If I see them in time, I ride really slowly, but I expect you do that, too.
Well, tbh...no, hence the thread, really - if I rode really slowly whenever i saw one, I would be riding really slowly for most of about 7 miles.
I do see the odd pheasant but they always tend to be predictable - they first run away in the same direction I'm travelling, and then pick one side or the other, and if they don't like either, realise they're going to have to make the effort to actually fly amidst much huffing and puffing and clucking.
Rabbits, it seems like they're quite fit and agile enough to get out of the way, but they seem to be chronically indecisive. They change their mind just as they've reached the verge, and decide that it would be better to go into the opposite verge. Then when they get to that verge, they think, oh, in fact the first verge would have been better.
When (small) birds are pecking roadkill in the path of your car, they stay pecking it for as long as they think they can get away with but fly off at the last minute, but they pretty much always fly off in time. I trust them to just because they always do. But I'm not sure whether the same can be said for rabbits, is the darting from side to side thing just the game they play or could their indecisiveness be fatal?
The only animal I have ever 'run over' was when I was about 14 doing a paper round on an old mtb, and a dog came careering out of a house, fortunately
missed my front wheel completely but got run over by just my
back wheel. Which means it may have had a nasty cut from the chain/chainring. I stayed upright, but was quite shaken. I don't know how injured the dog was if at all, I never stopped to find out, but obviously not enough to prevent it running off which it did.