HAZARD CURVES AND LIFESPAN PROSPECTS.

When we see centenarians among us, singing, swimming, driving, and hear of supercentenarians, ten years or more beyond a hundred, it seems to auger well for the hope that the end of steady progress against mortality is not yet in sight. Can the fact that most people in developed societies die in their seventies and eighties be altogether resistant to change, if some people are living so much longer? One may ask about specific causes, changing environments, social support, medical advances, but one must also ask about underlying biological potential. Humans are a special case, but also an example of the general case, molded like other species by principles of evolution, whose application to longevity is imperfectly understood. Comparing human survival at extreme ages with survival in other species, biodemography has been fostering a new view of biological potential. Early achievements of biodemography are recounted in the volume Between Zeus and the Salmon, edited by Wachter and Finch (1997). The papers in this special issue review what has been learned since then, over the last five years, and what we stand to learn today. This essay looks at those questions through the prism of connections between the forms of hazard curves and the prospects for future progress against old-age mortality. Hazard curves are mathematical summaries of the dependence of mortality on age. Understanding how hazard curves are shaped into their shapes helps tell us how much resistance to extended survival may be programmed into our biology. The mathematics of hazard modeling intertwines with evolutionary theory and empirical research. It is not the intention here to provide a synopsis of the contributions to this special issue. Rather, the aim is to take up one theme central to biodemography and draw selectively from the papers, reacting to suggestions that they offer and bringing out cross-cutting ideas and ties among them. The opening contribution to this special issue, by Jim Carey (2003), sets the stage for our discussion as for the rest of the collection. In particular, Carey outlines the context within which lifespan comes to be viewed as an evolutionary adaptation. He reviews the ecological correlates of lifespan and the roles of the elderly in social species, and he gives a roster of behavioral and scientific developments likely to propel the biological future of human lifespans, under the four headings of healthful living, disease prevention and cure, organ replacement and repair, and aging arrest and rejuvenation. Such specifics provide an essential backdrop for the general consideration of constraints and opportunities in this essay. It is important to keep in mind that the “lifespan prospects” under discussion here are prospects for gradual, incremental extensions of lifespans across large populations, progress of the kind seen around the world over the last century. Drastic bio-engineering and visionary advances like those surveyed in Michio Kaku's (1997) Visions, however enticing, are beyond our chosen scope. The mathematical representation of mortality to which we mainly refer, the “hazard function” or “hazard curve”, is a graph of the force of age-specific mortality as a continuous function of age. Equal to the downward slope of the logarithm of the survivorship curve, it is discussed in detail in Horiuchi's (2003) contribution. Hazard curves that rise very steeply at advanced ages seem to suggest formidable obstacles to broad-based extensions of life. Hazard curves whose steepening tapers off at advanced ages seem to suggest more manageable challenges. The evolutionary theory of senescence, developed by biologists over the last half-century, encourages the idea of a strong connection between the shapes of hazard curves by age and their resistance to reduction over time. The theory and the connection will be described shortly. What is important to say first is that under this theory the same general principles operate to shape the hazard curves of other species as to shape our own. In this essay, the word “tapering” is used as shorthand for reductions in the slope of the logarithm of the hazard curve at advanced ages. Taking logarithms puts measurements of slopes on a proportional basis and turns exponential curves into straight lines. Tapering hazard curves are often called mortality “plateaus”, but hazards may taper so far as to bend downward, stretching the analogy with terrestrial plateaus. So long as it was still widely believed that hazards in other species typically rose exponentially with age, free of tapering, such beliefs fostered the view that diminishing returns in the struggle against human mortality at older ages could not be far away. Then came the discoveries initiated by Carey et al. (1992) and Curtsinger et al. (1992) of tapering hazards at extreme ages in a number of other species, first Mediterranean fruit flies and Drosophila, later nematode worms and yeast. Data may be found in Vaupel et al. (1998) and in Figures 1, 2, and 3 of Horiuchi's (2003) contribution. Robine and Vaupel (2001) and the contribution of Robine and Saito (2003) show that the record human lifespans confirmed over the last few years demand human hazard functions that also taper beyond age 95 and level out or drop beyond 108.