Modelling survivorship kinetics: a two-parameter model

A mathematical model of survivorship kinetics is presented. It takes into account both deterministic and stochastic aspects of survival curves. Earlier reports [Piantanelli: Arch Gerontol Geriatr 1986;5:107-118; Piantanelli: Ann NY Acad Sci 1988; 521:99-109] described a model capable of making distinct predictions on the mean and standard deviation of an index of physiological function, fitting data even in the tail of survivorship curves, and accounting for the selection of the cohort at advanced ages. However, it contains four parameters whose biological interpretation is unclear. In the present paper we propose a modification of the model which maintains the main characteristics of the previous one and, in addition, results in two significant improvements. First, the number of free parameters is reduced to only two, making much easier both their estimation and interpretation, particularly when the model is applied to data from various animal groups manipulated in different ways. Second, it is possible to relate the parameters to well-defined deterministic and stochastic factors: specifically, a deterministic component describing the environmental and genetic influence on physiological functions, and a stochastic component representing the fluctuating interactions of the living organism and its environment.