I am playing v0.8.0. I am still having population problems. The village is producing roughly 2 babies a year, seems like some years 0 babies. So my village is in constant population decline. Immigration is just keeping up with the few deaths a year. Seems like something is off with the coding equations. With 100 Adults, the town should be having 10 babies per year, I would think. My village has become stagnant at 300 villagers.
You only have 4 months of food, you need at least 6 months. Lack of food for your villagers reduces their fertility and reduces immigration.
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Thank You SO MUCH for telling me! I had no idea… 
Gonna have to pull some other professions to get the food storage higher.
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Also, don’t expect miracles. With an infant mortality rate that could reach 50% before the first birthday, Medieval Era population growth was more like 2 - 3% than 10% per year, effectively. As @perdix said, keep your food stocks above 6 months’ worth, keep a bunch of ‘extra’ housing available, and the combination of births and immigration can approach 5%. I’m getting 8 - 12 immigrants a year for a population that just went over 300, with another 3 - 4 births every year. I’m getting that with an average 8 - 9 months’ food supply and about 10 - 15% extra housing available. My understanding is that if you jack up the extra housing to 25 - 50% and keep the food stocks up your population can increase even faster, but the current rate is just about right for my style of play (slow but sure!)
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It does seem as if Crate have changed something though. Several of us have hit population plateaus where no one or only very few immigrants come.
Yes from out play testing of 0.8.0 we needed to have lots of empty housing spots, like double the number of current villagers and then 6-8 months of food after taking away spoilage.
I didn’t like it at first but I like it more now having played for quite awhile. It really makes you concentrate during the early game but if people die off due to animals or other things then it can be quite hard to get your population back up. I think it could be tweaked to be a bit easier. Cheers.
It’s definitely something that I have to manage more closely in the early game, particularly when you’re needing every able body to maintain food and wood reqs.
What ended up happening to my latest was the forager, night next door to the hunter, got sick and didn’t seem to understand that they had everything to cure them right in their cabin, nor did the sick hunter next door realize he just had to go next door to get what he needed and they both ended up dying, which compounded the population crunch early on.
I am unable to get my population above 1000. I have 12 months food supply, people are quite happy in all of the categories. What am I missing ?
Welcome to the forum. 
There’s a cap of 1k on population atm to help with performance. The devs expect to remove it nearer to full release of the game.