The decision on where to place the cutoff to separate ‘‘high’’ eigenmodes from ‘‘low’’ eigenmodes is made using the Tracy- Widom distribution (see [21] for a detailed description and references to the literature), which provides the basis for the null hypothesis. Consider a matrix M of dimension N x N SNP samples (where N and N represent the number of SNPs and the SNP samples number of samples in the original data). Assume that the entries M are independent standard Normal Gaussian distributed ij variables for each SNP location. The product of M and its transpose MT represents the correlation matrix of SNP-SNP correlations which would be obtained by chance. The distribution of eigenvalues of MMT is the Tracy-Widom distribution which represents the null-probability to get a high eigenvalue by chance in data without population structure. We use a simple method (chosen to have a p-value,0.05) to find the cutoff x in eigenvalue to separate population structure from functional polymorphisms. We identify the highest k eigenvalues in the real data that represent more than a fraction f= 0.95 of the variation in the data as those representing population structure [21]. x is easily obtained by first finding k by solving: f= [S k l ]/N where the i=1 i SNP eigenvalues l are sorted from highest to lowest value. The value of i x is then obtained from: x= (l +l )/2. k k+1

It is known that population structure can introduce artificial correlations between SNPs and phenotypes. The classic example is SNPs in the lactase gene that spuriously correlates with the height phenotype. These spurious correlations can be easily understood by considering a simple example: imagine one homogeneous population that splits into two. Each of these populations evolves independently and develops a set of SNPs (markers) that clearly differentiate them. All these SNPs appeared as linked, because of the common ancestry of these populations. If, for any reason, one population has a different phenotype (height, disease, longevity) than the other, all these SNPs will correlate with the phenotype. However, this correlation does not mean that these SNPs are functional with respect to the phenotype. In fact, the association is merely due to the population structure of the data. It does not mean that the population does not have the distinguishing property as this is undisputable. What it means is that the association between the SNP and the phenotype is due to the appearance of the phenotype (for an unknown reason) after split

Results

Table S2 shows the number of samples in each haplogroup in of the 8 phenotypes. For statistical relevance, we have limited

haplogroup D4a. The rest of the SNPs are enriched at lower values and could explain the presence of a weaker longevity signal among the rest of the D4 haplogroups.

the haplogroup granularity to maintain at least 5 samples in each phenotype. Calculation of the L score showed that only H haplogroup D4a was enriched for longevity. Relaxing the p-value cutoff showed that the longevity signal is diffused among D4 haplogroups, becoming strongest in D4a. We found 1386 maximal patterns of mutations shared by at least 5 samples. For each pattern, we computed the L score and its q-value as described P above. We identified 124 ‘‘positive’’ patterns which were enriched in semi-supercentenarians compared to healthy Normals. We found no ‘‘deleterious’’ patterns which were depleted in semi- supercentenarians compared to healthy normals. The L scores for P all patterns are shown in Figure 2 and the enriched patterns are those shown in red.

Table 1 shows a summary of the SNPs from the heat map. Again, we note that there are four strong SNPs (3206T, 8473C, 14979C and 10410C which are markers for D4a. There are also 5 non-synonymous mutations: 5178A, 8414T, 8701G, 10398G and 14979C. The first 3 polymorphisms are outside haplogroup D4a (specifically, they are defining mutations for D, D4, M resp.) while 14979C is D4a specific.

One way to identify the possible functional basis of the mtDNA enrichment of D4a in longevity is to look for autosomal polymorphisms that are also enriched in D4a over other haplogroups. If SNP data on autosomes for our samples were available, we could look such enrichments directly. However, in the absence of such data, we looked in the HapMap database [5] for polymorphisms on autosomes that were significantly enriched in D4a. Unfortunately, the SNP coverage in HapMap was too sparse to even identify the D4a haplogroup within the 44 Japanese samples in the D clade in the HapMap data. The best we could do was to see if these 44 D clade samples as a group had any significant autosomal enrichment. Such an analysis (of the HapMap D clade samples taken together as a single group) identified a number of enriched autosomal polymorphisms. The top 26 by p-value are shown in Table 2. One of these polymorphisms, on chr7:17152350, was within an exonic region and was simultaneously non-synonymous. Several others were in intronic, promoter and non-coding regions. In addition to the SNPs shown in Table 2, we found three other non-synonymous coding sites that were also enriched in D but at lower p values: chr3:122690866(H/R) in gene POLQ (DNA polymerase) with a p-value = 0.0004 and chr17:53939507(S/G), chr17:53940871(L/ V) both in gene MTMR4 with p-values 0.0017 and 0.0024. MTMR4 is a dephosphorylation enzyme and exerts an effect on EGF (epidermal growth factor) receptor trafficking and degrada-

Figure 3 shows the mtSNPs enriched in the three datasets (centenarians, semi-supercentenarians and combined) compared to healthy normals using the score L at q,0.05. Once again, we S see a significant enrichment in several mtSNPs associated with the D4a haplogroup [6,7,12]. The top 4 enriched loci are 3206T, 8473C, 14979C and 10410C. The first three are defining markers for D4a. SNP 10410C is enriched (80% to 20%) in D4a compared to its wild-type form 10410T.