http://mtsnp.tmig.or.jp/mtsnp/search_mtDNA_sequence_e.html. The 672 sequences from [6] and the 112 new semi-super- centenarian sequences were pairwise aligned relative to the revised Cambridge Reference Sequence rCRS (http://www.mitomap. org/mitoseq.html) using the Miller-Meyers [8] algorithm as implemented in the ‘‘Stretcher’’ module in EMBOSS, 3H3Hhttp://emboss.sourceforge.net/). We applied a robust technique developed in [9] to the 672 sequences which identified all robust mutations in the data using Principal Component Spectral Analysis [10,18–21] to identify the mutations that represent most of the variation in the data. Following this, we separated the samples into haplogroup clusters by applying an ensemble consensus clustering technique which averages over probabilistic, agglomerative and hierarchical clustering methods and many data perturbations to build an agreement matrix from which a robust set of clusters is determined along with patterns of discriminatory mutations [9]. The optimum number of clusters (kmax) was estimated using the silhouette score [11] and gap- statistics [12]. The robustness and statistical significance of the clusters and mutations was validated by averaging over ten 2:1 training/test bootstrapped datasets on which we repeated the complete clustering analysis. Only 90% or higher sample assignments into clusters and predictive mutations were accepted. This analysis clustered the 672 Japanese samples into 31 robust haplogroups after the samples which had ambiguous membership in the clustering analysis because of small sample size were discarded. The 31 haplogroups, as defined also in Tanaka et al. [6], and confirmed by our unsupervised consensus ensemble clustering technique [9] were: A, B4a, B4b, B4c, B5, D4a, D4b1a, D4b1b, D4b2a, D4b2b, D4d1a, D4d1b, D4e1, D4e2, D4g, D4h, D5a, D5b, F1, F2, M10, M7a, M7b, M8, M9, C, G1, G2, Z, N9a, N9b. We also found 261 SNPs in the patterns of mutation that are characteristic markers for these haplogroups. The 112 semi- supercentenarian sequences were classified into haplogroups based on the patterns of these 261 characteristic SNPs

A similar score that measures haplogroup enrichment for longevity is defined as:

This measure is defined for each haplogroup H. f T is the H fraction of samples in the target (longevity) group (either centenarians or semi-supercentenarians) that belong to the haplogroup H, f C is the fraction of samples in the control group S (healthy non-obese males) that belong to the haplogroup H and s NT is the standard deviation of these fractions across the 6 non H target groups.

We used the method of [13] to identify maximal bi-cliques. We define a biclique as a set of polymorphisms shared by at least 5 samples across all the data, independent of the haplogroups or phenotypes. The algorithm looks for combinations of sets of mutations (bi-cliques) that are shared by five or more individuals in the data, using a recursive algorithm which combines the sets onto bigger sets until all maximal sets are identified. The software for this algorithm along with a brief description is available at the website: http://genome.cs.iastate.edu/supertree/download/biclique. These bi-cliques define ‘‘patterns of mutation’’ which seem to be associated synergistically to longevity. The association of each pattern to longevity is estimated using an enrichment score L for patterns. P

This statistic is defined for each pattern P. It represents the difference between the fraction of samples f T that exhibit the P pattern in the target longevity group (centenarians or semi- supercentenarians) minus the fraction of samples f C that exhibit P the same pattern in the control group, divided by the standard deviation s NT of these fractions over all the 6 non-target P phenotypes.

Out of the 261 mtSNPs identified above, we restricted the analysis to the 235 which were more than 1% polymorphic across the 112 semi-supercentenarian samples. We also eliminated several SNPs in the region from locus 303 to 317 and from 16180 to 16195, which are in the so called hypervariable regions HV1 (16024–16383) and HV2 (57–372). This was because we determined, by examination of the sequences in these regions, that they were length polymorphisms and not true mutations. This left us with a dataset with 227 SNPs and 782 samples which were used for further analysis (see Table S1 for the complete data used in this paper). The complete previous sequences used in this study (672 samples from [6]) can be downloaded from (http://mtsnp. tmig.or.jp/mtsnp/search_mtDNA_sequence_e.html). The new complete mtDNA sequences of 112 semi-supercentenarians are in Data S1.

The p-values for L , L and L were calculated by comparing S H P the experimental values to a null distribution created by computing their values in 1 million datasets obtained by a random permutation of phenotype labels. The fraction of values out of 1 million, that the enrichment score was greater than L , L , L S H P respectively, is the corresponding p-value. This permutation method for calculating p values is preferred because it avoids assumptions about the underlying distribution. We correct for the false discovery rate (FDR) using the method of Benjamini and Hochberg [14] which converts multiple hypothesis uncorrected p- values into corrected q-values [15].

To measure the degree of association of an mtSNP to longevity, we define a mtSNP enrichment score L follows: S