Man’s right to rule over God’s creation is linked with Adam being made in the image of God. Being in the "image of God" means that man is created to represent God over the creation. He is to rule over God’s creation for the glory of God. This truth is discussed in Psalm 8:4-8:
And the son of man that You care for him?
Yet You have made him a little lower than God,
And You crown him with glory and majesty!
You make him to rule over the works of Your hands;
You have put all things under his feet,
All sheep and oxen,
And also the beasts of the field,
The birds of the heavens and the fish of the sea,
Whatever passes through the paths of the seas.