Continuity mistake: When Rose is hanging off the back of ship she first isn't holding the train of her gown then suddenly she is.
Continuity mistake: After Old Rose watches the taped images of the sunken Titanic, Lizzy puts her hand on her shoulder. Then she takes it off and moves away. When the angle changes her hand is still on Rose.
Continuity mistake: When old Rose grabs the dragonfly jewel she places her left finger under the broken wing. When the angle changes her finger is away and she is repeating the previous movement.
Chosen answer: During the several years it took to construct the ship probably, or in any of the supplies/food brought on board, or in the furniture brought on board. A single pregnant female rat can be responsible for thousands of rats in a very short space of time (the offspring are not too choosy about who they breed with).
Soylent Purple
A pregnant female rat could have made a home in a underneath a third class couch and had the other rats then all the females would have baby rats quickly.