Kevin Aylward wrote:
> Guy Hoelzer wrote:
> 
>>Hi Kevin et al.,
>>
>>On "survival of the fittest" and tautology:
>>
>>in article btldlc$2svv$1{at}darwin.ediacara.org, Kevin Aylward at
>>kevindotaylwardEXTRACT{at}anasoft.co.uk wrote on 1/8/04 9:19 PM:
>>
>>
>>>Recognition of a tautology can be very useful. "Survival of the
>>>fittest" is actually fully equivalent to :
>>>
>>>"That which is observed mostly, is that which replicates
the most".
>>
>>Actually, this is a tautology because it is not necessarily true.
> 
> 
> A "tautology" is *defined* as something that is true by
*construction*.
> If it isn't always true, it not a tautology.
> 
> 
>>The
>>things that replicate most will not necessarily be the things that you
>>observe most.  I could give you several examples, but I hope the
>>following will suffice.  Imagine you have a large population of
>>organisms reproducing at some particular rate.  Now introduce a new
>>mutation occurring in one individual that causes it to replicate more
>>than the rest of the population. During the inevitable period when
>>this mutation is rare you would observe that the form which
>>replicates most is not the one mostly observed.
> 
> 
> Yes, I agree that this is true, but not applicable in the context of
> when it is used. Maybe I should have been a bit more clear on this. It
> should be inherently understood that the statement is to be applied only
> to steady state conditions, not transient conditions. In my papers, I do
> specify exactly the condition for its validity in its actual derivation:
> 
> http://www.anasoft.co.uk/replicators/replicatortheory.html
> "So, it can be ascertained that if there is a consistent and continuous
> replication rate advantage of one trait verses another, the one that is
> only slightly better, will, given enough time, completely dominate".
> 
> It is also possible
> 
>>that such a mutation will even be selected against if it involves a
>>trade-off with life-span, or its frequency could be influenced more
>>by stochastic factors than selective ones.
>>
>>The sense in which "survival of the fittest" is
tautological is that
>>fitness is often defined as those that survive.
> 
> 
> http://www.anasoft.co.uk/replicators/replicatortheory.html. The basic
> equation is:
> 
> dP/dt = f.P
> 
> P is the population, f is the fitness.  The issue is, how do we
> determine f?
> 
> This equation, actually *defines* f, so it can only be deduced by
> knowing both P, and dP/dt
> 
Fitness can be defined from life history theory (indeed that's how 
Fisher did it in 1930).  See, for example Brommer, J.E. (2000) The 
evolution of fitness in life-history theory.  Biol. Review 75: 377-404.

Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
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