Gompertz, B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philos. Trans. R. Soc. L. A, 1825, vol. 115, no. 1, pp. 513–585. https://doi.org/10.1098/rstl.1825.0026

Article  Google Scholar 

Deevey, E.S., Life tables for natural populations of animals, Q. Rev. Biol., 1947, vol. 22, no. 4, pp. 283–314. https://doi.org/10.1086/395888

Article  PubMed  Google Scholar 

Gavrilov, L.A. and Gavrilova, N.S., The Biology of Life Span: A Quantitative Approach, N. Y.: Harwood Academic Publisher, 1991.

Google Scholar 

Vaupel, J.W., Carey, J.R., Christensen, K., Johnson, T.E., Yashin, A.I., Holm, N.V., Iachine, I.A., Kannisto, V., Khazaeli, A.A., Liedo, P., Longo, V.D., Zeng, Y., Manton, K.G., and Curtsinger, J.W., Biodemographic trajectories of longevity, Science, 1998, vol. 280, no. 5365, pp. 855–860. https://doi.org/10.1126/science.280.5365.855

Article  CAS  PubMed  Google Scholar 

Khalyavkin, A.V., Influence of environment on the mortality pattern of potentially non-senescent organisms. General approach and comparison with real populations, Adv. Gerontol., 2001, vol. 7, pp. 46–49.

Google Scholar 

Jones, O.R., Gaillard, J.M., Tuljapurkar, S., et al., Senescence rates are determined by ranking on the fast-slow life-history continuum, Ecol. Lett., 2008, vol. 11, no. 7, pp. 664–673. https://doi.org/10.1111/j.1461-0248.2008.01187.x

Article  PubMed  Google Scholar 

Jones, O.R., Scheuerlein, A., Salguero-Gómez, R., Camarda, C.G., Schaible, R., Casper, B.B., Dahlgren, J.P., Ehrlén, J., García, M.B., Menges, E., Quintana-Ascencio, P.F., Caswell, H., Baudisch, A., and Vaupel, J.W., Diversity of ageing across the tree of life, Nature, 2014, vol. 505, no. 7482, pp. 169–173. https://doi.org/10.1038/nature12789

Article  CAS  PubMed  Google Scholar 

Ricklefs, R.E., Life-history connections to rates of aging in terrestrial vertebrates, Proc. Natl. Acad. Sci. U.S.A., 2010, vol. 107, no. 22, pp. 10 314–10 319. https://doi.org/10.1073/pnas.1005862107

Article  Google Scholar 

Myl’nikov, S.V., Towards the estimation of survival curves parameters and geroprotectors classification, Adv. Gerontol., 2011, vol. 24, no. 4, pp. 563–569.

PubMed  Google Scholar 

Akif’ev, A.P. and Potapenko, A.I., Nuclear genetic material as an initial substrate for animal aging, Genetika, 2001, vol. 37, no. 11, pp. 1445–1458.

PubMed  Google Scholar 

Markov, A.V., Can kin selection facilitate the evolution of the genetic program of senescence?, Biochemistry (Moscow), 2012, vol. 77, no. 7, pp. 733–741. https://doi.org/10.1134/S0006297912070061

Article  CAS  PubMed  Google Scholar 

Strehler, B.L. and Mildvan, A.S., General theory of mortality and aging, Science, 1960, vol. 132, no. 3418, pp. 14–21. https://doi.org/10.1126/science.132.3418.14

Article  CAS  PubMed  Google Scholar 

Seliverstov, A.V., Heuristic algorithms for recognition of some cubic hypersurfaces, Program. Comput. Softw., 2021, vol. 47, no. 1, pp. 50–55. https://doi.org/10.1134/S0361768821010096

Article  Google Scholar 

Makeham, W.M., On the law of mortality and the construction of annuity tables, The Assurance Magazine, and Journal of the Institute of Actuaries, 1860, vol. 8, no. 6, pp. 301–310. https://doi.org/10.1017/S204616580000126X

