We describe a novel method for analysis of marker genotype data from admixed populations, based on a hybrid of Bayesian and frequentist approaches in which the posterior distribution is generated by Markov chain simulation and score tests are obtained from the missing-data likelihood. We analysed data on unrelated individuals from eight African-American populations, genotyped at ten marker loci of which two (FY and AT3) are linked (22 cM apart). Linkage between these two loci was detected by testing for association of ancestry conditional on parental admixture. The strength of this association was consistent with European gene flow into the African-American population between five and nine generations ago. To mimic the mapping of an unknown gene in an ‘affecteds- only’ analysis, a binary trait was constructed from the genotype at the AT3 locus and a score test was shown to detect linkage of this ‘trait’ with the FY locus. Mis-specification of the ancestry-specific allele frequencies – the probabilities of each allelic state given the ancestry of the allele – was detected at three of the ten marker loci. The methods described here have wide application to the analysis of data from admixed populations, allowing the effects of linkage and population structure (variation of admixture between individuals) to be distinguished. With more markers and a more complex statistical model, genes underlying ethnic differences in disease risk could be mapped by this approach.

In the presence of gametic phase disequilibrium and inbreeding, multiple locus genotype frequencies cannot be written solely in terms of identity by descent (IBD) probabilities. Following Cockerham & Weir (1973) we introduce the concept of ‘equivalence by descent’ (EBD), an extension of the concept of IBD to include non-allelic genes. Two genes are said to be EBD if they derive ultimately from the same founding gamete of a pedigree. Allelic genes that are EBD are also IBD. For two loci 11 EBD probabilities, the ‘J-coefficients,’ are required and for three loci 117 J-coefficients are required to write genotype probabilities. It is shown how the 117 J-coefficients for three loci can be reduced to a basic set of 37. Computer programs, written in the algebraic programming language, MAPLE™, are described which are capable of calculating the two- and three-locus J-coefficients for any pedigree, subject only to size limitations. The MAPLE™ packages are available from the author upon request.

For diseases that do not follow a clear Mendelian pattern of inheritance nonparametric tests applied to affected sibs have been shown to be robust to the inherent uncertainty about the precise underlying genetic model. It is known that the weights optimizing the power of tests using IBD alleles shared by affected sib pairs or triples depend on the underlying model. We show how efficiency robustness techniques, used in other areas of statistics, provide a systematic approach for constructing a robust linear combination of the statistics that are optimal for the individual members of a family of plausible genetic models. The method depends on the correlation matrix of the optimal tests as these correlations reflect how different the models are. When the minimal correlation is less than 0.5, an alternate robust procedure is proposed. The methods apply to combining data from sibships of different sizes.

In recent years variance components models have been developed for localising genes that contribute to human quantitative variation. In typical applications one assumes a multivariate normal model for phenotypes and estimates model parameters by maximum likelihood. For the joint analysis of several correlated phenotypes, however, finding the maximum likelihood estimates for an appropriate multivariate normal model can be a difficult computational task due to complex constraints among the model parameters. We propose an algorithm for computing maximum likelihood estimates in a multi-phenotype variance components linkage model that readily accommodates these parameter constraints. Data simulated for Genetic Analysis Workshop 10 are used to demonstrate the potential increase in power to detect linkage that can be obtained if correlated phenotypes are analysed jointly rather than individually.

Ann. Hum. Genet. (1999), 63, 473–482

Correction

The authors wish to add the following correction to this paper:

The genomic organization of the human organic cation transporter (hOCT1/SLC22A1) has recently been described by us to consist of 7 exons [Molecular cloning, functional characterization and genomic organization of four alternatively spliced isoforms of the human organic cation transporter 1(hOCT1/SLC22A1); Ann. Hum. Genet. 63: 473–482]. A reexamination revealed 11 exons instead of 7. The mistake occurred through cDNA contamination. The corrected gene structure of the hOCT1 gene is available at EMBL under the following accession numbers:

AJ243995 (Exon 1), AJ243996 (Exon 2), AJ276051 (Exon 3), AJ276052 (Exon 4), AJ276053 (Exon 5 and 6), AJ245460 (Exon 7), AJ243998 (Exon 8), AJ243999 (Exon 9 and 10) and AJ244000 (Exon 11).

