Who owns a bird shot by a projectile that lands on another person's property?

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When a person shoots a bird with a pellet, and it lands on another's property, the bird belongs to the property owners if it is assumed that the bird fell there rendered incapable of flight, allowing the residents to take possession by catching it. This interpretation is preferred because if they do not own what God causes to fall there, they certainly should not own what results from a human action. Furthermore, it fell after the strike that would have granted ownership to the shooter.