A natural model of population heterogeneity fits observed mortality distributions, including their tail





A.D.N.J. de Grey

Department of Genetics, University of Cambridge, Downing Street, Cambridge CB2 3EH, UK



It has long been appreciated that the Gompertz-Makeham distribution, which very accurately describes observed mortality distributions over most of their extent, conspicuously fails to do so for the longest- lived subset of typical populations. Specifically, the "tail" of observed survival curves is much longer than that of a Gompertz-Makeham curve fitted to the whole population. A simple candidate explanation is based on heterogeneity: the longest-lived subset of a population may be enriched in individuals that intrinsically age more slowly than the bulk of that population. However, a number of investigators have concluded that this interpretation, while economical, is inadequate: that it can explain some, but by no means all, of the observed deviation from Gompertzian behaviour. Here it is shown that that conclusion may be premature. Previous work has modelled heterogeneity in ways that are computationally tractable but biologically oversimplistic; using a more computationally challenging but also biologically more realistic approach, however, it is found that observed distributions can be approximated very accurately by purely "Gompertz with heterogeneity" curves. Hence, no case can presently be made that some individuals cease to senesce after a certain age, as has been proposed.




Key words: mortality, Gompertz, heterogeneity







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