Stochastic studies of aging and mortality in multicellular organisms. II. The finite theory

We extend the development of a quantitative phenomenological theory of aging rooted in order theory. An organism is represented abstractly by a chain with a finite number of links. Each link corresponds to a possible rate-limiting event or process in senescence. A link is said to break when the corresponding event occurs or the corresponding process goes to completion. The chain is said to break, and the organism subsequently to perish, when the first link breaks, whichever link that might be. Two models are introduced to describe the failure of an arbitrary link. The first requires that a link break only after sustaining a fixed amount of deterioration; the second associates a non-zero probability of failure with each level of wear. The net deterioration of an intact chain is taken, crudely, to correspond to the decline in physiological vitality sustained by an organism during senescence. Failure of an arbitrary link is described in both models by a Markov process. The corresponding mortality rate derived in each instance describes aspects of available empirical data which cannot be accounted for by either the Gompertz or power-law relations. The decline in vitality is shown in both cases to be linear over time intervals of practical interest. The influence of temperature on the senescence of poikilotherms is briefly examined. We describe the effect of temperature both on longevity and the decline in vitality; indicate how substantial discrepancies can arise in the calculation of a macroscopic, effective, activation enthalpy; and lend theoretical support to the existence of temperature--memory effects in senescence.