Mechanisms of Ageing and Development, 27 (1984) 323-340 323 Elsevier Scientific Publishers Ireland Ltd. A RETURN TO TIME, CELLS, SYSTEMS AND AGING: II. RELATIONAL AND RELIABILITY THEORETIC APPROACHES TO THE STUDY OF SENESCENCE IN LIVING SYSTEMS MATTHEW WlTTEN Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616/U.S.A.) (Received February 24th, 1984) (Revision received June 5th, 1984) SUMMARY In this paper, we approach the problem of attempting to understand senescence by understanding the complexity and hierarchical structure of mammalian organisms. To do this, we make use of some concepts from abstract relational biology; in particular, graph theory. We subsequently utilize these concepts to develop the idea of an irreplace- able element in a mammalian system. We then make use of these elements, and some concepts from reliability theory, to show how senescence processes in mammalian sys- tems may be related to the failure of a critical number of irreplaceable elements. Finally, we show how we may derive formulas for the expected number of elements which fail by a given time, and how this time is related to actual lifespan and expected lifespan of the organism. In particular, we relate this to some recent work by Cutler on the evolution of longevity. Key words: Senescence; Relational biology; Graphs; Hierarchies; Lifespan; Irreplaceable elements; Longevity; LEP; SMR; LSP 1. BIOLOGICAL HIERARCHIES AND GRAPH CONCEPTS The inherent complexity of biological systems makes them a wealth of fascination for the mathematical modeler. Depending upon the level of detail one is interested in, it is possible to create very finely detailed mathematical models or rather coarsely detailed mathematical models. It is the subject of this paper to discuss the applications of the more coarsely detailed models of mammalian organisms, and how these models might be applied to the problem of understanding senescence mechanisms in these same organ- isms. 0047-6374/84/$03.00 Printed and Published in Ireland © 1984 Elsevier Scientific Publishers Ireland Ltd.