> My neighbours(the ones that moan a lot!)have chickens
If they have chickens, that's where the rats come from!! We had neighbours who kept chickens and we saw tons of them on their property which thankfully wasn't adjacent to ours.
Dogs won't attract rats - unless YOU are leaving dog food (including partly eaten bones) around.
However, if he's seen rats because of HIS hens, then you will have them around your property too. I hope your dogs' Lepto boosters are utd. I had to get my then two in for Lepto boosters a few years ago when we started seeing increasing numbers of rats around. Rat bait, in two boxes, sorted that out. We had no standing water around out there, although we do now, having seen a hedgehog around.
If there are knot-holes in your fencing, he may be able to look into your garden - and if he has a second storey to his property, ditto.
If this amounts to harrassment, so you might have a quiet word with your local police, on a non-emergency number.
Yes, if the food for the birds drops on the ground, that may well attract rats unless your ground feeding birds clear up any dropped seed as ours do. The pigeons prance round the feeders, waiting for seed to be dropped.