The growth factor independent 1 (GFI1) gene encodes a zinc finger protein which acts as a transcriptional repressor and confers growth factor independence on tumor cells, as suggested by the study of its mouse ortholog, Gfi1. We previously isolated the human GFI1 gene but no information about the structure and location of the promotor of this gene has been reported. In this study we have cloned and characterized the human GFI1 promoter. The nucleotide sequence of the promoter region is GC-rich and does not contain a typical TATA or CAAT box. Several Sp1 sites are present and computer predictions indicate that either of the two Sp1 sites might serve as the sites for transcription initiation. Analysis of various lengths of the promoter region using the luciferase reporter assay identifies a functional promoter that is active in NIH3T3 cells. The strongest activity lies within a region 312–602 basepairs upstream from the translation start site.

Spielman et al. (1993) popularized the transmission/disequilibrium test (TDT) to test for linkage between disease and marker loci that show a population association. Several authors have proposed extensions to the TDT for multi-allelic markers. Many of these approaches exhibit a ‘swamping’ effect in which a marker with a strong effect is not detected by a global test that includes many markers with no effect. To avoid this effect, Schaid (1996) proposed using the maximum of the bi-allelic TDT statistics computed for each allele versus all others combined. The maximal TDT statistic, however, no longer follows a chi-square distribution. Here, a refinement to Bonferroni's correction for multiple testing provided by Worsley (1982) based on maximal spanning trees is applied to calculate accurate upper bounds for the type I error and p-values for the maximal TDT. In addition, an accurate lower Bonferroni bound is applied to calculate power. This approach does not require any simulation-based analysis and is less conservative than the standard Bonferroni correction. The bounds are given for both the exact probability calculations and for those based on the normal approximation. The results are assessed through simulations.

It is well known that the TDT proposed by Spielman et al. (1993) is potentially anti-conservative if families with one missing parental genotype are included (Curtis & Sham, 1995). We now bring attention to another situation that could give rise to an inflated rate of false positive results. This occurs when families in which the affected offspring and both parents have the same heterozygous genotype are excluded. If the heterozygous genotype is denoted as AB, then it is clear that one parent must have transmitted allele A and the other allele B. The standard TDT procedure is to increment the counts for transmissions of both A and B by one. It may seem reasonable to disregard such trios because it is ambiguous which parent has transmitted which allele. Although the resulting test statistic would retain all the information concerning preferential transmission of alleles, it can be shown that referring it to a χ2 distribution would lead to an increased type I error rate (see Appendix A).

Editorial Note

This book review arrived here at the beginning of this year with a very apologetic note from the author, Bill Hamilton, about the long delay in producing the review and its ‘rambling essay format’. Sadly, Hamilton died just a few weeks later from complications following malarial infection. Several tributes have been published, such as Science (2000), 287, 2438, and we continue the tributes with a final unedited manuscript from the hand of this unique, colourful and idiosyncratic evolutionary theorist.

Dysgenics: Genetic Deterioration in Modern Populations. Human Evolution, Behaviour, and Intelligence Series. By R. LYNN (Series Editor: S. ITZKOFF). Westport, Connecticut and London: Praeger. 1996. Pp. 237. £47.50 (hardback).

In a sense a dominance hierarchy has only one satisfied individual – she or he at the top. If the hierarchy is bottom-numerous rather than linear, as is the case with most human hierarchies, it is all the more true that the vast majority of people are dissatisfied, wishing they were higher up, a thought which provides a basic reason why democracies (and especially, within democracies, such institutions as their state school systems) have to be unstable. We see a wobbly pyramid, and particularly within that pyramid we see certain side stairs all human examples have by which demagogues skip up a level or two so as to shout down to the restless base that the whole structure is somehow ‘wrong’. Under a different system, the demagogue shouts, ‘You could be higher too’.