"I am familiar with logistic growth (S curve) where the rate of increase is related to the distance to the level of saturation. How is that related to differential reproduction and the velocity of diffusion of advantageous characters? An empty space will stop diffusion, agreed, but a sparely populated space will not." 
 
If you look at the reaction term in the Fisher's equation, p(1-p), you can see that that is a logistic growth type of term. In this case, troughs in population density CANNOT stop the wave of advance. However, in the "bistable" version, p(1-p)(p-phat), the trough can stop the wave. The intuition for this is that if there is too steep a change in population density, then there won't be enough genes diffusing into the area to overcome the unstable point (recall what Agnostic explained about p < phat implying that the frequency goes down to zero), and hence it will be stopped dead in its tracks.

"In the PDE you show first, the term on the LHS has dimensions of inverse time. The two terms on the right are dimensionally incompatible with that and with each other. I'd guess that some sort of diffusivity and rate constant are missing, unless the equation had been nondimensionalised so that t and x are dimensionless already. But if so, it is odd that it is completely free of parameters, even dimensionless ones." 
 
Ah yeah, there is a diffusivity constant I left off. Technically there should be a "sigma^2/2" multiplying the partial wrt x, which is the variance in parent-offspring distance per unit time. "s" is the selective advantage of one allele over the other, given in units of 1/time---it can be interpreted as the less fit gene leaves (1-s) as many copies as the more fit gene per unit time. 
 
"So it seems that advantageous genes propagate rapidly through fixed populations, but slowly through space. Would I be correct in viewing this as good support for punctuated equilibrium?" 
 
Hrm, to be honest I've never thought about that. I don't think it would be a support for the process of punctuated equilibrium, but could explain the fossil record in some sense: suppose that many new advantageous genes arise in peripheral populations and have to diffuse into the central population, which may be where we get most of our fossils from. Just some speculation.

I should be clear that it's only in the case where there is an internal equilibrium that the wave can stop because of the population density. And technically it's due to the gradient in density, not just the actual density.

It's like a free version of mathematica in some respects, at least. It's fun to make it solve differential equations :)

Begging the question much, Agnostic? You're using your data support your assertion that most college kids don't care. Then, when your inference is questioned, you respond by saying most college kids don't care.  
 
Circular reasoning if I've ever heard it ;-)

Coolest. Paper. Ever.

I hope to get to this discussion soon in my series of posts... finals is over, but lab work is heavy :(

My problem with those kind of objections to the BSC is related to a problem I see a lot in philosophy. We really feel like there's some concept "out there" and we can tell when something falls into this or that category "intuitively", but when it comes down to it, we don't really know what we're talking about. 
 
So when we're studying these diverse morphs that are "obviously" different species, and we wonder how they got to be so different, we're not really talking about the process of speciation.

Oh yeah, definitely. This is actually one of my pet peeves. I absolutely don't think that the BSC applies to bacteria, for example. Among sexual organisms... I'd have to see a case where there's some question. 
 
As another quick note, I also think that some of the other species concepts are semi-parasitic on the BSC. Some phrasings of the phylogentic species concept seem to imply BSC, and the BSC certainly implies phylogenetic species concept...