Genesis 1:26 and 28 tells mankind to "subdue" the earth and "rule over" various animals. Exactly what is meant by this in relation to large animals?

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In Genesis 1, up until this command, the conflict in the narrative has been very muted. Sure the chaos waters were there, but God is portrayed as being unthreatened by it, and it soon becomes a mere building material, easily shaped just by speaking. By the time dry land and plants appear, the picture is of a safe and comfortable place for humans to live.

The only mention of any threat to humans are the great sea creatures, the livestock and wild animals all of which are singled out from among the all the other moving creatures presumably because of their size — being megafauna whose size make them rivals for humans.

But even then, they are portrayed as vegetarian.

So, my question is this: how are we supposed to picture the "ruling" and "subduing"? Are we supposed to guide them to ensure they fill the earth? Do we domesticate them? Do we destroy them to make a safe world? Or is it all a foreshadowing a time later in the narrative when we will be in conflict with animals? Is it really about subduing our carnal desires or subduing spiritual entities?