May 3, 1994
Dear AGEING LIST subscribers,
The purpose of this message is to invite you for scientific
discussion of the recent paper in NATURE:
Hughes, K.A. & Charlesworth, B. A GENETIC ANALYSIS OF SENESCENCE
IN DROSOPHILA. Nature 367, 64-66 (1994).
Our own comments on this paper are printed below. Your response
would be greatly appreciated.
Of special interest are responses of the authors:
Kimberly A.Hughes (Chicago Zoological Society, Brookfield, Illinois)
Brian Charlesworth (Department of Ecology and Evolution, Chicago)
By the way, does anybody know their E-mail addresses ?
Thanks,
Dr.Leonid A.Gavrilov and Dr.Natalia S.Gavrilova
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TESTING THE MUTATION THEORY OF AGING:
A SIMPLE EXPLANATION FOR MORTALITY DIVERGENCE
SIR - Hughes and Charlesworth [1] provide a fascinating picture
(Fig.1), demonstrating great increase in variability of mortality
in male Drosophila melanogaster at very late ages, as predicted
by the mutation accumulation hypothesis of senescence. In
particular, they demonstrate that regression lines of log(mortality)
on age, are starting virtually from the same point (similar intercepts)
but are diverging greatly afterwards (different slopes). Since this
observation is quite opposite to previous reports on relative
convergence of mortality rates at late ages both in drosophila and
humans (known as compensation effect of mortality) [2], we have tried
to find out the reasons for such a fundamental contradiction.
We suggest here a simple explanation for mortality divergence
observed by Hughes and Charlesworth [1] and for the contradiction of
this observation to previous reports [2]. Although Hughes and
Charlesworth followed the Gompertz model (exponential increase of
mortality rates with age) for data analysis, they used very unusual
non-Gompertz transformation of data to receive straight regression lines:
instead of calculating the logarithm of mortality rate as a function
of age (as they indicated on the plots of their Fig.1), in fact
they calculated log(mortality + 1) as it was written in legend
for Fig.1. Since mortality rates are very small (less than 0.1)
at young ages, even a great relative difference in mortality between
populations will be completely masked after adding 1 to these
very small numbers. For this reason only, all regression lines
will inevitably have virtually the same starting point (similar
intercepts). Since at very late ages the mortality rates are rather
high (up to 0.8), the relative difference in mortality between
populations will not be completely masked at high ages even
after adding 1 to these numbers. Thus, observed divergence of
mortality is an inevitable consequence of non conventional way
of data transformation (adding 1 under the logarithm) used by
the authors [1]. When conventional methods are used, quite
opposite phenomenon of relative mortality convergence is
observed both in drosophila and humans [2].
We can easily understand the reasons for non conventional
transformation of data used by the authors: in small populations
at young ages the observed mortality rates are often equal to
zero (when nobody dies) and it is impossible to calculate the
logarithm of mortality rate in such cases without adding some
positive constant number under the logarithm. The problem is
that this procedure produces artifacts through biased estimates
of both intercept and slope parameters. For this reason the
added constant should be extremely small to minimize biasing
(say, 0.001 instead of 1.0). The best way to escape this problem
completely is to estimate the Gompertz parameters directly by
the methods of nonlinear regression [2].
Leonid A.Gavrilov
Natalia S.Gavrilova
A.N.Belozersky Institute
Moscow State University
Moscow 119899, Russia
Fax: 7 (095) 939-0338/3181
1. Hughes, K.A. & Charlesworth, B. Nature 367, 64-66 (1994).
2. Gavrilov, L.A. & Gavrilova, N.S. The Biology of Life Span:
A Quantitative Approach (Harwood Academic, Chur, London,
1991).
Dr. Leonid A.Gavrilov, Ph.D.
Dr. Natalia S.Gavrilova, Ph.D.
******************************THE END*********************************
--
________________________________________________________________
-- Dr. Leonid A. Gavrilov, Ph.D. Phone: 7 (095) 427 0047
Principal Research Scientist FAX: 7 (095) 939 0338 or
A.N.Belozersky Institute 7 (095) 939 3181
Moscow State University E-mail addresses:
Moscow 119899 gavrilov at aeiveos.uucp.free.msk.su
Russia libro at genebee.msu.suaeiveos at glas.apc.org
Please send your answer to my most reliable E-mail address:
aeiveos at glas.apc.org
if you wish to be sure to reach me. Thank you !
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