Kevin Aylward wrote:
> Anon. wrote:
> 
>>Kevin Aylward wrote:
>>
>>>Anon. wrote:
>>
> 
>>>>>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 -
> 
> 
> Well, not in this context. What we measure, at any given point in time,
> is the population numbers. That's it. Sure, length of survival has an
> effect on he numbers, but it can all be included in the wash.
> 
> 
>>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,
> 
> 
> Its really in the time per generation, but this has been made constant
> in this approximation. This is just a simplified model, used to derive a
> couple of key features. It can be included in N, as N is really an
> average number, or another term.
> 
Don't let John see that!

Bob

-- 
Bob O'Hara

Dept. of Mathematics and Statistics
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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