Greatest Expansion of the Roman Empire - When?

[Gluteus Maximus]

I think it is possible that if the entire population was gathered to meet the
crisis, this figure is plausible(ish).

There was actually a fairly advanced culture in caledonia, if not exactly on par with the mediterranean civlisations. Farming and herders, the hillforts,
etc.

Hmm, and I remember tacitus saying that thousands were killed with only a couple of hundred Roman casualties. This would suggest that the 30'000 was made up of boys, elderly and infirm etc as well as the prime warriors. It would also explain why the area was no use to the Romans immediatly afterwards - the result must have been a huge drop in population, which would have taken a couple of generations to put right. About the same time, indeed, between the battles of Mons Graupius and Antoninus finding it neccesary to build his wall! I still err on the side of conservatism, though, with respect to Tacitus' figures and the population of the area.