In the pre-industrial societies, is there a strong correlation between of the human population and the available food? Can this serve as a solid basis for models in historical demography?
In this regard, can we use events like
etc. as indicators of depopulation events in the short term?
As a case example, what can we say about the demographic history of the Roman Empires (both) in this perspective?
Hiya, this sounds like a question for anthropologists! There are some in this sub, but it would be worth x-posting to our sister sub, /r/AskAnthropology, or even /r/AskScience (Social Sciences category)
There's certainly a strong correlation between population and available food supply: the problem in gauging the impact of particular shocks on population movement is that often the latter is itself often inferred largely from the former, while estimates of aggregate food supply are conversely derived usually from estimated population numbers. So there may a strong risk of circularity in correlating the two.
To consider a couple of the suggested factors, falling trade (or tribute in kind) is likely to impact on urban population specifically, since its food comes overwhelmingly from outside: it may not have such an effect on agricultural communities who may lose the luxury of cash income but whose fields may continue producing pretty much as before. We tend to assume that investment and productivity will fall without the stimulus of trade, money and buoyant prices, but engagement in the commercial economy will have varied even at its height.
Abandonment of arable through violence or other shifts should affect population unless the loss is made up elsewhere: it's been suggested that the Mongol conquests reduced Asian numbers less by the sword than by a shift to pasture which supports lower densities (on the other hand our numbers too leave much to be desired). Raiding itself seems less likely to have a large impact over time, as destructive capabilities and frequency were generally limited and there was land still available to support large later increases.
Abandonment also presents the familiar chicken-and-egg dilemma: did it cause fewer people, or did it happen (as in the 14th century) because there were fewer people? The same may go for irrigation systems, though destruction would clearly affect the productive capacity of lands depending on them.
Climate change may be the surest predictor of agricultural and population change, though results often seem contrary and capable of differing interpretation, and producers may have achieved varying success in responding over time with different crops and techniques. More results from paleobotany should shed more light on local trends, but it still seems early days.
In sum, I'd be wary of drawing too concrete conclusions from short-term shocks: each might be of limited scope, or even an expression rather than a cause of larger trends.