Interracial sex or Mendelian segregation?

Over at The Root Keith Adkins has a post, Sandra Laing: Born Black with White Parents:

I’m no geneticist or biologist, but it looks like Sandra is a product of an black South African and maybe a white Afrikaneer. I’m saying, it looks like somebody in her family was lying. The tests they used to prove her father’s paternity could have been faulty. And what about proving her mother’s maternity? Is it possible she was adopted? Is it possible Sandra’s mother was “getting love” from a undeniably-black man on the side? I’m not trying to throw salt on Laing’s game, I’m just not convinced the complete truth has been unearthed. I need to see more cases like this to be convinced these particular extremes are probable. Again, I know anything it could be true, but Laing’s story is extreme. If you’re in the Los Angeles Skin screens next month at the Pan African Film Festival before getting wider release.

The film which Adkins refers to is Skin, a biopic based on Sandra Laing’s life. A few years ago I thumbed through a book which detailed Laing’s tumultuous life, When She Was White: The True Story of a Family Divided By Race. Obviously the fact that a child who was obviously of non-white ancestry was born to conservative Afrikaner parents during the period of apartheid is a story which elicited some interest in South Africa at the time, and the “talk of the town” very literally. Sandra Laing’s paternity was under some debate, and it was a working assumption by many that the mother was unfaithful. Rather primitive blood tests did not reject that Laing’s putative father was her father, and one should probably modulate down the likelihood of a white woman having an affair with a black man in apartheid South Africa, and, keeping the child. How do we assess the probabilities of paternity vs. re-expression or recombination of genetic variants which code for African phenotypes within the Afrikaner population?

My previous posts about the fact that fraternal twins can appear to be of different races because of the way genes randomly recombine in offspring from parents shows that this isn’t impossible in principle. But in those cases the parents themselves were often of mixed ancestry (or at least one was). The farmer’s contention that “hybrids do not breed true” has empirical reality, and this manifests when mixed individuals mate with mixed & unmixed individuals. By “mixed” and “unmixed” I’m actually referring to a small subset of genes which code for physical appearance. For example, on the genes which control between population variation in skin color people of sub-Saharan ancestry and northern European ancestry are often disjoint in allele frequencies. In plain English these two populations express such different skin colors because their underlying genes which control this trait are totally different between populations. People whose parents are of these two populations (e.g., Barack Hussein Obama) can be expected to be heterozygous on the loci controlling this trait. So, for example, on SLC24A5 a biracial individual of African and European parentage will carry a variant which results in dark skin and another with results in light skin. Not surprisingly the this individual will express an intermediate phenotype. If they mate with someone of similar parentage, the outcome will be controlled by Mendelian expectations:

As you can see, on this locus some of the offspring are expected to be “more European” and some “more African,” while the largest number will reflect the parental combination. If you extrapolate this out to 4-6 loci you see that a full expected range may emerge. Across the total genome the ancestrally distinctive elements will not differ much between siblings because the error of sample variance decreases as you increase the number of “trials” (thinking of each gene as a trial).
But the Sandra Laing case is different. As judging by the pictures both parents are obviously white. One can easily imagine an African man and Laing’s mother producing a child who looks like she does. But two individuals who look white? First, it is important to remember that Afrikaners are an old settler population, most of their ancestors arrived in South Africa in the 18th century or earlier. Historically there are plenty of genealogical data which suggest an absorption of mixed-race individuals into the Afrikaner population, of Khoisan, Indian or Malay background (usually on the maternal lineage). This results in estimates of non-white ancestry among Afrikaners on the order of 5%. This is a small fraction, but not trivial. Remember that 5% is a population average, not the ancestry of any given individual. My memory of When She Was White is that Sandra Laing’s mother’s Coloured ancestry was confirmed through genealogical records. From that fact it seems plausible that Sandra Laing’s mother was more than 5% non-white, as she had more recent non-white ancestry than most Afrikaners, and so likely a greater quanta. On the other hand, her father’s background was less well known.
Is is possible that the Laings were substantially more than 5% non-white? After all, look at their pictures. Well, we know that individuals who are 25% African in ancestry can “pass” as white. As an example, to the left is Maya Rowell, who is 1/4 black. If 5% non-white ancestry is the expectation for Afrikaners, and ~50% are 0-5, then there is a “long tail” which extends out into domains of substantial non-white ancestry. I suspect this is plausible because there was admixture as late as the 19th century, as opposed to 2,000 years ago as for the Uyghurs. After ~100 generations the ancestry should be approximately equally distributed across the population, but far less so on the order of 5-15 generations.
Nevertheless, if both Laings are physically European in appearance, where exactly are those “African” genes which re-express in Sandra? To a first approximation something like skin color is additive & independent, in other words we can negelect dominance-recessive dynamics whereby genotypes imperfectly predict phenotype (heterozygotes and homozygotes may have the same phenotypic expression). But, I have noted that the arrow of dominance seems to mildly point to light skin being dominant over dark. This of course opens up the possibility for very light skinned parents having a darker skinned child than you would expect from simple assumptions of additivity. On the other hand, the normal assumption is that curly hair is dominat to straight, so the frizziness of Sandra’s hair is not easy to explain. I could bring up something like epistasis, gene X gene interactions which will produce outcomes outside of your linear extrapolations.
Let’s go back to numbers. Today there are ~3 million Afrikaners. If the mean non-white admixture is ~5%, the absolute number of Afrikaners with substantial non-white ancestry above 5% is large. The probably that any two of these Afrikaners will marry and have children is small, but, the probability that some of these combinations will occur within such a large population is high. In other words, in a population of millions where mean non-White ancestry is ~5% a substantial number in absolute terms of individuals with discernible ancestry will exist. The question here is what is the comparable likelihood of Sandra Laing’s mother having an affair with a black man, and, keeping the child, and, the putative father accepting the child as his, combined with the fact that both parents expressed society-typical racial attitudes in regards to apartheid? (confirmed later by their ostracism of their daughter when she entered into a relationship with a black man).
Here’s a photo of Sandra with her brother Adriaan. As you can see Adriaan has frizzy hair. Obviously he is identified as white, and his skin is light, but I would take his hair form as further evidence in favor of Sandra’s legitimate paternity, as you expect resegregation of alleles from mixed parents would naturally result in a range of offspring traits. On the other hand, her mother could also have been continuing her affair, though how she could continue this in the town of Piet Retief after Sandra’s birth god only knows.
Finally, we can settle this easily today. Sandra and her brothers are still alive. DNA fingerprinting could ascertain whether they are full-siblings or half-siblings. Ancestry kits could identify the proportion of non-European ancestry they have; one would expect if they were full-siblings and the offspring of their legal parents that they would all be mostly European, with a substantial non-European fraction. If Sandra’s father was a black man, she would be majority non-white, if one trusts the records which suggests significant non-white ancestry for her mother.
Note: Because I post on this topic now & then, I would like to add that I do get distressed emails from mixed-race women who are frantic to convince their significant other about paternity.