How would you model the effects of a mobile population on the land’s resources ?

Great question. Nomadic pastoralists tend to have a low population density, and tend to be semi-sedentary, moving once each season as they migrate with their herds.
The key element to understanding pastoralism is that the land is not what’s valuable. Speaking in very broad terms, nomadic pastoralism tends to occur only where the land is unsuitable for agriculture, such as the Mongolian steppe, or portions of Africa. Instead, what’s valuable is the herd.
We know from ACKS that 1 peasant farmer and his family farm 30 acres of farmland. 30 acres of farmland costs an average of 1,500gp in ACKS. Let’s assume that a pastoral family of 1 herder and his family need 1,500gp in livestock.
So let’s say that a pastoral family can extract the Land Value of any unoccupied area as long as they have a herd of 1,500gp. If they have less than that size herd, they get proportionately less gp. Pastoralists don’t have to secure a domain and they don’t have to have minimum strongholds.
(Is that realistic? Interestingly enough, courses.washington.edu offers a course on pastoralism that gives a sample household herd: 25 cattle, 10 camels, 100 goats, 10 donkeys. In ACKS terms that’s 250gp + 1000gp + 300gp + 80gp, or 1,630gp. So we are within the realm of reason.)
Because pastoralism takes more space, we’d divide the limits of growth by 4. A 6-mile hex can support 30 pastoral families, not 125. To keep them moving, let’s say that they need to migrate every 3 months (one season) or the Land Value decreases by 1gp per month.
Using Mongolia as an example, we know it is 603,000 square miles in land mass. That’s 18,843 6-mile hexes, with 1/4 being used at any given time (then the next 1/4th the next season, etc.). That means Mongolia could support 141,322 pastoral families, or 706,612 people. Mongolia has low Land Value, probably 3-4gp.
To make them bad-asses militarily, let’s rule that each pastoral family can be conscripted to get 1 horse archer or light cavalry per family, rather than the 1-3 militia per 10 families that a peasant population can support. That would give them an army of 141,322 or so. (Historically the Mongols invaded Europe in 1241 with an army of 150,000).
In contrast, the same area of land (603,000 square miles), if it could be used for agriculture, could support 6,000,000 to 10,000,000 families.

Thanks Alex - just what I was after

That’s an astute analysis Alex, and seems workable for the cases given. There’s room for experimenting with broader application though as it is not accurate to say that pastoralism, or more broadly, pastoralism and transhumance only occur on marginal land. That is mostly true at present because agricultural and colonial pressures have made it so. Even today however there are still transhumant populations dominating what is otherwise perfectly arable land. In such cases, you would have to use different (higher) pop figures per hex, depending on carrying capacity, and may want to vary them according to season, as they are quite likely to be traveling a territory more on the order of 20-25 miles.

Haven’t read it yet, but a quick scan of the wikipedia article on transhumance seems well done.

Good insights. I wasn't aware of the extent to which pastoralism was common even where land could have been farmed.

The rules above will at least work for nations like my own Skysos, historical Mongols, etc...

I’d love to see this refined into a stronghold type that I could apply to custom classes/races.