Dawkins on Kin Selection: A Correction

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A while ago I posted on this subject here.

An attentive reader (Omri Tal) has pointed out an error in my analysis. The point concerns Dawkins’s ‘misunderstanding 10′: that ‘Individuals should tend to inbreed, simply because this brings extra close relatives into the world’. My analysis agreed with Dawkins that bringing close relatives into the world has no evolutionary advantage if these merely replace equal numbers of genes that would be passed on by mating with non-relatives. But I then argued that this would not always be the case:

The crucial point is therefore whether incestuous matings would simply replace outbred ones. Dawkins notes this question, but does not mention the likely asymmetry between males and females: females can usually only have a limited number of offspring, whereas males can have a practically unlimited number. A male who mates with his sister (or daughter) is therefore more likely to gain in the number of offspring than she is, and the balance between gain of inclusive fitness (measured by the increase in genes identical by descent) and loss of physiological fitness will be different for the two sexes. Suppose that a brother can mate with his sister and thereby gain 2 extra offspring for himself, while she gains none for herself (since the mating with her brother displaces an outbred one); a gene causing him to mate with his sister will therefore gain on average 2 x 3/4 copies, [2 x 1/2 copies of his own genes, plus 2 x 1/4 i.b.d. genes from her] whereas a gene causing her to mate with her brother will gain only 2 x 1/4 copies [since she would pass it on to half her offspring anyway, and it is only the possibility of extra copies from her brother that counts]. We might therefore expect males and females to evolve different attitudes towards incest, with females being much more resistant to it.

Omri Tal has pointed out that this overstates the difference between the position of males and females. I somehow overlooked the fact that if a sister mates with her brother, he ‘loses’ the nephews or nieces that his sister would otherwise produce by mating with an unrelated partner. This needs to be taken into account in calculating the effect on his inclusive fitness. The result of doing so is that his net ‘gain’ is only 2 x 1/2 copies, not 2 x 3/4. This is still greater than the ‘gain’ of his sister (2 x 1/4), but the difference is not as great as I suggested.

In more detail…


Assumptions

We assume that a variant gene (allele) predisposes its bearers to mate with their siblings (though they can still mate with non-relatives), whereas an individual who does not bear the gene mates only with non-relatives.

Each mating pair produce 2 offspring.

A male who mates with his sister also produces 2 offspring with unrelated mates, but a female who mates with her brother produces only 2 offspring in total. Her offspring with her brother therefore replace the offspring she would have had with unrelated males.

We consider two siblings who are not themselves inbred. They may each have inherited a copy of the gene from a recent ancestor, but cannot each have inherited 2 copies. (Allowing for inbreeding in the siblings themselves would just complicate matters further.)

With these assumptions, we can calculate the ‘gain’ from inbreeding compared with non-inbreeding. To give a ‘baseline’ position, suppose that for some reason (e.g. distance) the siblings cannot mate with each other, and therefore mate only with non-relatives. In this case a male who has the gene for inbreeding will on average pass on 2 x 1/2 copies to his offspring. His sister has a 1/2 chance of carrying the same gene, and therefore on average passes it on to 2 x 1/2 x 1/2 offspring. The total expected number of copies of the gene passed on is therefore 1.5. We can do the same calculations for a female who carries the gene. Since the situation is symmetrical with that of the male, the result is also 1.5.

Suppose now that a male carrying the gene mates with his sister. By assumption, he has 2 offspring with his sister and 2 offspring with a non-relative. He therefore passes on 2 x 1/2 + 2 x 3/4 = 2.5 copies of the gene to his offspring. But he no longer has the nephews or nieces he would have had if his sister had mated with an unrelated male. His net gain from inbreeding compared to not inbreeding is therefore simply 2.5 – 1.5 = 1.

The position of males and females is no longer symmetrical, so we need to calculate the position of females separately. Suppose a female carrying the gene mates with her brother. She produces 2 inbred offspring with on average 2 x 3/4 copies of the gene. She produces no outbred offspring, but by assumption her brother still produces 2 outbred offspring, with on average 2 x 1/4 copies of the gene, so in total 2 x 3/4 + 2 x 1/4 = 2 copies are passed on. The female’s ‘gain’ from inbreeding is therefore 2 – 1.5 = 0.5 copies. The ratio of male:female gain is therefore only 2:1, not 3:1 as I originally supposed.

11 Comments

  1. 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.

  2. 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!

  3. “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!

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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?

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

  10. 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.

  11. 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.

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