Your analogies are Logical Fallacies. A person in a Coma is alive, perhaps they have machines keeping them alive perhaps they are breathing themselves, it doesn't matter if they can not move or can not think, it's only in death are they absent of sentient life. A tree can die just like a human can, a good example is Dutch Elm disease which killed a lot of Elms in the UK. Also if you take away Food sources, Water or a stable environment you can kill trees and plants in general. For them to Die means they must of been alive to begin with. Yes they are "Alive" as they go through Seasonal changes like people go through mood swings (obviously taking longer) and during those periods can signify reproduction (Fruit/Berries) or preparation for dealing with low levels of sunshine and frost/winter (Autumn/Fall, when the leaves fall to the ground). Obviously if the conditions for a tree are right it will grow far more than if they are wrong which also signifies it's Alive.