Mutation Theory of Ageing

Leonid Gavrilov gavrilov at aeiveos.uucp.free.msk.su
Tue May 3 07:09:05 EST 1994

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 ? 


   Dr.Leonid A.Gavrilov and Dr.Natalia S.Gavrilova


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, 

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.su
                                    aeiveos at glas.apc.org

   Please send your answer to my most reliable E-mail address:

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