I have a native wood pigeon in my garden at the moment (pigie). I think she is a she as a second (I assume a male) pigeon turns up every year, but he does not seem to have much luck. I assume that in the pigeon world it is the boys who chase the girls?
Wood pigeons can live for 25 to 30 years. She has been coming here for about 10 years now. She comes in every year for the street olives, and stays on through the winter to eat my tree lucerne leaves, then the kowhai leaves and then kowhai flowers. My tuis drink the kowhai flower nectar. Wood pigeons just eat the whole flower (very practical).
In the first year there was a pair of pigeons. They used to drink water from the street gutter. One day I found one of them dead in the middle of the street, struck by a car (presumably the boy). I have a fresh water feeder for her now so she is safe.
Pigeons are not territorial. They are very wide ranging, they follow the food supply. Every year she arrives, stays, eats, and one day she leaves for where the food is better. My neighbours and I keep an eye out for her every year. She is very shy, and very difficult to spot sitting in the tree unless you know to look for her. She does give herself away. If you know to look down, there is a pile of pigeon poo on the ground under her roost. Look down, look up.