Quote Originally Posted by Juvenal
I wasn't satisfied with just a vague feeling that growth was too high, so I have tried to model an upper limit on population growth. I am not familiar with demography maths, so I am doing this empirically.

Assumptions
Settlement population is number of males aged 15-50 (men of fighting age)
Couples are of same age (for simplicity).
Couples have children between ages 15-40 (i.e. for 25 years).

Mortality Rates (males)
Infant (0-14) 50%
Adult (15-44) 0%
Mature (45-64) 0%
Elderly (65+) 100%

Birth Rate
Assume 30% of adult females (15-40) stop producing children before age 40, due to death in childbirth, disease, malnutrition, accidents and loss of fertility.
1 couple, married at age 15 would have 16 children (out of a potential 25) in 25 years. This gives 4 boys and 4 girls surviving to age 16.
4 boys per couple in 25 years means 0.16 male children coming of age per year per men between 15 and 45.

Settlement Demographic
Assume men are evenly distributed between 15 and 50 years of age.
Proportion of new parents per year is 25 out of 35 = 71%
Coming-of-age rate per year is therefore 16% of 71% = 11.4%
Death rate is number of men becoming 65 = 1/35 = 2.9%

Conclusions
Result is 8.5% growth per year. That is no more than 2.2% per turn.

Even if infant mortality is zero, we only get 5% growth per turn.

Growth should be additionally limited by adult male mortality (disease, accidents, crime) and adult male sickness (making them unfit to fight). These could be offset by health and law buildings.

In my recent Casse campaign I was sometimes getting 8% per turn from recently exterminated settlements, so I think growth rates need to be cut back drastically.

Any comments or criticisms on my method would be welcome.
Yeah, you forgot migrations. Settlements are only city population, the majority of folks lived in the countryside. At the height of the Roman Empire, perhaps 30% of population were city dwellers (admittedly this wasn't surpassed until the 1870s or so), but for the most of the history and most of the regions, the number was probably closer to 5-10%.

So what happens after you exterminate a settlement? People from the sorrounding areas move closer to the city - cities were usually near rich farmland (that's what determined most city sites to begin with) - and soon came to live in the city.
You would also probably encourage some migrations by yourself through colonists, to improve the control of the area. Romans were particularily fond of that, but hardly unique.

McHrozni