Hello, I am preparing a table, and we have reached the conclusion that we want population growth to be found.
-city and guild
-lord of men
-conve (in Spanish alianza)
and I would like to know what I have to take into account or a formula to calculate population growth, at the moment the players are 4, 8 characters, 24 grocs, 3 families of 15 members each family (45 total families) I mean a small town of more than 70 people.
two characters are knights with lands, and a rich merchant (who comes and goes)
that depends on what you want to calculate the growth of?
The covenants population? the nearby towns population? the population of the entire order?
population of the human-geographic group, based on 70 people. being a geographically closed group, a month away from other groups, good Russian magicians at the top of the mountain with their family.
with such a small population why simulate growth?
Given the small size, isolated location and magical nature your group is highly likely to be subject to various forces that impact population growth in a manner that makes standard growth models useless. You could of course decide that your group grows by some amount pr. year like with a population growth model for a larger population. Say 2% per yer. The problem is that those models assume that population grow continuously, i.e. that humans start out as 0% of a human and then get created a little at a time. But there is not such thing as 0.4 human in real life. For a large population the error introduced is by this does not matter for the model but when you are looking at smaller populations it suddenly starts to matter.
if you want to make a more detailed model you can start looking at each person in the extended covenant individually. How many magi are there? are the magi included in the breeding population?
How many adult people are there and especially how many breeding pairs (charming term i know)? How frequently do they reproduce? Which of the offspring survive, probably most but not all.
There are various rules for producing children as a background activity in Ars magica that you can find on this forum and on the wider internet. Reproduction is as a larger phenomenon quite predictable and you could simulate it, and if you want to tell stories about the people who make up the covenant you should. But IMO you are better off simulating it in detail, by deciding which couple produce children, naming the children, keeping track of who turns into breeding pairs (by. e.g marriage) and otherwise keeping track of such events.
However such normal growth is only part of the story and given the nature of roleplaying games you are likely to have to consider many more factors that I have broadly termed: "migration and dramatic events". How likely is your covenant to see a sudden influx of migrants? do the magi attract skilled laborers for some project for example? what about migration away from the covenant? do some people leave as a result of the stories you tell, say because the covenfolk decide that magi are too dangerous to live near to? Does a monster show up and kill someone?
The problem with all these factors is that they are not very easy to take into account in a population growth model, since they are by nature not very predictable.
Lords of men has rules to simulate the dynastic growth of a single family, you could break the covenant down into families and simulate it that way- start with the question of what portion of them are never going to reproduce (confirmed bachelors or have longevity potions, etc) and then how many are of reproductive age (or when they will be) then break that down into families.
A factor to consider in growth is the impact of upcoming historical events such as the Golden Horde invading and then years after that in 1258 is a year without a summer where many crops failed due to it being too cold and rainy. Resulted in famine.
Will your saga get to that time? If so, will you have to deal with refugees?
And there's also magic to consider. For example, if a magus uses weather magic to assist crops, or they have a magical birthing chair to assist delivery of children, that skews population growth. If they use +Recovery magic on anyone who is sick, that skews mortality rates and thus population growth. As Euphemism mentions, the population is so small even a few events will skew it wildly.