From: szabo@techbook.com (Nick Szabo)
Newsgroups: sci.bio
Subject: Re: sexual selection
Summary: ESS explanation
Date: 6 Sep 92 15:24:19 GMT
Organization: TECHbooks --- Public Access UNIX --- (503) 220-0636

In article <28AUG199212530422@utkvx4.utk.edu> ljones@utkvx4.utk.edu (Jones, Leslie Lamont) writes:

>     I think the advantage of sexually-selected characters are better 
>described by the "sexy son" theory. In this model, females are attracted
>to certain males because they are hardwired to find the males attractive.
>Instances of hardwiring have been discovered, as in the case of sword-
>tailed fish which S.J. Gould discussed in his column a few years ago.
>     The advantage for the female is that she will bear some sons 
>who will be sexy, reproduce, and spread her genes, including those genes which
>find those particular male characters sexy. It then becomes a case of runaway
>selection, with females producing sexy sons and daughters who find the sons
>sexy (thought there is no implied incest; the lines can propogate separately 
>with distant cousins mating.)

Both this and the kerosene-drinker explanation seem incomplete.  Where did 
these two adaptations originate, and how could they spread?
How did the female get "hardwired" in the first place?  Why would her
sons prosper, if the only plumage lovers are mother and daughters, and
there is no incest?  How is it that both plumage-loving and plumage, two
completely different kinds of structures, arise at the same time?  What
is the probability that they would ever be genetically linked?

Let's see what happens using J. Maynard Smith's evolutionary stable 
strategy theory.  Let's postulate gene M for growing plumage, gene m 
for being plain, gene F for preferring plumage, and gene f for prefering 
plain Waynes.  Assume some males fertilize multiple females, some males 
none, all females are fertilized by one male, and choice is entirely the 
female's; ie polygyny.

Let's introduce F into a population with all (m,f).  Neutral: she's
going to breed with a male even if not her favorite, and she doesn't
lose by doing so. Let's introduce M into a population of (m, f). 
Neutral, assuming M has no cost, because f will as readily choose M as m.
Let's introduce f into a population (M, F).  Neutral.  m into 
population (M, F). m loses, because F's choose M's when they are
available.  . We can summarize this in a table:

s=spread,d=decline,n=neutral
		M	F	m	f
(m,f)		n	n	n	n			
(M,F)		n	n 	d	n

In other words, M and F can appear and survive by genetic drift, but
m can only survive where there are some f's.

We can also look at the relative gene frequencies in a mixed
population, where M>F means there are more M-bearing males
than F-bearing females, more plumage bearers than plumage
pickers.

s=spread,d=decline,n=neutral
		M	F	m	f
M>F		n	n	n	n	
M<F		s	n	d	n	
m>f		s	n	d	n		
m<f		n	n	n	n	

Thus M>F is neutral, but m>f, which is the same as M<F in our
simplified model, favors M. 

So here is a scenario: F appears in (m,f) and grows to, say, 10% of the
population via genetic drift.  M appears, and M<F, so M spreads to
10%.  

Let's say m's get lucky and M is reduced to 5% by drift. Soon M will
pop back to 10%, pulled by F's. If M drifts up, it can stay at the 
new level, since it is not limited by the number of F's.  Let's say
f drifts up.  M is not effected.  Let's say F drifts up.  M moves
up to join it.  Thus, M (if it has no cost) meanders when it is
above F, and is ratcheted up by F, but it does not drift below F.  

Let's say half of the M's die each generation from starvation due
to the extra cost, and no m's die, but F=2M.  M's still double their 
offspring in a generation, at the expense of m's: the overall M fitness 
is unchanged! If, however, a male is limited to y matings, then if the 
percent of M's killed exceeds 100%-1/y, M declines. As you can see, we 
assume y>1 for sexual selection to work at all, that is we assume polygyny.

If M has a cost it cannot drift up, it can only be pulled by the drift of F.  
As with the no-cost M, a costly M is driven by the genetic drift of F, 
which itself may have no cost it all, and may in fact be a side-effect 
of a gene with some other beneficial phenotype.  Thus, where female
is the receptor and chooser of male insemination, even a whimsical
method of choosing, as a side effect of a gene even slightly beneficial 
to her. can ratchet up very costly and seemingly beautiful but wasteful 
responses in male evolution.  This is sexual selection.

(P.S. I just did this on my own, but I assume I'm not the first to
apply ESS to sexual selection; does anybody have references to similar
work?  If not, reference me when you publish... :-)


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