Kevin Aylward wrote:
> Anon. wrote:
> 
>>Kevin Aylward wrote:
>>
>>>Anon. wrote:
>>>
>>
> 
>>>
>>>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.
>>
> 
> 
> I'll have to have a think on this. It seems similar to the approach that
> I have already taken e.g.
> http://www.anasoft.co.uk/replicators/replicatortheory.html
> 
> Where I have:
> 
> N = Quantity factor - average of replications in a generation period by
> a replicator. i.e. how many Replicators a Replicator combines with in a
> generation period. e.g. 10 mates per day.
> 
> Q = Quality factor - average number of surviving Replicators generated
> per Replicator combination. i.e. how many offspring Replicators are
> generated with each combination. e.g. 2 offsprings per mate (Q is
> usually < 1). The assumption here is that the offspring replicators
> survive for their own generation period.
> 
> GRR = Generation Replication Rate - GRR=Q.N e.g. GRR=mates/day x
> offsprings/mate = offsprings/day = replications/day.
> 
> Fitness = GRR.
> 
> I don't consider the life length (generation time), by itself, that
> significant. Its a numbers counting game.
> 
Alas it is - reproducing earlier will be better (everything else being 
equal).  You also haven't included survival in your definition.  It's 
perhaps implicit in N, but in practive survival is an important fitness 
component, so it would be better to include it explicitly at this point.

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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