The frequency is much higher in first generation crosses to affected breeds, and also higher in second generation crosses of affected breeds. For example, if you have a first generation German Shepherd cross with almost anything, the frequency is not that different from what it is in purebred GS. If you cross that mutt with an Akita/something else, you’re still likely to have HD
If Akita breeders have improved their situation since last time I had direct information, I apologize; the German Shepherd situation may never improve; they’re too popular, and too many that fall into the hands of backyard breeders.
If you’re talking about “Heinz 57” mutts, and they’re not very big (under 40 pounds is my best guess), then the likelihood is lower. The best way to be sure you won’t get a dog that winds up with HD eventually is to get a purebred dog that has three generations or more of OFA certified ancestors.
All of the giant breeds (Danes, Irish Wolfhounds, Great Pyrenees, Newfoundland, Old English Sheepdogs, Mastiffs (any kind), Saint Bernards, Komondorok … Can’t pull any more out of the memory bank right now) have shorter lifespans than smaller dogs. There are a variety of reasons, and I can list them for you, but in any breed, there are bloodlines that live longer than average, and each of those has a (different) most common reason of death, as well.
If a person absolutely demands that a dog have a very long expected lifespan, then there are several toy breeds that often live to 15 or more - toy Poodles, Chihuahuas (but not the teacups - they have much shorter average lifespans) and Affenpinscher are ones that come to mind just now. Any of these, if it’s a healthy puppy to start out with, and from a bloodline (there are real advantages to good linebreeding) that has a reputation for being healthy and long-lived, has a good chance. But of course when you do something like that, better hope the Fates aren’t listening. :dubious: Accidents can happen, and there are infectious diseases that can kill off any dog.
When you say “short”, what do you mean? The average is usually given as 7 years. Many dogs of my bloodline lived to 10 years. The champion that my line was based on lived to 12, and litters sired by him were born after his death (i.e., he was healthy and fertile up to the end). A number of his offspring lived to 10 or more. The oldest Dane I’ve heard of lived to 14, but that was another bloodline. I could tell you how to find one that would have a high probability of living to 10, but I shouldn’t do it here. If you want me to do that, send me an email.