In article ,
 dkomo  wrote:

> Suppose that animals remained at the age of peak fitness and sexual
> maturity indefinitely.  They wouldn't grow old and die from old age. 
> And they would also be able to mate and produce offspring without
> regard to how old they were.  Would such a situation quickly lead to
> ecological disaster, and is this the reason that senesence evolved in
> the first place?
> 
> Well, it's possible that under such an assumption the natural world
> wouldn't look too much different from the way it does now.  In the
> wild few animals have the luxury of growing old.  They die from
> environmental causes long before they can die from senescence.  They
> die from disease, starvation, thirst, predation, climatic changes,
> dominance and territorial disputes, natural disasters like flood and
> fire, and so.  In zoos many animals often live twice as long on the
> average as they do in the wild, and it is only in zoos that we can see
> them die from the diseases of old age.
> 
> Surprisingly, the age distribution of a population of "immortal"
> animals has the same exponential tail as a "survival chart" of aging
> animals does.  That is, plot the number of animals versus their ages
> and you'll see an exponential drop off as age increases.  It's
> counter-intuitive, but if the death rate of a population is *constant*
> without regard to age, then the age distribution will be a decreasing
> exponential.
> 
> This can be shown quite easily.  Let r be the death rate expressed as
> probability per unit time.  Take a large sample of ageless animals all
> of the same age.  Then in a small time interval dt the number of
> animals that die is
> 
>            dN = -N r dt
> 
> N is the number of animals at time t.  The minus sign indicates a
> decrease in N -- dN is negative in other words.  I'm using Mathematica
> convention where two variables separated by a space means
> multiplication:
> 
>                 A B = A*B
> 
> So  dN/N = -r dt  and integrating both sides we get 
> 
>     log N = -K1 r t     where K1 is an arbitrary constant
>                         of integration
> 
> and finally    N = N0 exp(-r t)  where N0 is initial size of the
> sample at t = 0.
> 
> This is exactly the same equation that as that for radiactive decay. 
> It also governs the decrease in the population of any set of things
> that are removed at a rate r, for example a population of glasses in a
> bar that break at a rate r.
> 
> Thus if we looked at a population of immortal animals that
> nevertheless get zapped by their environment at a constant rate, we'd
> see a lot of young animals, fewer older ones and *very* few really old
> ones.  In other words, the age distribution doesn't look much
> different from that of a normal population.
> 
> And this analysis leads to a mystery: why did senescence evolve at
> all?  From this perspective, there seems to be little use for it.
> 
> Well, it turns out that the above analysis has a serious flaw in it. 
> Can you tell what the flaw is?  Hint: it has nothing to do with the
> mathematical derivation.  Once this flaw is carefully analyzed, we can
> begin to understand why senescence in the plant and animal worlds is
> virtually universal.  Senescence evolved because it's critical to the
> survival of life.
> 
> 
>     --dkomo{at}cris.com
> 

Didn't _Why We Get Sick_ deal with this? Although given a certain level 
of fertility, it would be an advantage to live unlimited amounts of 
time, but that level of fertility is a result of tradeoffs, many of 
which result in pleitropic effects later in life.

-- 
|                   Andrew Glasgow                    |
| "We deal in the moral equivalent of black holes, where the normal laws of |
| right and wrong break down; beyond those metaphysical event horizons      |
| there exist ... special circumstances" - Ian M. Banks, _Use Of Weapons_   |
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