Telomeres are caps at the ends of chromosomes, and their average length, while dynamic, tends to become shorter with advancing age or illness. To my eyes this looks like a secondary effect of the damage of aging, but there are researchers who think that it might be a primary cause of degenerative aging and are working on ways to lengthen telomeres, such as through the use of the enzyme telomerase.
Natural variations in life span in humans are to some degree inherited, depending upon both genes and lifestyle choices. Here is a study that puts some numbers to telomere length inheritance:
Telomeres play a central role in cellular senescence and are associated with a variety of age-related disorders such as dementia, Alzheimer's disease and atherosclerosis. Telomere length varies greatly among individuals of the same age, and is heritable. Here we performed a genome-wide linkage scan to identify quantitative trait loci (QTL) influencing leukocyte telomere length (LTL) measured by quantitative PCR in 3,665 American Indians (aged 14 - 93 years) from 94 large, multi-generational families. All participants were recruited by the Strong Heart Family Study (SHFS), a prospective study to identify genetic factors for cardiovascular disease and its risk factors in American Indians residing in Oklahoma, Arizona and Dakota.
LTL heritability was estimated to be between 51% and 62%, suggesting a strong genetic predisposition to interindividual variation of LTL in this population. The strongest evidence of linkage for LTL in our genome-wide scan was localized to chromosome 13q12 in the Oklahoma population. [Among nearby genes, two] could represent promising candidate genes for LTL in American Indians. One is the well-known aging gene Klotho (KL) and [another] is poly (ADP-ribose) polymerase family, member 4 (PARP4). The PARP enzymes recognize DNA strand damages, and DNA binding by PARP controls telomere length and chromosomal stability by triggering its own release from DNA ends. Apart from KL and PARP4, the 13q linkage peak also includes known candidate genes for inflammation, e.g., arachidonate 5-lipoxygenase-activating protein (ALOX5AP), and cancer, e.g., breast cancer 2 early onset (BRCA2), all of which may be involved in the aging process.