Kevin Aylward wrote:
> Anon. wrote:
> 
>>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).
> 
> 
> Oh?
> 
Yes.  Fisher, R.A. (1930) The Genetical Theory of Natural Selection. 
Chapter 2.

> 
>>See, for example Brommer, J.E. (2000) The
>>evolution of fitness in life-history theory.  Biol. Review 75:
>>377-404.
>>
> 
> 
> Er.. how about actually posting the relevant bit? Like, we are all going
> troll around looking for references. By itself, this reference citation
> says nothing.
> 
My hope is that you would be sufficiently interested to read it. Jon 
reviews several different ways of defining fitness that has been used.

> I would be very surprised if it avoided the fundamental issue. As I
> noted in the bit you sniped.
> 
> F = d(mv)/dt, defines force and mass in a circular way. For example,
> what is inertial mass. wee, its a measure of how must it resist smotion
> when a force is applied. Well, what is a force, its something that
> accelerates a mass...
> 
> This is a basic issue absolutely inherent in any science. The
> fundamental defining equations are pretty much always circular.
> 
But as we do not need to define fitness using these equations, the 
problem can be sidestepped.

Fisher's insight here was to define fitness in terms of the probability 
of living to age x, the rate of production of offspring at age x, and a 
penalisation term for the time taken to reach age x (!).  this all gets 
put into the Euler-Lotka equation, which can be solved to give the 
Malthusian parameter, i.e. the rate of increase.

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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