Understanding population for the novice

The population on a planet is directly the amount of raw production. The buildings, bonuses, and economic settings applied to it then produce the end result of manufacturing, research, and wealth. Thus, the bigger your population the bigger your output, although bad approval will penalize it.

Example: You have a planet with 10 pop and 1 basic factory and you have set your economy to 50% manufacturing, 30% research, and 20% wealth. The 10 pop give you 10 units of raw production. This is split into 5 manufacturing, 3 research, and 2 wealth. The factory gives a +25% bonus to manufacturing so your total from this planet is 6.25 manufacturing, 3 research, and 2 wealth. If the population increased to 12 you'd get 7.5 manufacturing, 3.6 research, and 2.4 wealth.

The "clumps" of buildings of similar type give you adjacency bonuses that increase the effect of the building.

OK, thanks.

 I do understand the benefit of adjacency. To clarify: I meant on more an empire wide, rather than on a planet by planet basis. I have seen, in most games I have played, the AI pretty much devote most of a world to farming. Therefore, is this a boost to the sum amount of empire-wide raw production, or is it merely localised to that one planet?

Thanks again!

Building farms on a planet increases raw production on that planet only (well, and the empire's total raw production, of course). Nowheresville IV and Backwater II get no (direct) benefit from the 72 billion people on Overpopulated V, unless you happen to be into the "build a colonizer or transport at a high population planet and land them at low population planets to transfer population around" game.

I don't know that I understand the question. To me, the answer to each part of this question is yes; after all, increasing the raw production on one planet cannot help but increase the sum amount of raw production in the empire, and yes, only the planet where the farms are built sees any direct benefit from the farms.

By "sum amount of empire-wide raw production," do you mean something more like what Enhanced Production gives you (+1 production on all planets) than the sum of the production values of all planets in the empire? That is a very uncommon bonus; Enhanced Production is the only commonly available means of obtaining a flat empire-wide production bonus that I can think of, and if I recall correctly only the Thalan tech tree offers another flat production bonus that applies to every planet in the empire, and that's from a one-per-faction wonder.

Localised. Planetary output-enhancing buildings apply to the planetary population only.

"Half farms, half factories" (or labs, or market places) is actually a quite powerful mix. The factories only multiply the raw production but don't add to it. A small raw production multiplied by a big bonus can still be less than medium raw production multiplied by a medium bonus. The actual optimum depends on the planet layout, available bonuses, and your need for special buildings.

That said, the AI is notoriously bad in building its planets, so if you see it doing something stupid it's probably because it is stupid.

(According to those who have opted in to the beta testing, the soon-to-be-released v1.3 has a bit smarter AI, and Stardock says the v1.4 will see big improvements in the AI.)

No, you have understood perfectly. Thank you, that gives me a much clearer understanding.

I thought re the AI making some silly choices. I know it's still a work in progress, but it has been funny observing some generally good behaviours and then seeing stupid crap like a planet devoted almost entirely to some weird baby making farm.

Which brings me to another thought. I have been slowly learning the ropes an all. When I started playing at release, I gathered that the idea was to specialize a planet, but I did not utilize food production, etc. As I have learned, I began attaching one farm to every colony after becoming aware that having a higher population does actually affect certain outputs in this game. 

The 1/1 approach you describe sounds appealing! I'll give it a try!

Throw in some approval buildings, too, and remember to pick up the morale boosting techs. Keeping the pop happy gives a sizable bonus.

2 things to add 

1) population also affects your voting power in the UP 

2 ) dont forget to add economic starbases each econ SB adss 10% to raw prod as well as having manu/res/econ bonus's and morale bonus's. On top of that with the right techs you can stack 12 covering a single planet that more then doubles raw production before adding any of the other bonus's