Research article Does Makeham make sense? A. Golubev Institute of Experimental Medicine, 12 Akademika Pavlova Str., Saint-Petersburg, 197376, Russia; (e-mail: alalal@rol.ru) Received 27 July 2003; accepted in revised form 15 December 2003 Key words: aging, evolution, Gompertz–Makeham law, history, mortality, numerical modeling, Strehler– Mildvan correlation, survivorship Abstract Numerical modeling was used to explore the behavior of ideal cohorts obeying the Gompertz–Makeham (GM) law of mortality ()dn/dt Æ 1/n(t) = C + ke ct ) supplemented with the Strehler–Mildvan (SM) cor- relation (ln k = A ) Bc) 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 longi- tudinal gompertzian analysis of historical changes in human mortality patterns. The essential difference between the Makeham term C and Gompertz term ke ct 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 ke ct 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 survi- vorship 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. Introduction The Gompertz–Makeham (GM) Law The fact that the shape of human survivorship curves for the middle age span may be explained by an exponential increase in the age-specific mortality rate was recognized by Gompertz (1825). The function for such survivorship curves, which is named after Gompertz, is described by the well known Equation: nðtÞ¼ n 0  exp  k c ðe ct  1Þ   ð1Þ The exponential increase in the age-specific mor- tality rate that may be observed over time t in cohorts of different organisms (cohort analysis mostly used in experiments) or derived from sur- vivorship curves described by Equation (1) (cross- sectional or period analysis mostly used in demography) is known as the Gompertz law and is described by Equations (2) or (3): dn=dt  1=nðtÞ¼ lðtÞ¼ ke ct ð2Þ ln lðtÞ¼ ln k þ ct ð3Þ Makeham (1860) suggested that a better fit to real survivorship curves might be achieved by intro- duction of an additive constant to Equation (2) thus leading to lðtÞ¼ C þ ke ct ð4Þ The parameters of Equation (4) (and Equations (1)–(3) by inference) may be interpreted in bio- logically meaningful and intuitively comprehensi- ble terms. The additive term C represents the rate Biogerontology 5: 159–167, 2004. 159 Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands.