Fig. 4

SR model can explain the variability in mortality between individuals. a To model the relation between risk of death and SnC levels, we assumed a simple threshold model where death occurs when SnC abundance exceeds a critical threshold X_C. b Mouse mortality (C57BL/6J mice obtained from the Mouse Phenome Database⁶⁰, black line) is well fit by the SR model (red line) with parameters consistent with the data of Figs. 1, 2, with death defined when SnC exceed a threshold (η = 0.084 day⁻¹ year⁻¹, β = 0.15 day⁻¹, κ = 0.5, ε = 0.16 day⁻¹, X_C = 17). c Similar results are obtained by assuming a more general sigmoidal dependency between SnC abundance X and risk of death: \(h = \left( {1 + {\mathrm{{e}}}^{ - \theta \left( {X - X_{\mathrm{C}}} \right)}} \right)^{ - 1}\). Parameters are the same as b, except that X_C is adjusted according to the steepness parameter θ (inset). d The SR model with added age-independent extrinsic mortality of 0.4 × 10⁻³ year⁻¹ (red) matches human mortality statistics⁶¹ (black). Inset: approximate analytical solution for the first passage time in the SR model shows the Gompertz law and deceleration at old ages. The parameters are similar to b, except a ~60-fold decrease in η: η = 0.00135 day⁻¹ year⁻¹, β = 0.15 day⁻¹, κ = 0.5, ε = 0.142 day⁻¹, X_C = 17. e SR model describes rapid shifts in mortality when fully fed Drosophila transition to a lifespan-extending dietary intervention (LE), (inset: experimental data from Mair et al.⁴⁵), with β = 1 h⁻¹, κ = 1, ε = 1 h⁻¹, η = 0.03 day ^-1 h⁻¹ and X_C = 15. LE was modeled by a decrease in η: η = 0.02 h⁻¹ day⁻¹ (changes in other parameters lead to similar conclusions, see Supplementary Note 8). f Lifespan of C. elegans raised at different temperatures varies by an order of magnitude, but survival curves collapse on a single curve when time is scaled by mean lifespan (inset: data from Stroustrup et al. ³⁵). The SR model provides scaling for perturbations that affect η, but not other parameters (β = 1 h⁻¹, κ = 1, and ε = 1 h⁻¹, η = 0.07 h⁻¹ day⁻¹, X_C = 20, Supplementary Note 9). Source data are provided as a Source Data file.