Well, a battalion is an extremely small deployment. Especially for the area in question. Lets get an idea of the territory in question: lots of the Catatans having trouble is based on this being a large area: lets say the target is one hour helicopter flight: about 200 km. That's 10 days on foot if making reasonably good time. About 1 km a day road building like the trip to the home tree gives you roughly the three months that it took mining operations to reach.
So, it might be reasonable to guess a lot of the Navi stuff is at least 50-100 km out, and the magic tree may be 200-300 km out, about a full 1-2 hour flight.
But, for gorilla war terms, lets look at how much territory were talking about. A semi circle 200 km out from a base on the ocean gives you about 60,000 square km. This is about 30% of the land area of South Vietnam, which had closer to a million men involved. So, to reach South Vietnam troop densities, your talking about 300,000 men for an area this large, not 800.
But, as
@Agent23 hunter gathers have lower population densities than peasant farmers. 1 per km was my quick research number. This suggests though over the distances being discussed that there may be roughly 60,000 Navi in the area discussed, especially since a lot of it is fertile area, not marginal wasteland no one else wants as in modern hunter gatherers.
Now, some of evidence from the film suggest there may be a good gap of few Navi living in very close proximity to the base. This however is a disadvantage to the Humans because it puts more of the Navi at further distances from base, pushing for longer logistical tail.
Still, 50,000 Navi in the area makes sense, suggesting roughly 2,500 prime warrior aged (roughly if 50 year lifespan, equal spread between ages, so 20% are in the 20-30 range, or 5,000 and assuming mostly male half of that for roughly 2,500).
This lines up with the force Jake's able to mobilize quickly: light horse forces can do 30-50 km in a day burst, or 20-30 sustained. Mongols could allegedly manage 100-200 km in a day, though I don't know if that was a burst or sustained, regular or a particularly notable campaign. Flight is also going to make the Navi way more mobility than standard natives too: flight might make a 200-300 km day journey quite doable, especially with friendly bases on the other side. RDA meanwhile would be very limited by the need to keep operations within round trip flight distance, else it requires setting up forward bases which they don't really have the manpower for. Catachans would have a similar need, and be similarly lacking in manpower.
So, this lines up roughly with the movie, which honestly suprises me a bit: those in the immediate area might be roughly 50,000 Navi, who can mobilize 2-3k Warriors, and within the close reachable, say 400 km as the, whaterver those flying things fly, your talking about 500,000 km, and thus maybe half a million Navi. Now, were talking about an area roughly the size of Ukraine, but, well, hunter gathers are fairly mobile people, traveling light, able to live on the land, etcetera. That's still only 25,000 Navi warriors, with maybe a manpower pool of 100,000. Which would definitely eventually overwelm the RDA/
If they can draw from a Europe wide area, with maybe a population of 4 million, you have roughly 200,000, though drawing on that wide is reaching logistical limits, especailly at once: a distant tribe might be able to migrate a warrior band of 30 flyingers who spend a couple days in transit, fight, and leave, as long as local food sources held out.
You still have the problem though of a divisional (5-10 thousand) at least task being carried out by a battalion.