Ω3 and probiotics are at the top of the pyramid as they are needed in smaller quantities but are also one of the most important link for a healthy diet.

Omega-3 fatty acids are a type of unsaturated fatty acid that may reduce inflammation throughout the body. Inflammation in the body can damage your blood vessels and lead to heart disease and strokes.
Omega-3 fatty acids may benefit heart health by decreasing triglycerides.

Probiotics are live bacteria and yeasts that are good for your dog but also for you, especially your digestive system. We usually think of these as germs that cause diseases. But your body is full of bacteria, both good and bad. Probiotics are often called "good" or "helpful" bacteria because they help keep your gut healthy. So don't be afraid to include in your dogs diet cottage cheese, yogurt, spirulina, kelp, bananas and even small quantities of garlic.
read more

Dogs need some carbohydrates, about 10% should be more than enough.some veggies are considered to also have probiotic values and most fruits and veggies are ok for your dog to eat but some are not. avoid at all cost onions, and from fruits avoid grapes, as both of that products could do great harm to your dog
Some dogs under special climate environment like in alaska don't even eat carbohydrates. read more
other important probiotics are spirulina, yogurt, kefir.
read more

meat, fat and bones are the largest portion of your dogs diet. Don't forget to include intestines as they hold the most important nutrients but don't over do it with the liver which has also some toxins so keep it at 5% of your dogs daily portion.
MEAT is the best source of protein, include white and red meat in your dogs diet.
FAT is also essential and shouldn't be confused with saturated fat which occurs after heating or cooking which destroys all the value and becomes a byproduct to the body and suppresses the immune system.
you can also add peanut butter to your dogs diet which has good unsaturated fat.

BONES have many nutrients in them and should also be included in your dogs diet. But beware, only raw bone is digestible by your dogs stomach
Glucosamine and chondroitin is a natural compound found in cartilage — the tough tissue that cushions joints.
Dogs that eat raw bones can delay the effects of degeneration as the animal ages. For older dogs or if there is an injury or concern, the therapeutic value can slow the progression of the injury and expedite the healing process. Larger breeds of dogs are typically more prone to hip dysplasia.