Twelve SNPs spanning 4.3 kb (Figure 1) were genotyped in 212 Gambian and 84 Malawian adults with no missing data. Allele frequencies for each SNP are listed in Table 1. The Gambian genotypic data had 354/2,544 (14%) sites where gametic phase was unknown, and the Malawian data had 188/1,008 (19%) sites where gametic phase was unknown. Where available, genotypes from offspring of the adults were used to phase these data (using the program PHAMILY), which reduced the number to 127/2,544 (5%) phase-unknown sites in the Gambian dataset and 75/1,008 (7%) phase-unknown sites in the Malawian dataset. The data were pooled and the program PHASE was then used to assign the remaining phase-unknown sites. After inferring haplotypes, only 6/2,544 (0.2%) phase assignments were less than 90% certain in the Gambian dataset, and only 2/1,008 (0.2%) phase assignments were less than 90% certain in the Malawian dataset. All other assignments (121/2,544 and 73/1,008) were greater than 90% certain. These 424 Gambian haplotypes and 168 Malawian haplotypes (Table 2) were the basis of subsequent analyses reported.

In the Gambian sample, we observed 24 different haplotypes, and the distribution was dominated by one major haplotype (37.0%) and two others (16.7%, 16.5%) (Table 2, Figure 2). Thirteen haplotypes of low frequency made up another 28%, and 2% of alleles were singletons (haplotypes observed only once in the sample). The gene diversity, or probability that two haplotypes chosen at random from the sample are different, was 0.80 (standard deviation (SD) 0.01). There is one nonrecombinant haplotype that is found only in The Gambia (8).

The Malawian sample included 21 different haplotypes, 13 of which were shared with the Gambian population (Table 2, Figure 2). The predominant haplotype in Malawi was not as common, at 25.0%, and there were three other haplotypes with frequencies greater than 10% (23.2%, 16.1% and 10.1%). Haplotype 9, bearing the -1031C and -863A alleles, is much more common in Malawi than in The Gambia, at 16.1% versus 5.4%. Four percent of the Malawian alleles were present as singletons. The gene diversity in Malawi was slightly greater at 0.85 (SD 0.01).

Wright's F statistic reveals differences between populations by calculating the reduction in heterozygosity that is expected after random mating between the two populations. For the Gambian and Malawian populations the F_ST = 0.021. Permutations of the data under a null hypothesis of no differences between the populations gives a probability of 0.0001. An exact test of population differentiation finds the observed haplotype distributions to be a poor fit of a model of random mating between the Gambian and Malawian samples, with a probability less than 10^-5.

Results of the four-gamete test on pairs of SNPs in each population reveal that in The Gambia, 19/66 (29%) pairs of loci have all four possible haplotypes present; while in Malawi, 15/55 (27%) pairs of SNPs have all four haplotypes present (Figure 3). Some high-frequency (and presumably older) SNPs show evidence of recombination in both populations (TNF-3025, TNF-1031). In The Gambia, the TNF-308 SNP shows evidence of recombination with six other SNPs. In Malawi, the TNF-244 shows evidence of recombination with many other SNPs. Interestingly, the TNF-863 SNP, of relatively high frequency in Malawi, shows no evidence of recombination with any other SNPs in the Malawian sample. Recombinant haplotypes of frequency greater than 1% are represented in Figure 2 with dotted lines. Although the branching structure of the TNF genealogy is similar in both populations, there are unique recombination events that have differentiated the two samples (haplotypes 17, 20 and 26). In Malawi, there appear to be more recombinant haplotypes of greater than 1% frequency.

Consistent with the evidence for recombination, linkage disequilibrium is variable across the TNF locus (Figure 4c,4d) and generally low. Values of pairwise linkage disequilibrium, r², are different between the two populations, though well correlated (r = 0.83). In The Gambia, 80% of SNP pairs have the minor alleles in the repulsion phase, while in Malawi, 65% of SNP pairs are in the repulsion phase. Most of the SNP pairs in the repulsion phase have very low linkage disequilibrium (r² = 0). There are six pairs of SNPs that are in the coupling phase in the Malawian sample, but are in the repulsion phase in The Gambian sample, reversing the allelic associations. Most of these occasions involve the TNF-244A allele, which is found on only one haplotype in the Gambia (in phase with the TNF-3025G allele), but on five different haplotypes in Malawi.

