As the only earthly critter created in the image of God, man (and woman) is the crowning act of creation by Elohim. The human species, remarkably enough, inhabits what appears to be a universe that is Planet-Earth-centered. This is not to say that our multi-galaxy universe is unimportant, or that critters other than human beings are unimportant. It is to say that there is something special, something of infinite worth, in the one of whom God said,
"'Let Us make man in Our image, according to Our likeness; and let them rule over [have dominion over all animal life]" (Gen 1:26).
Having said this, I must go on to say that just as God has dominion over everything and everyone He created, including the angelic host, both celestial and infernal, God delegated some of His authority to Adam as his representative on planet Earth. While I may be oversimplifying here, man's dominion over the earth was and is expressed in at least three ways:
in his caring for, tending to, enjoying, and investigating what God had created on, in, and above the earth, as well as in the sea. We know that Adam was given the task of naming all the lesser creatures God had created (Gen 2:19,20). For Adam to be able to do these things (and much more) and in so doing be a good steward or caretaker of God's creation, God gave Adam intelligence, rationality, and creativity.
in his ability to communicate and to have fellowship with his Creator-God. That is part of what it means to be created in God's image, since God, too, has intelligence, rationality, creativity, and above all the ability to communicate and have fellowship with His image bearers. God, of course, has these abilities to an infinite degree. We call them omniscience, omnipotence, and omnipresence. By contrast, our intelligence is finite; our strength is finite; our creativity has limits; our physical presence is constrained by gravity and the impossibility of being in more than one place at the same time; and our fellowship with God, interrupted by sin, occurs in fits and starts.
in hisfamily relationships, with the man being the head of the woman, and both man and woman being responsible for the rearing and well being of their progeny. They in turn have a responsibility to respect and obey their parents. Just as there is a relationship of love within the Godhead (i.e., Father, Son, and Holy Spirit; see John 5:20; 14:31), so too is there a relationship of love within each earthly family (See Eph 3:14,15 for the "family connection", and 5:22-30).
Unfortunately, the first man Adam surrendered part of his dominion when instead of preventing his helpmeet, Eve, from doing what God had prohibited, he allowed her to be deceived by the tempter. What is worse, he also followed her in disobedience. Had he told his wife to ignore the tempter, instead of simply standing by and letting her be seduced by the serpent, Adam would have retained his position of dominion. Unfortunately (and no surprise to God), he did not.
Even after man and woman sinned and thus became unworthy to have fellowship with Holy God, God already had a plan from eternity past to redeem man, in love, and to restore him to fellowship with Himself. This plan cost Him His only begotten Son, but again, there is something of infinite worth in each human being. God obviously and lovingly looked beyond our sins and saw and met our needs.
In conclusion, and more in answer to your question, man is still lord over the animals. Prior to sin's entrance into God's paradise, man was not endangered by being in the presence of any animal. After sin appeared, however, man was not as free in his interactions with animals, particularly those which present a threat to his very life (the big cats; poisonous snakes, spiders, and fish; killer whales, sharks, piranhas; and so on).
It is a good thing, I believe, for the human species to preserve and maintain as many animal species as possible, and not to hunt them into extinction or deprive them of their natural habitat, thus threatening their very existence. God cares for the animals. Read, for example, the last verse of the book of Jonah in the Old Testament. Jesus said that a single bird cannot trip on the ground without our heavenly Father taking notice (Lk 12:24). (He also added, however, that people are worth much more than many birds (Matt 6:26.)