Fig. 6: Steepening (rectangularization) of human survival curves in the past century is mainly due to declining extrinsic mortality.

a Survival curves and rescaled survival curves of cohorts of Swedish women born in 1820–1824 and 1890–1894. b Hazard curve (death rates by age) of Swedish women born in 1890–1894, and of SR model fitted to this cohort. The SR model parameters that correspond to the blue and orange hazard curves are η = 1.04 × 10⁻⁵/day², β = 0.45 /day, κ = 0.50, ε = 0.48 /day, X_c = 19.9³². The extrinsic hazard (additive Makeham term) in the orange curve is m = 0.0036 per year. c–e Mortality component trends of Swedish (Blue), Dutch (Red), French civilians (Green) and English & Welsh civilian (Red) cohorts born 1810–1900. For each 5-year-wide birth cohort, we estimate extrinsic hazard rates, Gompertz slopes and Gompertz intercepts from death rates from age 36 onward, using the Gamma–Gompertz-Makeham model⁶⁸. In the SR model, the Gompertz slope can be approximated by ηX_c/ε and intercept is proportional to e^{βXc/ε 32}. The Gamma–Gompertz correction term s(t) is s(t) =e^c/(e^c-1 + e^bt), where c is an additional parameter that ranges from 7.5 to 10, such that s(t) only comes into effect at old age. Mortality components estimates are presented as mean values +/− SE. The average (min-max) cohort sizes (N) in units of 100,000 for women and men, respectively, are 1.7 (1.2−2.5) and 1.6 (1.2–2.4) for Sweden, 11.0 (6.1–16.7) and 9.8 (5.8–15.5) for England & Wales, 13.7 (12.3–16.1) and 12.9 (7.1–15.9) for France, and 1.7 (1.1–3.2) and 1.7 (1.0–3.1) for Netherlands. Source data are provided as a Source Data file.