Wednesday, September 21, 2005

Dawkins on Kin Selection: A Correction   posted by DavidB @ 9/21/2005 02:12:00 AM

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...


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.