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January 15, 2005

Interracial Marriage: Salter's fallacy

English people and Bantus have different frequencies of many genes. Suppose for simplicity that all English people are homozygous for a certain allele at a given locus, while all Bantus are homozygous for a different allele. An English man who marries an English woman will therefore have children with two ‘English’ genes each at the relevant locus. If on the other hand he marries a Bantu woman, his children will only have one ‘English’ gene each.

Therefore an English man who wishes to maximise the number and frequency of ‘English’ genes in the next generation should marry an English woman and not a Bantu.

Discuss.

The fallacy is that the argument considers only the offspring of the man, and not the other people affected by his choice. Let us assume for simplicity that there are equal numbers of English and Bantus, that all people marry, that all marriages are strictly monogamous, and that all couples have two children. (Relaxing these assumptions would just introduce irrelevant complications - the outcome would be the same, unless we introduce arbitrary assumptions about differential mating success of English and Bantus, or differential fitness of different mating combinations.)

On this basis, if an English man marries an English woman, 2 English people between them have 2 children with 2 ’English’ genes each. 2 English people therefore transmit in total 4 ’English’ genes to the next generation, giving 4/2 = 2 ‘English‘ genes transmitted per English person.

If on the other hand an English man marries a Bantu, we have to consider what happens to the English woman he would have married otherwise.

Suppose she marries a Bantu man, in which case 2 English people in total have 4 children with 1 ’English’ gene each. 2 English people therefore transmit in total 4 ’English’ genes to the next generation, giving 4/2 = 2 ‘English‘ genes transmitted per English person.

Alternatively she marries an English man, in which case 3 English people (one English couple and one English man married to a Bantu) in total have 4 children. 2 of the children have 1 ’English’ gene each, and 2 have 2 ‘English‘ genes each. 3 English people therefore transmit in total 6 ’English’ genes to the next generation, giving 6/3 = 2 ‘English‘ genes transmitted per English person.

Of course, if she does marry an English man, then some other English woman is left ‘spare’. Ultimately, given neutral assumptions, if an English man marries a Bantu woman, then an English woman somewhere along the line is constrained to marry a Bantu man, which gives us the case analysed in the last paragraph but one.

In each case the number of ’English’ genes transmitted per English person is the same. The number and frequency of English (and for that matter Bantu) genes in the population is therefore unaffected by the marital choices of the parents. Indeed, it hardly needs any examples to prove the point, since this is just a case of assortative mating, and assortative mating does not in itself affect gene frequencies in the population [Note 1].

It might seem unlikely that anyone would actually commit the fallacy described above, but Frank Salter, in his book On Genetic Interests (pp.260-264), certainly comes very close. In discussing marriage between different ethnic groups, he points out that partners from the same ethnic group will share some of the same distinctive genes, as a result of distant common ancestry, and that their children will therefore be more closely related to them than if they married someone from another ethnic group. Using the English/Bantu example, he calculates that endogamy (marriage within the group) increases kinship between parent and children by 92 percent as compared with exogamy. I have no strong disagreement with this part of the argument (though as I pointed out here, distant shared ancestry is not equivalent to recent ancestry for the purposes of kin selection). But Salter goes on to argue that ’choosing an English spouse over a Bantu one yields a fitness gain of 92 percent… The same applies in reverse order, so that a Bantu who chooses another Bantu instead of someone of English ethnicity has 92 percent more of his or her genes in offspring as a result. It is almost equivalent to having twice the number of children with an English spouse. Thus assortative mating can have large fitness benefits, the largest derived from choosing mates within geographic races.’

I think that anyone reading this, in the absence of any clear explanation to the contrary, would reasonably interpret Salter as concluding that interracial marriage reduces the aggregate fitness of the races concerned, or, what comes to the same thing, the overall frequency of their distinctive genes within the combined population. If it doesn’t, why worry? But for the reasons I have given, this conclusion would be quite fallacious. Either Salter has overlooked the fallacy, or he is aware of it but uses a misleading form of words. I think it is more likely that he has simply overlooked it, because he goes on to consider, in a confused way, the possible counter-advantages of exogamy, but nothing in this further discussion suggests he has grasped the point that population gene frequencies are not (in general) affected by assortative mating. He persists in assuming, fallaciously, that mating within an ethnic group in itself produces a fitness benefit. There is less excuse for the error because it is just another form of ‘Misunderstanding 10’ in Dawkins’s ’12 Misunderstandings of Kin Selection’, which I discussed here.

It may still be said, in a last-ditch defence of Salter, that an English man who marries a Bantu woman reduces his own aggregate ’genetic interest’, as defined in Salter’s theory, and therefore in some sense suffers a loss of fitness. If this does follow from the theory, so much the worse for the theory. But I am not sure that it does follow from the theory. ’Genetic interest‘, if interpreted consistently with Salter‘s other principles, can be either negative or positive. If you are positively related to someone in a given population, he increases your aggregate genetic interest in that population; if he is negatively related to you, he must therefore reduce it. In Salter’s own treatment of issues such as immigration, negative as well as positive relatedness is certainly taken into account: for example, he says ’it would appear to be more adaptive for an Englishman to risk life or property resisting the immigration of two Bantu immigrants to England than his taking the same risk to rescue one of his own children from drowning’ (p.67). By the same token, an English man enhances his genetic interest just as much by reducing the reproduction of pure Bantus as by increasing the reproduction of English people. Salter can’t have it both ways, counting negative interests when it suits him but ignoring them when it doesn’t.

