Figure 1.

(A) Evolution of mortality rate (at birth, q₀ and at 80 years, q₈₀) with chronological year for Swedish (q₀, O, q₈₀, x) and Japanese (q₀, ●; q₈₀, +) females. (B) Agreement between theoretical and lifetable mortality rates q_x (in all cases the age x is in years) for 1891/1898 Japanese (O, q₀ = 0.1612), and 1926/1930 Swedish (□, ℓ₄₀ = 0.81) males; 1992/1994 German (⋄, q₀ = 0.0515), and 1990 Japanese (+, ℓ₄₀ = 0.983) females. The calculations according to the data in brackets are presented by thick lines for Eqs. 1–3 and thin lines for Eqs. 3–5. (C) Evolution of the survival probability ℓ_x with ℓ₄₀ for 1891–1995 Swedish (10, 11), 1891–1990 Japanese (10), and 1871–1992 German (13) males and females. The ages x = 20, 60, and 90 yield upper, middle, and lower curves, respectively. Solid lines are linear approximations. Note a rapid and nearly simultaneous, for different ages, change in the slope at ℓ₄₀ ≅ 0.97. (D) Evolution of the mortality curve in the vicinity of ℓ₄₀ ≅ 0.97: 1947 Japanese female (O, ℓ₄₀ = 0.709); 1960 Japanese (⋄, ℓ₄₀ = 0.897) and 1980 Swedish (+, ℓ₄₀ = 0.959) males; 1995 Swedish (∗, ℓ₄₀ = 0.897), and 1990 Japanese (Δ, ℓ₄₀ = 0.983) females. (E) Agreement between theoretical and life table survival probabilities ℓ₄₀ for 1891/1898 Japanese males (▹, ℓ₄₀ = 0.582); 1891/1900 Swedish (□, ℓ₄₀ = 0.695), and 1947 Japanese (X, ℓ₄₀ = 0.709) females; 1926/1930 Swedish males (⋄, q₀ = 0.0668); 1990 Japanese (+, q₀ = 0.00418), and 1995 Swedish (O, q₀ = 0.00358) females. Calculations according to Eqs. 1 and 2 and 3–5 are presented by thick lines for Eqs. 1-3 and thin lines for Eqs. 3–5. (F) Accuracy of the universal survival law: mean square deviations Δ₁(O), and Δ₂ (□) of Eqs. 1 and 2 from experimental data (10-13). (G) Accuracy of the universal survival law: mean square deviations δ₁ (O) and δ₂ (□) of Eqs. 1–3 from experimental data. (H) Accuracy of the universal survival law: probability (on a semilogarithmic scale) of relative (with respect to their mean quadratic values) deviations exceeding d for Eqs. 1–3 (O for ℓ_x + for q_x) and for Eqs. 3–5 (□ for ℓ_x, ∗ for q_x). The probability of random fluctuations is presented by the solid line. (I) Same as in F, but for Eqs. 4 and 5. (J) Same as in G, but for Eqs. 3–5. (K) Probability P of |q̃_x − q_x|/q_x > 0.25 for Eqs. 1 and 3 (O) and Eqs. 2 and 3 (□) vs x. (L) Same as in G, but for life tables with |q̃_x − q_x|/q_x < 0.25 only.