your best food city will be the fastest growing - but not for very long, as the surplus gets reduced from growth. So to maximize food trade, you need a city with very large surplus that never grows. How? by having one city specialize in food - and then only build colonists there, so city never grows but the base is high.
Nono. This is flat out incorrect. Larger cities grow slower because they have larger food bins, not because they have smaller surpluses. In fact, mature cities in the 15s often have extremely large surpluses if they're farm-focused.
Every citizen consumes 2 food, but every additional citizen that gets put back onto a farm creates more base surplus, not less. This is transparently because farmers generate more food than they eat, so the more farmers in a city, the more surplus it generates as it increases in size.
A size 3 city with 3 farms at +4 food each generates 6 surplus food. A size 10 city with +4 food farms generates 20 surplus food. When linked to a city that generates no surpluses whatsoever, the 10 size city will consistently generate +7 food on the route, and it'll only get bigger as the city works more food tiles or otherwise gets more food.
The incoming value is definitely not maxxed at 3. I've seen larger incoming yields than that!
It is notable to say that omniclast3 here is completely incorrect:
It seems incredibly bizarre that the yield is always given to the outgoing route, regardless of the direction of the difference in food supply. So if my 1 pop new city is sending food to 20 pop cap, it generates an insane amount of food/prod for... the cap. How does that make sense?
Not to mention the strats it seems to motivate. Here's what I propose: build three central cities and grow them big and powerful. Then build a pile of incredibly crappy 1 pop cities on the worst tiles you can find, make sure they never grow or expand borders. Buy depots and autoplants in all your crappy cities and send the 3 TRs from each of them to each of your 3 core cities. Since the larger bonuses will always go to the 3 big cities, the gap in pop will keep growing rapidly, as will the food/prod bonuses to your 3 big cities. If I may be permitted an anology... it is a free energy machine.
Makes no sense. Higher benefit should always go to the smaller food/prod city, regardless of whether it's incoming/outgoing.
If the surplus is what is counted, then it doesn't matter one whit what size the city is. What matters is how much food it's drawing from its tiles. So long as it remains food-neutral or food-negative, then the food route will always be based purely on the surplus generated by the food city, even when the sending city is size 20.
This is actually a good argument for specialization. You do NOT want to build too many food buildings in those cities not only to keep the route large, but also because you will presumably be building something more beneficial.
Likewise, a Production City will almost always be a good target for hammer-poor cities so long as they remain hammer poor. They will boost that city's production significantly, and gain no small amount of hammers in the process.
What this means is that you now have a reason to keep the food surplus in your big farm cities high even when their bins grow large enough for them to not individually benefit from the food directly - instead of assigning specialists, you distribute the food to all your other cities who will all presumably be building something other than farms.
The farm city will benefit directly from the incoming hammers and the other cities benefit by not having to work farm tiles at all, especially if they're sequentially targeted for growth by large outgoing Food Routes from the main farm cities.
So you don't need to adjust the yields manually. So long as you improve the tiles intentionally, the governor takes care of it all for you automatically.