Golubev A
Institute of Experimental Medicine, 12 Akademika Pavlova Str., Saint-Petersburg, 197376, Russia.
Biogerontology. 2004;5(3):159-67. doi: 10.1023/B:BGEN.0000031153.63563.58.
Numerical modeling was used to explore the behavior of ideal cohorts obeying the Gompertz-Makeham (GM) law of mortality (-dn/dt 1/n(t) = C + lambda egammat) supplemented with the Strehler-Mildvan (SM) correlation (ln lambda = A - Bgamma) and to show how changes in the age-independent parameter C will produce an apparent SM correlation if C is ignored in mortality data treatment as in the case of the so-called longitudinal gompertzian analysis of historical changes in human mortality patterns. The essential difference between the Makeham term C and Gompertz term lambda e(gammat) has been suggested to be not that the latter is age-dependent whereas the former is not, but that C comprises the contributions of inherently irresistible stresses to mortality, whereas lambda e(gammat) comprises the contributions of resistible stresses and shows how changes in the resistance to them are translated into changes in mortality. This assumption was used to show by modeling how the transition of stresses from irresistible to resistible may result in decreased late survivorship as the cost of increased early survivorship, in line with the antagonistic pleiotropy theory of aging. On the whole, the modeling suggests that the GM equation is not only a mathematical tool for treatment of mortality data but that it also has a fundamental biological significance, and its Makeham term C should not be ignored in any analysis of mortality data.
数值建模被用于探究遵循冈珀茨 - 马克姆(GM)死亡率定律(-dn/dt 1/n(t) = C + λeγt)并补充施特雷勒 - 米尔德万(SM)相关性(lnλ = A - Bγ)的理想队列的行为,以展示如果在死亡率数据处理中像在对人类死亡率模式历史变化进行所谓的纵向冈珀茨分析那样忽略年龄独立参数C,它将如何产生明显的SM相关性。有人提出马克姆项C和冈珀茨项λe(γt)之间的本质区别并非后者随年龄变化而前者不随年龄变化,而是C包含对死亡率具有内在不可抗拒压力的贡献,而λe(γt)包含可抗拒压力的贡献,并展示了对这些压力的抵抗力变化如何转化为死亡率变化。这一假设被用于通过建模表明,压力从不可抗拒向可抗拒的转变可能导致晚期存活率降低,作为早期存活率增加的代价,这与衰老的拮抗性多效性理论一致。总体而言,该建模表明GM方程不仅是处理死亡率数据的数学工具,而且还具有基本的生物学意义,并且在任何死亡率数据分析中都不应忽略其马克姆项C。