The natural distribution of survival

Great similarities in survival patterns permit the Gompertz and other established equations to describe parts of mortality curves in various species. These patterns appear non-random and invite inference of biological meaning, though no unifying explanation is agreed. Under the theory described here, linear decline of an initial quantity of species or strain-specific redundant reserve interacts with extrinsic hazards via a 'nested binomial' model, which is presented both in a simple, four parameter form, and a more complex form that incorporates inter-individual and inter-functional biological variation. This approach demonstrates exponential rises in mortality, late-life deceleration and Strehler-Mildvan correlation. Biological variation within the complex model, specifically in the redundancy decay rate parameter, is shown to generate mortality plateaux, while outlier phenotypes produce mortality decelerations, supporting inter-individual heterogeneity as the cause of these phenomena. The model is robust to large variations in organism complexity, and to broad intra-population hazard variation. Specific parameters appear analogous to observed elements of ageing, and a central role for redundancy depletion provides a context for longevity genes and rapid evolution of increased lifespan. This approach offers a unifying model for a great variety of ageing phenomena across a wide range of species.