A critique of the demographic

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A critique of the demographic evidence that the
oldest old age very slowly Aubrey de
Grey Department of Genetics, University of
Cambridge
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Why do too many individuals live to
extreme ages? The first approximations
Gompertz 1825 m(t) Aebt Makeham
1867 m(t) Aebt c The problem Actually,
m(t) Aebtc until most are dead, but then
slows hugely The hypotheses 1) (Curtsinger
1992, Rose 1996) Individual senescence behaves
like m(t) Mathematically simple biomedically
tantalising biologically outrageous 2)
(Vaupel 1979, 1993, Service 2000) Individual
senescence is broadly Gompertzian, but slow
agers progressively dominate the surviving
subset. Biologically plausible biomedically
undistracting mathematically horrid
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Ukraintseva and Yashin 2001, Mech Ageing Dev
1221447
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Gompertz-Makeham with heterogeneity the
options Null hypothesis A, b and c are normally
distributed for each individual mi(t)
Aiebit ci Ideal fit ?A, ?b, ?c, ?A, ?b, ?c
to data. Not mathematically tractable! Tractable
if we set ?b ?c 0. This gives a very much
better fit that a simple G-M curve, but ?A/?A
has to be implausibly high. Easy to see that a
much smaller ?b/?b should fit the data. Also,
eventual m(t) decline (Carey 1992) needs
variability in b. Requirement allow ?b gt 0.
But how?
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Binomial approximation to normal distribution
gives mathematical and computational
tractability Approximate the population as n1
subpopulations of sizes nCi(n/2) with bi
b.(1?b)i , -n/2 lt i lt n/2. Assume A and c are
uniform (i.e. ?A ?c 0). Then,
n/2 m(t) 2-n ?
nCi(n/2)c(A et.b.(1?b)i)
i-n/2 Choose n big enough
(e.g. so that 2n gt dataset size) Fit A, b, c if
needed and ?b
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Swedish males born in the 1880s, surviving to 40
data from JR Wilmoth, Berkeley Mortality Database
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Swedish females born in the 1880s, surviving to 40
data from JR Wilmoth, Berkeley Mortality Database
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One million medflies
Carey et al 1992, Science 258457
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One million medflies
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Evidence for an extra synergy parameter
Previously, bi (1?b)i Here, bi
(1?b)(is.i2) for i gt 0 bi (1?b )(i-s.i2)
for i lt 0
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Are these fits quantitatively plausible? Swedish
males extremalcentral value for b
1.29 (central MRDT is 7.59 years, extremal MRDT
is 9.85) Swedish females extremalcentral
value for b 1.29 (central MRDT is 7.67 years,
extremal MRDT is 9.95) Medflies
extremalcentral value for b 22.5 -- hm.....
Compare Vaupel 93 (?b0, fit ?A)
extremalcentral A1010! Also consider worker
vs. queen bees
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• Conclusions
• Aging may slow down as it progresses (and be not
  very heterogeneous between individuals) or it may
  speed up (and be somewhat more heterogeneous).
  Models of either sort fit existing data
  comparably well when constructed with the same
  number of free parameters.
• 2) We cannot distinguish these hypotheses -- let
  alone more similar ones such as Gompertz vs.
  Weibull -- without very large datasets or new
  methods of analysis. The latter has been
  attempted (e.g. Drapeau et al, Exp Gerontol
  3571) but without success (Service, Exp Gerontol
  351085)