Is race a social construct where dogs are concerned?
No, at least among dogs (
Canis lupus familiaris) it isn't. Dogs, like humans, are social creatures. In general and provided there is no "zero-sum" resource shortage appertaining to the circumstance of the dogs' interactions and shared existence, dogs get along with other dogs. Dogs generally have little compunction about welcoming new members into their pack and what the other dog(s) looks like doesn't factor into it, unless the would-be new member is particularly infirmed or physically handicapped. It's probably worth noting too that while there is a hierarchy among dogs in a given community, a pack, the hierarchy has nothing to do with what pack members look like; it has to do with demonstrated capability and tenure.
Unlike
Canis lupus familiaris, humans have created a social construct concerning race. Race is not the only partitioning construct that humans conceived and emplaced. The zero-sum construct of political borders is another. While animals, including dogs have some sort of territorial concept, "ownership" of the territories they claim constantly changes, sometimes by battle and other times because the current "owner(s)" decides it's time to move. The presence or absence of food is largely what drives that behavior, though the quest for sex in some instances does it too. If a dog is in place where its survival and reproductive needs are adequately met, it's not going anywhere until one of those things ceases to be so.
In reading the above remarks about territory, be sure not to confuse "territory" with "home range." Also, be sure to keep cognizant of the distinction between trained and instinctual responses to stimuli.
- A dog's (dog pack's) territory is analogous to a human's house, whereas it's home range is more akin to a country, city, county or state (pick one; it doesn't much matter at this point in the discussion which one picks). What's the key differentiator between the two areas? Dogs defend their territory from encroachers, but they don't defend their home range. Other dogs can come, hunt, drink, cavort, chill, traverse, have territory of their own, etc. in a dog's home range. Other dogs cannot take up residence in a dog's territory. In other words, home ranges overlap whereas territories do not. (Territory size varies and depends on a host of factors, but as noted above, proximity to food, shelter and water are the key drivers.)
- Dogs are "man's best friend" in large part because of their innate amenability to take training. That training over time basically creates a "working model" in dogs' minds whereby the dog perceives its survival and that of its "pack of two" (it and it's pack-leading owner) is partly predicated on/enhanced by its actively serving what you and I would call the will of its owner (pack leader). Dog training, which is nothing more than a more focused and less consistently implemented form of domestication, simply takes one or more aspects of dogs' instinctual behaviors and places far greater emphasis on them than would be fitting (in the dogs' mind) were it feral or even just not-trained yet also not feral.
OT:
The difference between house cats and dogs has always stuck me. Cats seem to want everything and nothing to enter their home range. It doesn't matter what moves through or exists in a cat's range, if the cat knows about it, the cat will in some way interact with it: pee on it, play with it until it's dead, kill it (though if it's not learned to eat wild food, it probably won't eat it), chase it off, or watch/follow it around. Dogs, on the other hand, seem always have foremost in their minds one thought: "hmm, is this something that'll play with me?" Sometimes the answer is "no," in which case there's aggression, but if it's not no, dogs are "down with" a new creature's presence. (Unless, of course, the dog is trained as a guard dog, but that's trained behavior, not innate behavior.)