Explaining mortality rate plateaus

Abstract

We propose a stochastic model of aging to explain deviations from exponential growth in mortality rates commonly observed in empirical studies. Mortality rate plateaus are explained as a generic consequence of considering death in terms of first passage times for processes undergoing a random walk with drift. Simulations of populations with age-dependent distributions of viabilities agree with a wide array of experimental results. The influence of cohort size is well accounted for by the stochastic nature of the model.

Figure 1

Mortality rates according to Eq. 9 with τ = 10 and τ_r = 2, 50, and 150 corresponding to the solid, dashed, and dot-dashed curves, respectively.

Figure 2

Mortality rates obtained via numerical simulations of a homogeneous population of N = 10⁶ organisms, the dynamics of which is that of Eq. 1, with v₀ = 1, τ = 10, and τ_r = 2, 50, and 150 corresponding to the solid, dashed, and dot-dashed curves, respectively. Note that ɛ = 1/τ and σ = τ.

Figure 3

Survival probability at time t for experimental cohorts and theoretical predictions based on Eq. 6 where ɛ̂ = 0.0448 and σ̂ = 0.0975. (Inset) A comparison of the probability of dying at time t between experiment and theory. In both cases open circles signify data points from Carey et al. (5), and solid lines are predictions from theory.

Figure 4

Age-specific mortality rates for cohorts of sizes ranging from n = 25 to 100,000. Going from top to bottom, rows 1 and 3 are randomly sampled from experimental data. Rows 2 and 4 are from simulations of Eq. 1 using MLE estimates as explained in Application to Mortality Rate Data.