i've been pondering the same question. there are rat holes in the goose run (they have indoor and outdoor facilities) same with the ducks, and often there is a bit of a commotion in the early dawn, and i am guessing that it is the rats annoying them.
the hens are shut up into their shed, overnight, so the eggs they lay first thing i collect when i let them uot. i have 11 hens, and production has been quite scanty lately, which i was putting down to the time of year. although only one is in moult, the rest of the right agegroup look like they should be laying. 4 of them are young, 2 of which are now in lay, so production is better, yay!
one of the older hens was in the habit of laying under a tree, i deliberately left an egg there ofernight, and it was gone in the morning, so something is definately stealing! we have witnessed crows flying off with eggs, but not for a while, the population is reduced, can't think why! (bang bang)
so, the rats don't have access to the eggs at night, the ducks are not laying, and the geese lay during the day and i collect promptly. but i would like to set traps, get rid of them, need to devise a way of putting traps near the holes without the ducks and geese getting caught in them!