Thanks. We don't have any large snakes here at all, or raccoons either (in the UK). There are not large predators except foxes and they would have killed all the ducks too. I had a look around and couldn't see any obvious rat burrows though there is growth around the run
fence that could be concealing entrances. I'm just totally shocked since we haven't had any problems with broken or stolen eggs at all before, and am particularly perplexed about the fact that the inside of the house looked normal - didn't look like there had been any sort of kerfuffle, or anything digging around, and the nest was just levelled.
Previously, we shut the ducks in in the evening and let them out 8.30-9 am and collect eggs at that time, so very shortly after they have been laid, so I guess it's possible that rats just never had a chance to get interested before. The most logical thing I can figure is that the duck gave up sitting and all ducks were outside, leaving the eggs in the house alone all day, and then maybe the rats made off with them. But they would have had to get them out of the house - 3 feet to the door - and then across the concrete outside the door - another 3 feet - before they could possibly have gotten to a burrow. And it still doesn't explain the nest being flattened.
It is possible it was a human, but seems very unlikely especially as the run gate was all shut up, and the
chicken run is much closer to the road and there were 4 eggs in their nest boxes.