Different places have different laws. But if you are not sure whether the birds are protected by law, it is better for you not to harm them to avoid trouble. Who knows, maybe your neighbor sees you killing them and calls police for animal cruelty. I have the same problem as you. The flowers in my front yard have been eaten by wild deers all the time, and all that I have got so far for the past year are roots bared above ground. Should I kill the deers? Definitely no. I am planting something diff