Xjyuk

There was an apocalypse. Humans left cities in swathes, leaving their canine companions behind in the ruined cities. My question is, which types of dogs survive?

Criteria
-The dogs are going to be left up to their own devices for the next few generations.
-The general ecosystem is the same as it was before the war

Dogs are dogs. Barring some of the more physically-incapacitated dogs, as long as they have a means of escaping their homes, there is unlikely to be any particularly advantageous breed.

• A feral dog lost as a puppy easily sustained itself off hunting.


• Millions of dogs live on the streets in Mexico


• The St. John's water dog lived as a feral breed for decades or centuries in Newfoundland


• 
  Chihuahuas are surprisingly vicious, and do well in warm climates as feral dogs.

That last one does offer some insight - the dogs that would do best in any given city would be the dogs who are best suited for the local climate. A husky or eskimo dog, used to air-conditioning in South Carolina, would probably fare poorly if suddenly left to the elements. A chihuahua or doberman, with velvety-thin fur, would probably do badly without humans to put their coats on in a Chicago winter.

But when it comes to being able to hunt for their food - dogs are dogs. They're generally pretty good at it.

Edit: It's worth noting that most responsible dog owners will spay or neuter their pets, so after a decade or so, the number of dogs will be drastically reduced. This will presumably rebound after an interval, but most pets will die without reproducing, because they cannot.

None.

Dog breeds are a human invention. Eventually they will breed out to look more and more like wolves as they bred with wolves (because they are a subspecies of wolves). In fact the more 'bred' a dog is the less survivable it becomes. Think of the contemporary pug with their squished faces, or this: http://blog.vetdepot.com/top-10-dog-breeds-with-the-most-health-issues

also for more discussion:

https://www.quora.com/How-many-generations-would-it-take-for-dogs-to-revert-to-wolves-if-a-wide-cross-section-of-modern-breeds-were-left-to-breed-freely

Mongrels

There is no reason to think that left to themselves, dogs will remain in breeds. They will cross breed. In a few generations, there won't be any separate breeds. All dogs will be mongrels.

There may be some specialist types. For example, smaller dogs may specialize in hunting in tunnels (e.g. rabbit warrens). The largest dogs will likely become smaller, as large dogs are subject to back and joint problems. Long-haired dogs may appear most often towards the poles and short-haired may tend towards the equator.

Mongrels exhibit hybrid vigor and are healthier than purebred dogs. If dogs are left to themselves, mongrels will take over the world.