are you supposed to build food production buildings in high fertility regions

https://i.imgur.com/NJFK0P5.png

So in the manual it says fertility influences base food production. But its not a multiplier, so any farms or ranches (which one is better?) you build there are just added to it. But fertility increases "regional supply cap". And only after thats filled up, does it go into storage. Is that was contributes to the global food surplus? which i still dont understand cause my regions are all negative food production in the description but I still get a surplus globally sometimes. and i presume replenishment is based on regional food production, not some global number? so you need to have food stored in every region where you sent your armies to replenish? so maybe its bad to build farms in high fertility regions cause it takes longer for them to fill up ? or am i not understanding the whole system and mixing up supplies with settlement food requirements. perhaps high fertility regions with farms in them give more leeway to export food to other places in emergencies?

It's not a multiplier. Supplies and food are unfortunately separate mechanics. Replenishment is based on supplies and population, and you'll take attrition if your global food supply is also negative. Attila has some better fertility and food mechanics, but it doesn't work that way in Rome 2. Basically, build food buildings where ever you want, as long as your global food supply is positive. The supply system is separate from this, though some food buildings influence your supply production as well.