"Anon."  wrote in
news:cp25jl$1ln9$1{at}darwin.ediacara.org: 

> William Morse wrote:

>> So what we would like to have is a definition that, like yours, takes
>> into account alternate future environments, but that can be extended 
>> farther into the future. I have a rather fuzzy mathematical intuition
>> that if you somehow combine Markov chains with a discount factor for 
>> expected future gains you might come up with a reasonable
>> approximation of a fitness function - recognising that fitness is
>> always going to be ultimately only definable in retrospect.
 
> If you know how the discount declines with generation, this will work
> as well.  Especially as you don't need the whole Markov chain: you
> only need to take expectations.  This simplifies the calculations (at
> the cost of a bit more maths).
> 
> The approach is similar to Fisher's original definition of fitness (in
> his "Genetical Theory of NS"), but extended over several generations. 
> Until I get involved in an actual application, I can't be bothered to 
> work out the precise derivation (or check to see who has already done
> it). 


You know, I really need to sit down one of these days and read "Genetical 
Theory of Natural Selection". At best I have only read a few excerpts and 
lots of references. Perhaps after I finish with "Sociobiology" - which 
isn't going all that quickly. Wilson may find ants fascinating but they 
keep putting me to sleep - fortunately I am using it as bedtime reading 
:-)

But as you implied,  I would guess that if there is any validity to the 
idea someone has in fact come up with a mathematical treatment along 
these lines - it isn't exactly a stunningly original thought. 

Yours,

Bill Morse
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