Making an automated loop for food with fishes (all caviar going to incubator) slowly eradicates your fish pond. You have to keep hunting new fish from further and further away faster than anything else is making you expand.

Balance tested. On average, in half an hour the amount of food can be increased by 80%. If you are short of food, try spending less. For example, stop using craft with your hands. If you want less hardcore, use cheat mods that increase the amount of food produced for the same initial resources.

In my game, using Assembly Machine 2 to process all of the fish (including the ones not caught from our fish pool) with all caviar going to an incubator and half of the food (unless the buffer is full) to a feeder and half into food for players. The fish population decreases consistently. Is that intended? We've 3 players on the server.

The number of players does not affect the fish.
In 1/3 of the cases, the caviar disappear in the incubator. If this does not happen, then a tiny fish appears, while in 1/3 of the cases a second tiny fish appears. That is, out of 100 caviar, an average of 89 fry will appear. From an adult fish (see recipe) on average we get 1.95 (almost 2) units of caviar. As a result, for one cycle on average we get an increase in the fish population of 73%.

How large area can one feeder cover? Perhaps the fish are dying outside it's coverage then? Our fish population just keeps declining every time I add fish to it.

Most likely. Feeding area 4x4 cells. Added to the description of the feeder.

Well ye, that explains. Think you could also add the area highlighting like the drills have?

I’ll add it when I learn how to do it.