ABSTRACT
Survivorship curves, describing the fraction of a cohort alive as a function of age, have three typical forms; linear, convex, and concave depending on whether mortality is constant over all life or is greatest in early or late life. A successful survivorship model must be able to describe these forms. In addition, model parameters should be biologically meaningful in a self-consistent and rigorous framework. Few models, if any, have achieved these goals. In this paper I present a novel individual-based survivorship model that fits virtually all survivorship data tested and has parameters with clear intuitive meanings. Survivorship curves of organisms are described in terms of an individual’s vitality and accidental mortality rate. Mortality is thus partitioned into two parts: one dependent on an individual’s history and another independent of it. The balance of processes is characterized by a ratio of population half-life from accident only and vitality-related death only. Vitality dynamics are described by a random walk through two parameters: initial vitality and vitality rate of change. Accidental mortality is described by a Poisson process characterized by average time between accidental deaths. Parameters are estimated by fitting the model to survivorship data using a Marquardt nonlinear least squares technique. The model fits survivorship curves well, including examples of plants, insects, molluscs, fish, birds, mammals, and humans. Initial vitality varied by two orders of magnitude and increased linearly with adult weight for homeotherms. The rate of vitality change and accidental mortality rate varied by one and three orders of magnitude respectively. For different races of an insect, parameters varied within a factor of four.
