My Labrador is losing fur on his tail. Is it thyroid or alopecia?

Great question. Hypothyroidism is very common in labradors but can easily be diagnosed with a simple blood test performed by your local veterinarian. Seasonal alopecia can also occur but typically can be eliminated with routine bathing and grooming. Since your dog is un-neutered, much of your dog's nutrition is going into energy and activity, so be sure to feed a high quality diet with plenty of fat for energy and haircoat production. Usually the better diets are highly digestible and produce low stool volume compared to cheeper diets.
Bottomline, if you're worried about thyroid disease, ask your veterinarian to pull blood and rule it out, otherwise feed great diet and bath/groom as needed to control hair loss. If the coat doesn't look right, then schedule an appointment to have it examined to check for other possible causes such as parasites, allergies, or nutritional causes, Good luck and thanks. Steve Popish, DVM