b Subdivision by origin 
Allele N.I. (160) S.I. (126) N.I. (136) S.I. (180) 
33 20 12 30 34 
> 33 140 114 106 146 

By applying the above procedure to the analysis of linkage disequilibrium between the Xba-RFLP and APOB-VNTR, the data shown in Table 6 were obtained. The same allelic associations were favored in the two samples (X+ with VNTR alleles 37 and 39, pooled in class W; X with the remaining alleles, pooled in class Z), and in both samples, the disequilibrium between the polymorphic systems was significantly different from 0 (χ2 = 34.45 with 1 df; P < 0.001 in sample S; χ2 = 21.87 with 1 df; P <0.001 in sample C). In this case too, the associations X+W and XZ were greater in S than in C (D/Dmin =79% in sample S; D/Dmin =67% in sample C).

In case and control gene pools, let us consider firstly the analysis of linkage disequilibrium between the XbaI-RFLP and EcoRI-RFLP (Table 4). In sample S, the linkage disequilibrium value (D) is significantly different from 0 (χ2 =22.54 with 1 df; P <0.001). On the contrary, in sample C, the value of D does not reach statistical significance (χ2 =3.58 with 1 df; P >0.05). Furthermore, the haplotype X+R, although at low frequency, is present in C but absent from the S allele pool.

Now let us consider the analysis of linkage disequilibrium between the EcoRI-RFLP and APOB-VNTR. A preliminary evaluation of haplotypic frequencies was carried out by the maximum-likelihood method. It enabled us to group the VNTR alleles into two classes: the A class consisting of VNTR alleles with a repeat number lower than 41 (preferentially associated with the R+ allele in both S and C samples), and the B class consisting of the remaining VNTR alleles (preferentially associated with the R allele). In this way, the multiallelic VNTR system was recoded as diallelic (Table 5), and the statistical significance of D was then tested. In both S and C samples, D was different from 0 (χ2 =101.4 with 1 df; P <0.001 in S; χ2 =70.15 with 1 df; P <0.001 in C); however, the associations R+A and RB were greater in S than in C (D/Dmax =90% in sample SItaly). The study aimed to investigate the association between gene alleles and longevity in centenarians compared to controls. The study analyzed two multiallelic loci, APOB and TPO, and found that the frequency of VNTR alleles with fewer than 35 repeats was lower in centenarians than in controls. This trend was more pronounced in female centenarians. The loss of specific alleles from the centenarian gene pool suggests the elimination of unfavorable alleles that could contribute to disease and death. The study found significant linkage disequilibrium between the APOB gene polymorphisms and the 3 APOB-VNTR alleles, indicating that the loss of specific VNTR alleles could be a consequence of selection against APOB gene alleles that predispose to disease and death. However, it is possible that the copy number of the 3 APOB-VNTR array itself has some kind of function that affects longevity. Ethnic or geographical differences did not explain the observed differences between centenarians and controls, suggesting that recombinant chromosomes are preferentially lost in the aging population. The study concludes that VNTR alleles with low repeat numbers are unfavorable to long life expectancy due to their association with coronary heart disease.The following text presents research on the genetic differences between long-lived individuals and control groups in Italy. 

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