Using Equation (2) (see Materials and methods) we calculate the apparent relative risk at one marker given a relative risk of 10 at a second marker for all pairs of markers. As an example, we assign a relative risk of 10 to the TNF-376A allele (this is the relative risk of the A allele compared to the G allele) and calculate the relative risks at all other SNPs in the TNF gene using the haplotype frequencies from The Gambia (Figure 5). Log₁₀ of the relative risk is plotted on the y-axis, so values above the x-axis correspond to disease risk while values below the x-axis correspond to disease protection. We find that the relative risk varies greatly across the TNF gene region. The three SNPs that are in maximum positive linkage disequilibrium (D' = 1) with TNF-376A show relative risks of 2.2, 3.3, and 2.2 when TNF-376A gives a relative risk of 10. The remaining eight SNPs in the TNF gene would have a relative risk between 0.8 and 0.9 when the relative risk at TNF-376A is 10 (Figure 4).

Data for all pairs of markers are given in Figure 4a,4b. Hypothetical disease alleles are given along the x-axis, and marker alleles are given on the y-axis. Each cell indicates the apparent relative risk (R) of a marker on the y-axis when the hypothetical disease allele indicated on the x-axis has a relative risk of 10. Using an arbitrary cutoff of 0.5 <R < 2.0 (indicated by blue color), some markers perform poorly: for example in The Gambia TNF-308 can only detect TNF-3025 (R = 2.9). Interestingly, if the TNF-308 SNP were a disease allele, most of the other SNPs in TNF would show a moderate protective effect. TNF-1031 is good at detecting associations at seven other SNPs. In Malawi, the pattern of association efficiency is different, and generally stronger. Most hypothetical disease SNPs in Malawi would be detectable by other SNPs in TNF, with the exception of TNF+476 and TNF-1073 which have very low frequency and little prospect of being detected by other markers.

To illustrate the relationship between the association efficiency parameter and measures of linkage disequilibrium, we plot the log₁₀ of relative risk for all pairs of SNPs (when one SNP is assigned a relative risk of 10) against r² (Figure 6a,6b). Above the x-axis, r² appears to be correlated with the association efficiency parameter (correlation coefficients of r = 0.77 in The Gambia, and r = 0.91 in Malawi). Below the x-axis, where the marker SNP gives an apparently protective effect, the correlation is not as strong (r = -0.61 in The Gambia, r = -0.60 in Malawi). In this situation where minor alleles are in the repulsion phase, the values for r² remain low even when association efficiency parameter shows a strong protective effect.

The association efficiency parameter is correlated with D, the un-normalized linkage disequilibrium parameter (Figure 6c,6d). When the absolute value of D is great, the association efficiency tends to be high; however, many SNP pairs also have high association efficiency even when the absolute value of D is low.

When we plot the association efficiency parameter against the normalized disequilibrium parameter, D', we see a strong positive correlation: r = 0.89 in the Gambia and r = 0.91 in Malawi (Figure 6e,6f). Linkage disequilibrium is necessary to detect association; however, it is not sufficient. Despite D' = 1.0, some pairs of SNPs are poor markers of each other, showing relative risks between 0.5 and 2.0 when the linked hypothetical disease allele gives a relative risk of 10.

Entropy (E), a measure of haplotypic diversity, was calculated for the full 12-SNP haplotypes in each population (Equation (4) in Materials and methods). In the Gambian sample, E = 2.95; in the Malawian sample, E = 3.23. To determine if a subset of these 12 SNPs could account for most of the haplotypic diversity in these samples, we calculated entropy for all possible subsets of SNPs, increasing the number of SNPs in a subset from 1 to 12. In Figure 7 we plot the subsets of markers with maximum entropy. We begin with a single SNP, and with each additional SNP we include, the entropy increases. The entropy plateaus when the additional markers contribute little additional information. To account for 95% of the haplotypic diversity of TNF, one must genotype 8 of 12 SNPs in The Gambian sample (in order of decreasing informativeness): -3025, -308, 851, -1031, -857, 467, -244, -238; and type 7 SNPs in the Malawian sample: -3025, -1031, 851, -308, 1304, -244, -1073.

