An independent clause is a unit of grammatical organization that includes both a subject and verb and can stand on its own as a sentence. In the previous example, "I went running" and "I saw a duck" are both independent clauses, and "and" is the coordinating conjunction that connects them. Consequently, we insert a comma.
Why don't these sentences require a conjunction grammatically:
God is watching over you, I know because I asked him to.
God will open doors that no man can shut, you just be ready to walk through them
Put the book in the head, not on the head
The above are independent clauses so I would always put 'and' for example. The comma can represent contrast but it can do this with the conjunction also. What does the ommission represent gramatically.