Those 2-3% portions of your dog’s DNA might in a region of the DNA that influences those traits — body shape and personality — though there’s still much to discover.
Scientists use an approach called “ancestry mapping” to find those regions that influence traits based on ancestry. We will be using this approach to study behavior in a few ways; for example, studying retrieving behavior by looking at Poodles, Retrievers, and a variety of “-doodles”.
Say there is a part of the DNA that influences whether a dog fetches. A 4/5 Poodle & 1/5 Golden Retriever might be a fetching fanatic because they have retriever ancestry at that place in their DNA; likewise, a 1/5 Poodle, 4/5 Labrador might not be into fetching, just because they don’t have retriever DNA at that spot. This is what we hope to find out using ancestry mapping!
As for DNA being static — yes, and no. The genetic code of DNA is very stable, but many traits are not dominant-recessive and depend on many parts of DNA as well as environmental factors.