Article  Google Scholar 

Gavrilov, L.A. and Gavrilova, N.S., Mortality measurement at advanced ages: A study of the social security administration death master file, N. Am. Actuar. J., 2011, vol. 15, no. 3, pp. 432–447. https://doi.org/10.1080/10920277.2011.10597629

Article  PubMed  PubMed Central  Google Scholar 

Gavrilova, N.S. and Gavrilov, L.A., Are we approaching a biological limit to human longevity?, J. Gerontol. Series A, 2020, vol. 75, no. 1, pp. 1061–1067. https://doi.org/10.1093/gerona/glz164

Article  Google Scholar 

Oeppen, J. and Vaupel, J.W., Demography. Broken limits to life expectancy, Science, 2002, vol. 296, no. 1, pp. 1029–1031. https://doi.org/10.1126/science.1069675

Article  CAS  PubMed  Google Scholar 

Shilovsky, G.A., Putyatina, T.S., Markov, A.V., and Skulachev, V.P., Contribution of quantitative methods of estimating mortality dynamics to explaining mechanisms of aging, Biochemistry (Moscow), 2015, vol. 80, no. 12, pp. 1547–1559. https://doi.org/10.1134/S0006297915120020

Article  CAS  PubMed  Google Scholar 

Golubev, A., A 2D analysis of correlations between the parameters of the Gompertz–Makeham model (or law?) of relationships between aging, mortality, and longevity, Biogerontology, 2019, vol. 20, no. 6, pp. 799–821. https://doi.org/10.1007/s10522-019-09828-z

Article  CAS  PubMed  Google Scholar 

Bohk-Ewald, C., Ebeling, M., and Rau, R., Lifespan disparity as an additional indicator for evaluating mortality forecasts, Demography, 2017, vol. 54, no. 4, pp. 1559–1577. https://doi.org/10.1007/s13524-017-0584-0

Article  PubMed  Google Scholar 

Frolkis, V.V., Aging and Life-Prolonging Processes, Wien, New York: Springer Verlag, 1982. https://doi.org/10.1007/978-3-7091-8649-7

Book  Google Scholar 

Wrycza, T.F., Missov, T.I., and Baudisch, A., Quantifying the shape of aging, PLoS One, 2015, vol. 10, no. 3, p. e0119163. https://doi.org/10.1371/journal.pone.0119163

Article  CAS  PubMed  PubMed Central  Google Scholar 

Burger, O., Baudisch, A., and Vaupel, J.W., Human mortality improvement in evolutionary context, Proc. Natl. Acad. Sci. U.S.A., 2012, vol. 109, no. 44, pp. 18210–18214. https://doi.org/10.1073/pnas.1215627109

Article  PubMed  PubMed Central  Google Scholar 

Burger O., Evolutionary demography of the human mortality profile, in The Evolution of Senescence in the Tree of Life, Shefferson, R.P., Jones, O.R., and Salgnero-Gomez, R., Eds., Cambridge: Cambridge Univ. Press, 2017. https://doi.org/10.1017/9781139939867.006

Book  Google Scholar 

Skulachev, M.V. and Skulachev, V.P., New data on programmed aging—slow phenoptosis, Biochemistry (Moscow), 2014, vol. 79, no. 1, pp. 977–993. https://doi.org/10.1134/S0006297914100010

Article  CAS  PubMed  Google Scholar 

Galimov, E.R., Lohr, J.N., and Gems, D., When and how can death be an adaptation?, Biochemistry (Moscow), 2019, vol. 84, no. 12, pp. 1433–1437. https://doi.org/10.1134/S0006297919120010

Article  CAS  PubMed  Google Scholar 

Skulachev, V.P., Shilovsky, G.A., Putyatina, T.S., Popov, N.A., Markov, A.V., Skulachev, M.V., and Sadovnichii, V.A., Perspectives of Homo sapiens lifespan extension: Focus on external or internal resources?, Aging (Albany, New York), 2020, vol. 12, no. 6, pp. 5566–5584. https://doi.org/10.18632/aging.102981

Article  Google Scholar 

Keyfitz, N., What difference would it make if cancer were eradicated? An examination of the Taeuber paradox, Demography, 1977, vol. 14, no. 4, pp. 411–418.

