John Rennie - I think so.

I think the title was created by the AI. I really do recall a story about an asteroid-dweller who ends up ordering larger and larger animals. The AI sent me down the wrong track, however. I was thinking about it because I was discussing when colonists come to a new place and bring their rats, etc, with them, and the rats take over. Then the colonists decide to bring in cats to eat the rats, etc. etc. Though, a story based on what the AI cobbled together could be pretty entertaining and thoughtful.

Even more wow. When I went through my search history to find the AI entry, what came up was a nearly identical entry, but with different character names. The AI created a summary of the story for me, without any such story actually existing???

Wow. Thanks to everyone for your attempts. Buzz is on point, because what got me thinking about the story was that nursery rhyme, which I was thinking of because of a discussion about using house spiders to control fruit flies. When I search for the story, the googlety AI comes up with a plot, characters, Arlo Jensen and Maya, and more. But there is no reference to the author or where such a story was published.