Tim Tyler  wrote in message
news:...
> Name And Address Supplied
 wrote or quoted:
> > "John Edser"  wrote in message
news:...
> > > Tim Tyler  wrote:
> > > Name And Address Supplied
  wrote or quoted:
>  
> > > > > NAS:-
> > > > > The appropriate maximand is something which might
be called 'relative
> > > > > fitness'.  This obviously doesn't increase over
time, since the
> > > > > expectation of relative fitness at all times is 1.
>  
> > > > TT:-
> > > > That sort of relative fitness has some problems of its
own.  Who else
> > > > do you include in the population?  Only other members
of the species?
> > > 
> > > JE:-
> > > The biggest problem with the concept of "1" 
> > > as relative fitness comparison maximum is that
> > 
> > 1 is not the maximum; the average is 1.
> 
> Relative fitness is often defined as being a value between 0 and 1 - e.g.:
> 
> ``Relative Fitness
> 
>   The selection coefficient is used to model the health of an individual 
>   relative to the health of the rest of the population. 
> 

This is sensible

>   The relative fitness of an individual, denoted w, is defined to be 
>   w=(1-s)^n where n is the number of mutations the individual carries. 
>   Note that w is also a value between 0 and 1, where 1 indicates a 
>   perfectly healthy individual (no mutations) and values less than 1 are 
>   relatively unhealthy individuals.''

This contradicts the previous statement. (1-s)^n is not the fitness of
the class of individuals with n mutations relative to "the rest of the
population", but rather it is relative to the zero class. If we really
were to measure the fitness relative to the population as a whole,
then some of the population members would have relative fitness
exceeding unity.

> I guess you are probably referring to something like offspring / average 
> offspring - but fitness is notoriously a tricky term - so you might want 
> to spell out what you are talking about yourself.

I don't pretend that I can define it *exactly*, however it is clear
that the maximand is a ratio with the population average on the
denominator. I am confident that the expectation of the relative
fitness is unity, and so not something that can be increased,  i.e.
not a suitable measure of 'progress'.
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