This is not a branch of agriculture but a branch of medial science.
The FBI would be under the Executive branch, the branch if government that is responsible for enforcing the law.
Geography
veterinarian
The career of veterinary medicine is classified with medical professions.
Nutrition would be the broad field.
Say the executive Branch is Republican. The Cabinet is then full of Republicans. The Shadow Minister of agriculture would be the Democratic Party's critic who focuses on agriculture.
There is no particular branch which deals with extinction, but it would fall under zoology,
this would happen to be veterinarian
The phenomenon of buoyancy would be classified under the category of hydraulics.
2
It could be many reasons and only a Veterinarian would be able to find out what is wrong with your dog. It could be demodex, a type of mange mite. You should take your dog in to be checked out by a Veterinarian.
The Executive Branch would have to approve of the new law (in most cases), and use the agencies under its authority to enforce that law.