Within the combined English-Bantu population, an English man is positively related to other English people, negatively related to Bantus, and has an intermediate relatedness to mixed English-Bantu people. If he marries a Bantu woman, he produces mixed offspring who are less closely related to him than English offspring would have been. (In my simplified example the relatedness is actually zero.) By marrying a Bantu woman he also constrains some English woman to marry a Bantu man, producing two more mixed offspring. But at the same time he constrains two Bantus (i.e. his own Bantu wife and the Bantu husband of the English woman) to marry English people, thus producing mixed rather than pure Bantu offspring. The overall reckoning is that four mixed offspring are produced instead of two pure English and two pure Bantu offspring. But the English man’s aggregate genetic interest is unaffected, since he is substituting one equivalent net outcome for another. The same conclusion holds, by a more technical route, if we use Salter’s own algebraic formulae. [Note 2] Salter’s fundamental error is that he considers only the immediate effect of a mating choice on the offspring of the person making the choice, while ignoring its repercussions elsewhere in the system. In particular, in considering the effect of marriage between an English man and a Bantu woman he fails to allow for the fitness benefit to the English man (from the point of view of his aggregate genetic interest) of preventing the birth of pure Bantu offspring. This must be an error even by Salter’s own principles.

I will return to the subject of Salter’s ‘ethnic genetic interests’ in general, but I thought it would be worth getting this more specific point out of the way first. It is quite an important one, as it invalidates most of what he says about inter-ethnic marriage.


Note 1: as usually defined, assortative mating is a tendency for individuals to mate more frequently with phenotypically similar individuals than would be expected in random mating. For example, Dictionary of Genetics, ed. King and Stansfield, says: ‘Assortative mating: sexual reproduction in which the pairing of male and female is not random, but involves a tendency for males of a particular kind to breed with females of a particular kind’. Mating may be either positively or negatively assortative (the latter tendency, ‘like mating with unlike‘, also being known as ’disassortative’ mating). Neither process in itself necessarily leads to any difference in mating success or the number of offspring, and the neutral assumption is that all phenotypes have the same average mating success. On this assumption any particular gene in any individual has the same probability of entering successful gametes, and the frequency of any given allele in the population is unaffected, though there will be departures from Hardy-Weinberg equilibrium in the proportions of homozygotes, and from linkage equilibrium between loci, if the genes concerned are implicated in the phenotypic resemblance . Of course, it is possible to imagine some circumstances in which assortative mating would affect mating success, for example, if one phenotype is very rare. Unless all phenotypes have the same frequency, it is also impossible to have perfectly disassortative mating without increasing the frequency of the rarer types. But there is nothing to suggest that Salter has such special cases in mind.

Note 2: we need to consider the effects of two alternative scenarios. In scenario A, an English man marries an English woman, and a Bantu man marries a Bantu woman. In scenario B, an English man marries a Bantu woman, and in consequence a Bantu man and an English woman somewhere along the line are constrained to marry each other. Using Salter’s formulae for relatedness (technically ’kinship’ rather than ’relatedness’, to be precise), in case A the English man has 2 offspring who are related to him by ¼ + ¾FST, while the Bantu couple have 2 offspring who are related to the English man by minus FST, where FST is the ‘coefficient of ethnic kinship‘ within each ethnic group as contrasted with the other. (See the Appendix to Salter’s book by Henry Harpending for an explanation and derivation of these formulae. Harpending shows that FST, which is usually a measure of genetic distance between populations, can also be interpreted as a measure of positive kinship between people in the same population, or negative kinship between people in different populations.) The overall effect of the first scenario is therefore to increase the English man’s aggregate genetic interest by 2(¼ + ¾FST) -2FST = ½(1 - FST). In case B, the English man and his Bantu wife have 2 offspring who are related to him by ¼ - ¼FST, while the Bantu man and the English woman (who we assume is unrelated to the English man except as a co-ethnic) have 2 offspring whose relatedness to the English man is ½FST - ½FST = 0. The overall effect of this scenario is to increase the English man’s aggregate genetic interest by 2(¼ - ¼FST) + 2(0) = ½(1 - FST). Thus the addition to the English man’s genetic interest is the same, i.e. ½(1 - FST), whichever choice he makes. In my simplified example, with English and Bantus 100% homozygous for different alleles, FST = 1, so the net effect on the English man’s genetic interest would be ½(1 - 1) = 0 for either option.

Related posts:
Ethnic Genetic Interests: Part 2
Ethnic Genetic Interests
Limits to Hamiltons Rule
Dawkins on Kin Selection
On Genetic Interests
Dissin' Dawkins
Green Beard and Ethnic Nepotism

Posted by David B at 04:32 AM