History XV: It Might Be Famine All Around

A hegemony's capital (or largest cities) should be limited by the amount of people they control (hence the working classes ability to keep them supplied).

Currently, this is limited by the carrying capacity, $K$. Therefore, the upper bound on $K$ will be affected by this control.

Assume that $P$ is the population of a city. The farmer ratio $\alpha=3$ can be defined in this case as 3 farmers necessary to support 1 other individual. I'm leaving this as a variable, not a hardcode, because this number is very dependent on who you ask and what time period we're talking about. Therefore, the number of people required to support a city of population $P$ is \[n = \alpha P\]. How many people do we have available? Assuming 100% of the rural population is involved in food production (a bad assumption, again something we can change), then we just need the total amount of rural people in that hegemon $P_r$. How many of those are available to send their goods to our city? If the total urban population of the hegemon is $P_u$, then our city will demand \[{P \over P_u}\] of the resources. This means that only \[{P P_r \over P_u}\] are specifically available to it. We can compare this number to the needed number $n$, and see that \[K_n = \min\left(K, {P P_r \over \alpha P_u}\right)\], that is, if there is enough manual labor, then the city can realize its full potential.

I grabbed a random capital to use for this, Chivenkare. Chivnekare has a population of $P=49920$, and $K\sim55000$. So it is a good test case. It has a good number of cities spread over a large island. Givne this, $n = 149760$. We find that $P_r = 177865$. Already we see danger signs, as Chivenkare is not the only city in its hegemon. However, $P_u = 85887$, so ${P \over P_u} = 0.58$, there may be hope yet.

Ultimately, we find that $K_n = 34460$, meaning that a huge famine is imminent. Sorry, fellas!

This implies a few things for the overall simulation:

• Cities cut off from the major area of the hegemon will starve and collapse. This is true regardless of the diplomatic relations with the hegemon which surrounds it. Resources are scarce.
• Hegemons at war could collapse very quickly as food runs out, even if they are technically winning overall. This would be a cascading collapse.
• Another cascade could be precipitated by an unrelated catastrophic event.
• Land will be a premium. My automata are not "smart," because they will not seek more land; but those unable to acquire it, spreading influence, infrastructure, and gaining rural working hands, will quickly perish. This mirrors the historical expansion and collapse of many empires, which outgrew their ability to feed themselves and were destroyed in short order.