What evidence for non-ageing species?

Carl Boe fzcboe at rocky.ucdavis.edu
Sun Oct 1 17:36:50 EST 1995

Peter Hynes (pjhynes at ozemail.com.au) wrote:
: On Mar 16, 1995 steve at chambers.ak.planet.co.nz (Steve Chambers) wrote :
: >In an article in Scientific American on the very old, it reported 
: >that after 80 there was no relationship between old age and high
: >death rates in humans.

: As I recall this topic has reared its head several times. I have two
: queries which appear to be loosely related to Steve's - and others'-
: interests.

: 1/ The alleged independence of death rates from chronological age
:    in the very old.

: *** Is this not merely an artefact of the Gaussian Curve ?

: When t>2*sigma, dN/dt --> 0 as a bit of algebra or simple inspection
: of the curve will show.
: So long as a group of individuals is far from its specie's mean age
: of death, the death RATE looks approx constant.
: In human males the mean age appears to be around 70.7 yr with an
: SD of about 8.5 yr. (The death rate curve is approx normal.)
: So IF you make it past say 85, your chances of dying APPEAR to
: level out.
: Comments?

Of course, this is a statement about declining numbers at risk with age. 
In older ages, N is quite small and so the rate of change in absolute
terms (i.e. the number of deaths occuring per unit time) is also small. 
The death rate, as usually defined, conditions on the average 
number of individuals exposed to mortality risk in the interval (cf. Qx 
below).  Statements about mortality leveling off and non-Gompertz 
mortality at old age is a statement about the normalized tail behavior 
(i.e. dN/dt / N --> ??? ).

: 2/ An oft used index of death rates is the "Age Specific Mortality,
:    Qx".
:    See : Carey et al, "Slowing of Mortality Rates at Older Ages in
:                        Large  Medfly Cohorts"
:          Science Vol 458, 457-461, 16\10\92
:     and  Curtsinger et al, "Demography of Genotypes : Failure of
:          the Limited Lifespan Paradigm in D. melanogaster",
:             Science 258, 461-464, 16\10\92

:  These guys have real good data - over 10^6 flies fed and pampered
: till they all kicked off from old age. Trouble is, even if you 
: start with a million, at the end you have just a handful left.
: And that leads to LARGE fluctuations in the stats for the tail
: enders. (Small sample noise.)
There is always increasingly large fluctuations in the tails.  The point 
of the million is that you can go much further into the tail region 
before demographic stochasticity becomes a problem.  

 : Bad for Qx which is supposed - in the above papers - to show
: departures from the Gompertz Law in a large, ageing population.

For any fixed x, the s.e. of the estimated Qx will be smaller, the larger
the number of flies alive at x.  So to get lots alive at x, you start 
with huge numbers.  Of course there will always be an age old enough so 
that you don't have very many left alive and, at that age, the estimates 
wil be quite uncertain.

: ***
: So, who thinks these papers really do show that? who has read'em,
: anyway? If Qx does not validate non-Gompertzian trends, where
: does that leave the assertion of a slowdown in death rates
: among the really old?
Well, I think the phenomenon cannot be denied, although the *reasons* for 
the decline as well as the extent of the levelling off in other species 
remain important issues for current research.  Alternative explanations 
include cage and density effects, genetic heterogeneity of individuals.  
These effects could produce a leveling off in the following way.  If 
mortality increases with density, then as time progresses, the density 
within a cage falls, as more and more flies die off.  This leaves the 
oldest flies with very low density and therefore with much lower 
mortality levels.  The argument for genetic heterogeneity is that the 
initial population consists of a mixture of genetically different 
individuals and genetic endowments strongly influence mortality rates.  
Thus flies with high mortality genes die off early, leaving a greater and 
greater proportion of flies with low mortality genes.  Selection proceeds 
thorugh the ages so that only the most robust of flies live to old age.  
If the selection process is fast enough, mortality rates can decline in 
the aggregate (even when they are remaining constant or even increasing 
for all individuals).

I think to a large extent these were addressed in the original articles 
and responses to letters that appeared later in Science.
The Carey et al. article conducted three separate experiments, two of 
which did not involve flies caged in groups but rather in isolation.  
There is still "confinement" in these isolation experiments, but there is 
fixed density.  The qualitative findings were the same as for the 1 
million  experiment that used grouped cages:  the mortality 
slowdown persists across all three experiments.   The experiments in 
Curtsinger et al. controlled  for genetic variation by using pure strains 
of Drosophila.  While genetics played a considerable role in determining 
longevity, within each strain the same mortality levelling off was 

: Bye all ... PJH.

--Carl Boe
UC Davis

p.s. disclaimer:  I have a vested interest in the above as I am Jim 
Carey's lab at Davis.

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