May 21, 2018

Settlement Growth

The basic model for population growth is a logistic function.

This is most representative of the entire population, not necessarily cities themselves.

The rate of change itself will change from year to year. It could even go below zero. However, since this isn't a history simulator, a random rate r = N(x,0.0035,0.0001). From this we can either specify the founding date and thus the current population, or the current population and from that the founding date. The rate could also be influenced by the terrain, but this is difficult to work out. We could give a slight bonus to settlements located on oceans or rivers, or in pleasant climates. A penalty could be enacted for cities in harsh climates.

There are a few parameters left to choose. The starting population should probably be around 20 or so: the minimum necessary to be considered a thorp or hamlet. This can change but will be static across all settlements. The carrying capacity (K) of the city is dependent on many local, unobtainable factors. However, we could say that it's influenced by what cities already surround it. A settlement within a few days travel of a metropolis will have a much lower K than it would otherwise. If we look at it this way, K also can represent the effect of population flow from the "suburbs" to the "big city."

How does this factor into my world? Not sure yet. I don't want to nail an Earth date down and say "this is the rough technological age equivalent," but I do prefer to avoid the classic medieval setting. Not that there's anything wrong with it, but if I'm going to be different I might as well go for broke.

Historically speaking, cities topped out at less than 50,000 inhabitants. A few, like Uruk and Memphis, were significant outliers, even around 2000 BC. By the time we get to 1000 BC, we have a few that are reaching 100,000, like Babylon and Xi'an. We don't hit a million (in Alexandria or Rome) until almost 0 AD, depending on who you ask. And those were made possible partially by giantic empires funneling labor, food, and wealth into them, carefully ordered by massive beauracracy. So we can see K as partially a result of the level of technology available as a whole.

Of course, any demographic historian worth their salt knows that's a gross oversimplification. But who cares? I just need something that works, makes sense, and is internally consistent. I have to draw the line somewhere. Can always redraw the line.

Both of these parameters vary widely in the real world. But I'm not concerned about making a real world; I'm concerned about making a world that feels real. Setting up parameters like this will allow me to change them later if they don't have the desired effect. Even having a model in the first place allows me to change it if I wanted, for example, to allow unlimited exponential growth or even (shudder) linear growth.

Another issue is that not every person lives in a city. In fact, most people don't live in cities. Urbanization rates in the Middle Ages range from about 10-20%. So if I say a hex has a population of 5000, there's a better than good chance that the local settlement only has 500 people. Not exactly a bustling metropolis, by today's standards at least. A rough solution that springs to mind is just to have a "town" wherever there are people. So even if the "population" is 5000, I can understand when my party visits that most of these are in the countryside.

However, I'm a little uncomfortable with that bespoke solution (or any bespoke solution, to be honest). I'd rather a set of rules that determined population regardless of the presence of a town, but that might be a little harder to implement into the trade system. Currently, named towns are treated as nodes in the trade network. Since each name is unique, that's fine. But unnamed nodes present a new problem. So for now, I'll take the rough solution and define a "settlement" for anywhere that has population. Unless it's big enough to have a market it won't matter much anyway. These can still be named as regions, just not as settlements proper.

Placement of cities themselves is a separate topic, covered pretty well here. However, the topics are somewhat related, because new settlements are partially formed because the people from one place want to live in another (more space, more food, better climate, etc).

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