that they exist. Are you saying that for the female the cost would have to be not just 2x but 4x as low as it would for a male to make incest worth while? I haven't really thought this aspect through. I would be suspicious of double-counting somewhere!

BTW, here's a Trinity: a woman mates with her half-brother, who is also her father, and she has a son. The child is son, nephew and brother to the woman.

By: michael vassar

michael vassar — Thu, 22 Sep 2005 07:36:41 +0000

The nephew is also a child, but the genes that make it a nephew are distinct from those that make it a child. The two can be treated seperately and additively.
As usual, looking at the gene level resolves confusion.

By: David B

David B — Thu, 22 Sep 2005 04:06:16 +0000

“The sister gains a low fitness nephew in exchange for some fitness in a child.”

- I’m not sure what you mean. Her child is also her nephew. I suppose with a bit of ingenuity we could get a Trinity!

By: elli

elli — Wed, 21 Sep 2005 08:00:44 +0000

well, check out my view on gender specific difficulties in scientific areas on
http://www.soulkin.com/index.php/2005/09/21/who-put-them-in-mathematics/

Enjoy!

By: michael vassar

michael vassar — Wed, 21 Sep 2005 07:59:54 +0000

The sister gains a low fitness nephew in exchange for some fitness in a child. The brother gains a low fitness child in exchange for some fitness in a nephew. For the female, the benefits of incest are 1/2 as large as for the male, and the costs are 2x as large.
Of course, if the brother’s number of children is to be unchanged, he must have no paternal investment, further lowering his expected gain and that of the sister, and possibly magnifying the loss.