Mixed Race Studies

Deconstructing Jaco: Genetic Heritage of an Afrikaner

Annals of Human Genetics
Volume 71, Issue 5 (September 2007)
pages 674–688
DOI: 10.1111/j.1469-1809.2007.00363.x

J. M. Greeff, Professor of Genetics
University of Pretoria

It is often assumed that Afrikaners stem from a small number of Dutch immigrants. As a result they should be genetically homogeneous, show founder effects and be rather inbred. By disentangling my own South African pedigree, that is on average 12 generations deep, I try to quantify the genetic heritage of an Afrikaner. As much as 6% of my genes have been contributed by slaves from Africa, Madagascar and India, and a woman from China. This figure compares well to other genetic and genealogical estimates. Seventy three percent of my lineages coalesce into common founders, and I am related in excess of 10 times to 20 founder ancestors (30 times to Willem Schalk van der Merwe). Significant founder effects are thus possible. The overrepresentation of certain founder ancestors is in part explained by the fact that they had more children. This is remarkable given that they lived more than 300 years (or 12 generations) ago. DECONSTRUCT, a new program for pedigree analysis, identified 125 common ancestors in my pedigree. However, these common ancestors are so distant from myself, paths of between 16 and 25 steps in length, that my inbreeding coefficient is not unusually high (f≈0.0019).

Introduction

‘After three centuries of evolution the population structure of the Afrikaners is still far from stable, and there does not appear to be much prospect of its ever attaining uniformity… The numerous and often mutually contradictory genetic statements frequently made about them can consequently all be simultaneously true. The Afrikaner is a product of miscegenation, the last ‘pure European’, pathologically inbred and a manifestation of hybrid vigour, all at the same time.’ (Nurse et al. 1985)

Afrikaners are often considered a rather homogeneous, probably rather inbred, white population of Dutch ancestry. Yet, as the above quotation illustrates, there are uncertainties about the genetic composition of Afrikaners. Due to Afrikaners’ high linkage disequilibrium, they are seen as a fruitful hunting ground for genes associated with disease (Hall et al. 2002). It is thus important that we have a clear appreciation of the Afrikaners’ genetic heritage. In what follows I address the questions of racial admixture, nationalities, founder effects and inbreeding in the Afrikaner. I do so in a novel way: rather than taking a sample of modern Afrikaners and genotyping them, I start with one living Afrikaner and trace most of his South African ancestors. In this way I cast a net into his past and hope to get an impression of what the genetic heritage of a typical Afrikaner may be…

…Given that genealogists could show that as much as 7% of Afrikaner genetic heritage is not of European descent (Heese, 1971), I find it curious that a system such as apartheid worked in South Africa. Seven percent is not a trivial amount, and is equivalent to having slightly more than a great-great-grandparent who was non-European. Since most of this non-European genetic heritage came into the Afrikaner population via female slaves, one would expect that as much as 14% of Afrikaner mitochondrial DNA is not even European. This female bias influx stems from the fact that emigrants were predominantly male, resulting in a male biased sex ratio of adults (Gouws, 1981).

Similarly, genetic studies also give support for this mixed racial ancestry. Working with a number of blood group gene frequencies, Botha & Pritchard (1972) estimated that beween 6–7% admixture between western European and slaves from Africa and the East, and/or Khoikhoi, would be required to explain the allele frequencies. Nurse et al. (1985) listed a number of alleles typical to the Khoisan and Bantu-speaking peoples that are found in low frequencies in Afrikaners (ABO system: A^bantu; glucose-6-phosphate dehydrogenase: Gd^A- and Gd^A; Rhesus: Rº; Haemoglobin C)…

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The Estimation of Admixture in Racial Hybrids

Annals of Human Genetics
Volume 35, Issue 1 (July 1971)
pages 9–17
DOI: 10.1111/j.1469-1809.1956.tb01373.x

Robert C. Elston, Professor & Chair, Distinguished University Professor
Case Western Reserve University

When a racial hybrid population has arisen from the intermarriage of two or more parental populations, a problem of interest is to determine what the relative contributions are from each parental population to the hybrid. Various distance measures have been proposed whereby, on the basis of several traits, the distance between the hybrid and each of the parental populations can be estimated: these distances are then sometimes interpreted, as a first approximation, as being inversely proportional to the parental contributions (Pollitzer, 1964). In the particular case that all the traits considered are discrete in nature and each is determined by alleles at a single locus (or system of tightly linked loci), it is possible to estimate the parental contributions more directly. It in the purpose of this paper to reconsider two main methods of doing this when the traits involved are determined by a random set of independently assorting loci.

Robers &. Hiorns (1962, 1965) proposed a least-squares solution to the problem, and Krieger et al. (1965) gave a maximum-likelihood solution. Both methods, as given by these authors, can be improved. We shall here restate both methods, using a common notation, and point out the improvements possible; furthermore, some resumes of using these method will also be presented, so that the methods may be compared empirically.

Least-Squares Method

Suppose ther are p (> 1) parental populations and for each we have gene frequency estimates of the same k genes.  Let X = (x_ij) be a k x p matrix, x_ij being the estimate of the ith gene frequency in the jth parental population. Let the k x 1 vector y have as its elements the corresponding gene frequency estimates in the hybrid population; and let the proportion of the hybrid population’s genes that come from the jth parental populatio be µ_ij the jth element of th p x 1 vector µ.  Then if the estimates are all exactly equal to the gene frequencies; and if the k chosen genes represent perfectly all the genes for which there has been no selection or drift, y-Xµ = 0, where 0 is the null vector. The least squares estimate of µ is that value of µ, m say, which minimizes the sum of squares of the diserepancies given by y-Xµ, i.e. which minimizes (y — Xµ)′(y — Xµ), where the prime denotes transposition. The least squares estimate is accordingly

m = (X′X)^-1 X′y provided X′X is non-singular.

Now it should be noted that the k genes fall into allelic systems, the sum of the gene frequencies for each syatem being unity in each population. Thus, for example, the gene frequency for M and N add to unity, and it is impossible to estimate a gene  frequency for M without at the same time implicitly estimating a gene frequency for N. When Roberts & Hiorns (1963) use (1) to obtain least squares estimates they eliminate one allele from each system, so that tho rows of X and y can no longer be grouped by system with the column totals for each group adding…

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