Article  CAS  PubMed  Google Scholar 

Aburto, J.M., Alvarez, J.-A., Villavicencio, F., and Vaupel, J.W., The threshold age of lifetable entropy, Demogr. Res., 2019, vol. 41, no. 4, pp. 83–102. https://doi.org/10.4054/DemRes.2019.41.4

Article  Google Scholar 

Demetrius, L., Adaptive value, entropy and survivorship curves, Nature, 1978, vol. 275, no. 2677, pp. 213–214. https://doi.org/10.1038/275213a0

Article  CAS  PubMed  Google Scholar 

Zhang, Z. and Vaupel, J.W., The age separating early deaths from late deaths, Demogr. Res., 2009, vol. 20, no. 29, pp. 721–730. https://doi.org/10.4054/DemRes.2009.20.29

Article  Google Scholar 

Boldrini, M., Corrado Gini, J. R. Stat. Soc. Ser. A Stat. Soc., 1966, vol. 129, no. 1, pp. 148–150. https://doi.org/10.1111/j.2397-2327.1966.tb02144.x

Article  Google Scholar 

Shkolnikov, V.M., Andreev, E.M., and Begun, A.Z., Gini coefficient as a life table function: Computation from discrete data, decomposition of differences and empirical examples, Demogr. Res., 2003, vol. 8, no. 11, pp. 305–358. https://doi.org/10.4054/DemRes.2003.8.11

Article  Google Scholar 

Smits, J. and Monden, C., Length of life inequality around the globe, Soc. Sci. Med., 2009, vol. 68, no. 6, рр. 1114–1123.

Gavrilova, N.S., Gavrilov, L.A., Severin, F.F., and Skulachev, V.P., Testing predictions of the programmed and stochastic theories of aging: Comparison of variation in age at death, menopause, and sexual maturation, Biochemistry (Moscow), 2012, vol. 77, no. 7, pp. 754–760. https://doi.org/10.1134/S0006297912070085

Article  CAS  PubMed  Google Scholar 

Shilovsky, G.A., Putyatina, T.S., Lysenkov, S.N., Ashapkin, V.V., Luchkina, O.S., Markov, A.V., and Skulachev, V.P., Is it possible to prove the existence of an aging program by quantitative analysis of mortality dynamics?, Biochemistry (Moscow), 2016, vol. 81, no. 12, pp. 1461–1476. https://doi.org/10.1134/S0006297916120075

Article  CAS  PubMed  Google Scholar 

Shilovsky, G.A., Putyatina, T.S., Ashapkin, V.V., Luchkina, O.S., and Markov, A.V., Coefficient of variation of lifespan across the tree of life: Is it a signature of programmed aging?, Biochemistry (Moscow), 2017, vol. 82, no. 1, pp. 1480–1492. https://doi.org/10.1134/S0006297917120070

Article  CAS  PubMed  Google Scholar 

Rubanov, L.I. and Seliverstov, A.V., Projective-invariant description of a meandering river, J. Commun. Technol. Electron., 2017, vol. 62, no. 6, pp. 663–668. https://doi.org/10.1134/S1064226917060201

Article  Google Scholar 

Chen, J., Senturk, D., Wang, J.L., Müller, H.G., Carey, J.R., Caswell, H., and Caswell-Chen, E.P., A demographic analysis of the fitness cost of extended longevity in Caenorhabditis elegans, J. Gerontol. A Biol. Sci. Med. Sci., 2007, vol. 62, no. 2, pp. 126–135. https://doi.org/10.1093/gerona/62.2.126

Article  PubMed  Google Scholar 

Evans, F.C. and Smith, F.E., The intrinsic rate of natural increase for the human louse, Pediculus humanus L., Amer. Naturalist, 1952, vol. 86, no. 830, pp. 299–310. https://doi.org/10.1086/281737

Article