Of course I also don't know what inheritable traits would make any given zombie more likely to survive and reproduce than another zombie.  Pointier teeth?  Faster shambling?  A fondness for liver in addition to brains?
These are some of the premises I use when considering zombies.
First off: Zombies Are Dead.
It's what makes a Zombie a Zombie.
If they weren't dead you'd be talking mind control, parasites, brain injuries, drug addiction, or mental retardation.
Zombies as an Organic Disease:
If you view zombies as a viral or bacterial infection then evolution is possible, but of the disease and not the host. The pathogen would evolve with each new host, and different strains would emerge with dominance being determined by the zombies who are the most effective at transmittal but not necessarily survival. The most common theme concerning transmission is that a host can catch zombie only through an exchange of bodily fluids; most frequently bite wounds, followed by scratches (presumably the fingers are hemorrhaging from injury or tissue failure), and then indirect contact (blood spatter).
As viruses can alter the genetic code inside cells, it 
might be possible to say that they 
could alter the physical properties of the host in small ways. This is not likely, nor do I believe it is adequately supported as I've yet to see a zombie do anything a sufficiently motivated human couldn’t.
Zombies as a Chemical Phenomenon:
If zombies are created thru man-made drugs (voodoo drugs and funny mushrooms count here too), than zombies could not evolve. Although bodily function could be interrupted and altered the drug would still have to act inside of the limits of human capability. All abilities would be based on the host's preexisting attributes: A zombie man could punch through a wood-covered window; a zombie weight lifter could rip the door off a car.
Zombies as a Paranormal Phenomenon:
Anything is possible, and your ass is probably grass. Go find an old priest and a young priest and a shotgun.
On Island Overpopulation:
It's nice to think that we can all get along, once the end comes, but we'll be competing for some rather scarce resources. The grim truth is that until things chill out and the zombie epidemic has peaked, it will probably be kill or be killed. You can't let your ship/castle/island/bunker be over crowded, and most likely you won't be able to afford the luxury of trusting strangers. Aside from being unable to support everyone and the heightened chance of infection (really, a full strip search and 2 minute medical check up, followed by a 24 hour quarantine would reduce the chance to near zero. Parties are always over run by the guy who hides that he was bit, not because no on knew), but because people in extreme situations often take extreme action. Anyone here a lifeguard? What is the risk of saving someone who is drowning? 
Teamwork is important, but no matter where you are you can only support so many people, and to exceed that for even a few people is to risk dooming everyone. Mothers and fathers know how far they'd go to protect their children (Flat Diane anyone?), so what happens when it comes down to one father vs. father? When it comes down to one or the other?
Defending your conclave from humans will be the harder part of surviving the zombies.