With that information I agree with Rachel, they will not kill those trees. That was easy.
The answer to the other one is, it depends. There are things you can do to encourage them to lay in the nests, but they are living animals. No one can give you guarantees. I think most of us that give them much room to range have had some hide nests on us at one time or another.
If you can get the first ones in the habit of laying in the coop, you are way ahead of the game. Chickens like to lay where other chickens are laying. I don’t know why. Maybe they think it is a safe place to lay since another hen is laying there. Maybe they think if they lay there the other hen might go broody and hatch her babies. It’s instinct, somehow. One trick is to put a fake egg in the nests to make them think another hen is laying there. I use golf balls, but some people use ceramic or wooden eggs or plastic Easter eggs. I’ve even heard of people with bantams using ping pong balls. You might need to fill those Easter eggs with something heavy and glue them shut to keep them from scratching those light things out of the nest.
Many people recommend keeping your nests blocked until they start to lay. For the life of me I can’t understand that logic. I’ve had pullets start to lay at 16 weeks, I’ve had some start at 9 months. There are some clues that they might be ready to start, but those are only hints, not dead giveaways. I can’t tell when they are really going to start.
It is not unusual for a pullet to drop her first egg or two wherever she happens to be, either from the roost or just wandering around the coop or run. But as soon as she gains control of the process, she looks for a safe place to lay her egg. They are creatures of habit. Once they start laying somewhere on purpose, they want to return to that place to lay eggs. I want that first controlled egg to be in a nest, not somewhere else because the nest is blocked. What is surprising is how many pullets get it right to start with so the nests need to be open before they start to lay.
Since they do like to lay where another has laid, try to keep those randomly dropped eggs cleaned up. Another pullet might think she do that on purpose.
One reason given for blocking the nests is so they won’t roost in the nests. They poop a lot at night and you don’t want them doing that in the nests. If they are going to roost in the nests, I want to know that before they start dropping eggs in that mess so I can train them to roost somewhere else before it is a problem. So my preference is to have the nests open and with fake eggs in them before they start to lay.
Sometimes even a hen that is used to laying ion the cop will decide to hide a nest somewhere else. Other than the molt, this is probably the main reason people think their hens have stopped laying. They haven’t really stopped they are just hiding them. When this happens, it will take an effort to break her of that habit unless you are OK with her laying there. For some people, that is perfectly acceptable.
I’ve used different strategies to get them to break that habit. I have a run that is big enough I can keep them in it, so I lock all of them in the coop/run until that hen has laid her egg for the day. You can tell which hen it is because you will often see her pacing the fence, looking for a way out when it is time for her to lay her egg. But eventually she gives up and lays it, hopefully in a nest. I normally keep them like this for about a week, which usually works. Not always but usually. And if you can at all, find that other nest, take the eggs away, and mess it up so it no longer looks like a good place to lay.
I built a couple of my nests so I could lock a chicken in there if I wished. If I have a hen laying on the coop floor and catch her on that nest, I lock her in a nest until she lays that egg. That usually takes a half hour, though I had one go 3 hours. Usually once is all it takes and they start laying in the nest, but some take more than once.
So the short answer to your question is that if you can get the first one or two to lay in your coop most of them probably will. But don’t be too surprised if some try to hide a nest on you.
