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February 28, 2006

Comments

Frank McGahon

I'm not clutching at straws, I'm trying to point out that there are more conditions for bipaternal twinning than just promiscuity so you can't just dispose of the improbability by assuming a promiscuous mother to be sufficient. And further that an alleged difference in promiscuity rates between Americans and Britons alone is enough to raise the estimate of 1 in 400 up to 1 in 100.

[Your last point seems to overlook the fact that it takes between 3 and 7 days for eggs to get down the Fallopian tube and implant in the uterus - which actually means that if 2 eggs are released during the fertile period of the same cycle, they will *usually* both be available for fertilisation.]

Granted, but then the sperm can survive up to five days so the first "instalment" still has a better chance of fertilising the second egg too than any subsequent "instalments".

Abiola

Frank,

Even the argument you're making still concedes too much to David B.; let's face it, if this mother were the tramp he's insinuating she most probably is, what are the odds that this guy with her wouldn't have heard about her reputation in all of two years, and why would he stick around once he'd done so, without any formal marriage ties to bind him to her?

Superfecundity and all the rest are red herrings: what's dubious is the very idea that we've got good reason to assume she's a slut who must have been with two men within days of each other, simply because she has two children whose appearance happens to be perfectly in keeping with what one might expect of two biracial parents.

João da Costa

"what's dubious is the very idea that we've got good reason to assume she's a slut who must have been with two men within days of each other, simply because she has two children whose appearance happens to be perfectly in keeping with what one might expect of two biracial parents."

... And the guy surely doesn't know anything about paternity tests!

dsquared

I don't see why the probability of twins who look like this should be so low. Abiola knows brothers and sisters who look as different from one another as these two girls, and so do I, so I can't believe that this is something that happens more rarely than once in ten thousand cases. So why can't we just multiply the frequency of two different-race-looking siblings by the frequency of fraternal twins and get the posterior probability of this event having happened? I would guess somewhere close to one birth in a million, which would suggest it would happen in the UK roughly every ten years, which is roughly what has happened. Is there really anything to explain here?

oh yeh, and of course, lots of English people have blonde hair when they are very young which darkens as they get older.

David B

All I have ever argued is that discordant paternity is prima facie more likely than Mendelian segregation in this case. This would still be true if the probability of discordant paternity is 'of the order if 1 in 1000', not 'of the order 1 in 100' as I suggested.

But just to recap my reasons for thinking 'of the order of 1 in 100' is reasonable:

a) we are assuming that DZ twins have in fact been born. Required is the probability that they have different fathers.

b) I assume that the probability that a woman in present-day Britain has 2 or more sexual partners during the same fertile period is around 1 in 20. I base this on the usual claims about the prevalence of 'false paternity', but I freely admit that these may be overstated.

c) given that a woman has 2 or more sexual partners during the same fertile period, the probability of discordant paternity is not negligible. I suggested 1 in 5, but I freely admit this is just hand-waving. But my critics should recognise that the probability can only be negligible if only 1 partner has any significant probability of fertilising *either* egg, and this is a very strong requirement. To illustrate the point, suppose one partner has a .9 chance of being the fertiliser of each egg, and there is one other partner with only a .1 chance. This still means that there is a .18 probability of discordant paternity. Or suppose one partner is certainly the fertiliser of one egg, and .9 likely to be the fertiliser of the other. The probability of discordant paternity is then .1, which is not negligible in this context.

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