"There Is Alwayes Warre Of Every One Against Every One. Hereby it is manifest, that during the time men live without a common Power to keep them all in awe, they are in that condition which is called Warre; and such a warre, as is of every man, against every man. For WARRE, consisteth not in Battell onely, or the act of fighting; but in a tract of time, wherein the Will to contend by Battell is sufficiently known: and therefore the notion of Time, is to be considered in the nature of Warre; as it is in the nature of Weather. For as the nature of Foule weather, lyeth not in a showre or two of rain; but in an inclination thereto of many dayes together: So the nature of War, consisteth not in actuall fighting; but in the known disposition thereto, during all the time there is no assurance to the contrary. All other time is PEACE."War is seemingly something approaching a default metaphysical state, or at least a given and established tendency in nature. War is to be assumed, peace is what is to be explained. Bellicosity comes first, co-operation second. Moreover, war per se is divorced from any specific actions or means and becomes like a climatic state.
Is Gaia a Leviathan? Without deference to such a terrestrial deity—"that Mortall God, to which we owe under the Immortal God, our peace, and defence"—are we in a state of war? I'd prefer to retain a sense of concrete practise to 'war'—i.e. to insist that the means matter. However, it is a more complex question than just this.
Gaia does not much resemble Hobbes' deity in the details (or the illustrations) but certainly the concept of sovereignty needs to be re-evaluated at its roots and that must surely mean a meeting of these figures.