Avoid absurd population growth in a game world

Game designers have a responsibility to make their game world logical and realistic within its own reality. So instead of just making up some numbers that describe the behaviour of entities, you should try to calculate the implications.
As an example of miscalculation I remember an old fantasy strategy simulation game where - according to the rules of system - humanlike population grew 10% every month. My guess is that creators of game thought it as a appropriate number taking in contrast to game turn and general flow of game. And when you play the game and observe only two or three consecutive turns, it may feel OK.

Exponential Growth

From larger perspective this scenario starts to look quite weird. Unless there is a huge death ratio this population will explode in couple of years, because it more than triples in a year, leading to exponential growth. Besides, when it says "grows 10%" my assumption is, that all decreasing effects have already taken into account.
Lets assume that these humanlike creatures have average human life span. If there are no other causes of death but old age, then a 1000 head population will grow in 6 years to approximately 1 000 000. In 10 years there will be almost 100 000 000 population.

Breeding like rabbits

However, when you start to think it deeper, this is absurd from reproduction point of view, also. Assuming that this humanlike population follows human reproduction patterns, we know that there are two sexes and pregnancy lasts 9 months, and humans are not reproductive in their 10 first years of life. For simplicity's sake we assume that male/female distribution is 50/50.
Lets start with that 240 head population. Since system clearly says that population grows 10% every month, it means that there has to be women giving birth every month. Lets assume that one woman is not constantly pregnant, but has 3 month "rest period". This way we can divide the 120 woman population (50% of whole population) into 12 groups, giving birth every month.
When the first group of 10 women gives birth, they have to produce 24 children to reach that 10% growth quota. This means that on the average every woman gets twins (and we know that twins are rare in normal life), but 4 of them (40%) has to get triplets. When months and years go by even twins are not enough, since population has now grown, and those newborns won't produce children for a decade, at least. So, in couple of months those mothers have to give birth to triplets, then quadruplets and so on. Well, they still have that 3 month rest period to gather strength.

Burden to community

Combine reproduction and exponential growth with age distribution and you have a population where large part of the population are little children needing food and care, all mothers are constantly pregnant and men are doing hard time providing sustenance to all of them, which will be harder and harder to find. Actually at the end of the year 3 there will be the original 240 adults and almost 600 2-year old, about 1500 1-year old and about 5000 newborns. In total, for every adult couple there are about 30 children to take care of.
Actually those adults were lucky. There was also a game where population increased by 5% every week. However, I leave those calculations as an exercise to the reader.

Lesson learned

I can only guess the reasons for this absurd growth rate. Maybe it was needed to compensate losses in battle, sickness, famine, child death etc. Maybe it was needed to give players an impression that something is really happening in monthly game turn.
But even then, the wording should be different, like birth rate. Growth means usually net increase (or decrease) and is a sum of newborns adjusted with death figures (battles, sickness, accidents etc.). Anyway, if that 10% were birth rate, it would be absurd.
What should have been done is quite simple. First do some groundwork and calculate a realistic birth rate taking into account the age structure of population, fertility rate, reproduction age, pregnancy time. Then adjust it with death at birth and death of old age figures. Then you could list all possible random causes of death like famine, disease, accident and battles. This gives you equations to estimate how your population could grow and you can simulate what happens if some variable is increased or decrease.
In reality, the annual growth rate of human population on Earth has never been over 2%. Before Middle Ages it was not under 0.2%. Currently this growth rate is declining.

My point is that any game designer should make some calculations and look if his scenario is plausible or totally ridiculous. More importantly those calculations help in game design, because you can simulate various scenarios, especially if it is any kind of strategy or simulation game. Otherwise there will always be at least one nitpicker like me, who will quickly make some calculations and put the results in Internet for everybody's amusement.