Icelandic Chickens

My Icelandic chickens have taken to roosting in trees. They are very smart, and a bit wild, but they are also an old and hardy breed that is known for being good at foraging for food. Because of this, they supposedly need substantially less grain that other chicken breeds during the summer months. I am hoping, next summer once they are full grown, to measure their grain intake vs their egg output and then compare it to some common chicken breeds. But I must admit that at this point, I am worried that they will lay eggs astray and I won't find any.