Best practices for adding data

Let’s say I have created a database with 4 tables: Animals, Classes, Orders and Species. Each animal belongs to one class, one order and one species.

When an user wants to add an animal, it chooses a class, order and species from 3 different comboboxes. Sometimes, these are not already loaded into the system. Therefore, the user needs to visit Classes/add, Orders/add and Species/add and then go back to Animals/add and refresh the page.

Which is the best to fix this problem? can I get an explanation or some example?
I’ve been thinking using cells or ajax but I’m not sure which is the best way to keep my code simple and DRY

What I have personally done for such cases is show a button/icon next to the select box which loads the /foo/add page in a modal using AJAX. Then upon successful submission the new option is added to the select box.