It's an interesting question- under the generally accepted definition, if two types of animals cannot breed to create fertile offspring, that would make them different species.
Under that definition, we would have to carve up dogs into several different species, as many breeds of dog cannot naturally mate with other breeds (Great Danes and chihuahuas).
You're right- species is a human construct.
"Under that definition, we would have to carve up dogs into several different species, as many breeds of dog cannot naturally mate with other breeds (Great Danes and chihuahuas)."
Not only that, but what about two breeds of dog that can only produce fertile offspring 50% of the time? 90%? 10%?