Healthy unrelated adults were recruited in Banjul, The Gambia and in Blantyre, Malawi. All were parents of children who presented to hospital with severe malaria. All subjects gave informed consent and the study was approved by the Gambia Government/Medical Research Council Joint Ethical Committee and the College of Medicine Research Committee of the University of Malawi.

After excluding erroneous pedigrees, the 187 parent-child pairs plus 45 other adults comprised the Gambian sample (a total of 212 adults), and 70 parent-child pairs plus 14 other adults (a total of 84 adults) comprised the Malawian sample. We also studied DNA from two chimpanzees, one gorilla and two orang utans.

In a previous study, we described the nucleotide diversity of the TNF locus in 36 healthy, unrelated Gambian adults 13. There we identified 11 SNPs by forward and reverse sequencing of the entire TNF gene from -1,389 bp relative to the start of transcription to +3,004 bp on 72 chromosomes. Here we have genotyped the 11 SNPs identified in TNF, plus one SNP in the neighboring gene, LTα, in a sample of 212 Gambian and 84 Malawian adults. The amplification refractory mutation system PCR (ARMS-PCR) was used to genotype the polymorphisms identified by sequencing. Methods are as previously described 13. The accuracy of the ARMS-PCR method was tested on sequenced individuals before extending it to DNA samples of unknown genotype.

For most of these adults, genotypes were available from their children, raising the question of how to construct haplotypes most efficiently from a dataset where pedigree information is available for some but not all individuals. We developed a program PHAMILY, which uses information from two-generation pedigrees to construct parental haplotypes at all unambiguous sites. These partial haplotypes of unambiguous sites serve as input for PHASE 2425, which uses the Stephens-Donnelly method of haplotype construction to assign the remaining phase-unknown sites among the unrelated parents. The two study populations were pooled before haplotype construction; after haplotype construction, individuals were assigned to their original populations on the basis of their sample identifiers.

To assess the ability of one marker to detect a given disease association at a second marker, we derived a measure we call association efficiency, which is the relative risk at one SNP by virtue of its association with a second SNP. Consider a disease-modifying SNP A that is in linkage disequilibrium with a neighboring nonfunctional SNP B. We define R_A as the relative risk associated with allele A₂ compared to allele A₁. Under a multiplicative mode of inheritance, the frequencies of the different haplotypes (A₁, A₁B₂, A₂B₁, A₂B₂) found in diseased individuals is expected to be ƒ₁₁, ƒ₁₂, R_Aƒ₂₁, and R_Aƒ₂₂ (see Table 3). Given the risk associated with A₂ and the frequency of each haplotype, we can derive the frequency of allele B₂ among diseased individuals (q₂').

The frequency of allele B₂ in the general population is defined as q₂. Thus, in a case-control study where diseased individuals are compared to individuals drawn from the general population, we would obtain an odds ratio for allele B₂ of

This odds ratio provides an approximation of the relative risk that is associated with the non-functional allele B₂ by virtue of its association with the disease allele A₂.

When locus B is considered to be the disease-modifying locus, with R_B as the relative risk associated with allele B₂ compared to B₁, it can be shown that the relative risk at locus A is

In this paper, we consider the possibility that the rarer allele gives a true relative risk of 10 for a given disease, and calculate the apparent relative risk at all other loci. We do this for all pairs of loci. Because this property does not commute (that is, the apparent relative risk at locus B given a true relative risk of 10 at locus A is not necessarily equal to the apparent relative risk at locus A given a true relative risk of 10 at locus B) we calculate two values for each pair of SNPs.

A measure of haplotypic diversity, entropy (E), was calculated using

where p_i is the frequency of the ith haplotype, and k is the number of unique haplotypes in the sample. Entropy is maximized when all haplotypes have the same frequency. We developed an algorithim that chooses SNPs, first individually, then in multi-SNP haplotypes, that maximize entropy 35. Thus we can define a subset of SNPs that represent the greatest proportion of the full 12-SNP haplotypic diversity. This method provides for the selection of optimal haplotype-tagging SNPs even in the absence of a clear haplotypic block structure.