Path: utzoo!attcan!uunet!shelby!snorkelwacker!bloom-beacon!eru!hagbard!sunic!news.funet.fi!hydra!hylka!xia
From: xia@cc.helsinki.fi
Newsgroups: bionet.population-bio
Subject: Average Fitness, Evolution of Sex and Others
Message-ID: <3347.2719f222@cc.helsinki.fi>
Date: 15 Oct 90 17:30:10 GMT
Organization: University of Helsinki
Lines: 59


          Average of Fitness, Evolution of Sex and Others
          ===============================================

In case that someone forgets, let me remind you that the average 
of fitness of a gene over generations is represented by geometric 
mean, not by arithmetic mean. Allow me to use an example to 
illustrate the reason behind this.

If a population of a gene makes 100 copies of itself in one generation, 
but 0 copies in the next generation and become extinct, then the 
average fitness of the gene is 0 (=square root of 100*0), not
50 (=(100+0)/2).

Suppose a locus with two alleles, A and a. Allele A always makes X
copies of itself per generation, but allele a makes X+s copies in
50% of generations and X-s in the other 50% of generations. After 
2N generations, the number of copies of allele A will be

                 
                 2N  
	N(A) =  X  ,

while the average fitness of allele a during the same period is

                    N      N                N
	N(a) = (X+s) *(X-s)  = ((X+s)*(X-s))


                2   2 N
             =(X - s ) .

                                 2    2    2
Apparently, N(A) > N(a) because X  > X  - s. Therefore, allele A
will eliminate allele a over the long run.

(BTW, the above simple formulation is the foundation of the so-called
bet-hedgeing in life-history theory.)

One theorem we can draw from above is that an allele with less
variable fitness over generations will eliminate an allele with
more variable fitness over generations, although both have the
same arithmatic mean fitness over generations.

A corollary of the theorem is that any gene that reduces fitness
variability of its carier will be favoured by natural selection.

The gene for sexual reproduction is such a gene, it reduces the 
fitness variation of its carrier 1.414 (=square root of 2) times.

The gene for promiscuity is also such a gene when an animal is not
sure of fitness potential of its mates. This may even be applied 
to human societies.

(to be continued)

(Please let me know if my writing is interesting so that I won't
keep posting things that you do not read.)