anthropic - you ask
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Given a set food budget, would it be best to focus on feeding smaller pellets to the BG, or big pellets to the LMB?

Obviously the big pellets will benefit more the LMB that eat them, but not all are feed trained. Most especially wild bred LMB may not come to the feed much. But those that eat big pellets, may ease off on BG predation, helping that population.

The small pellets help the BG that serve as LMB food, of course. Some LMB eat small pellets, too, but most of them end up in BG bellies. One pound of BG is nowhere near as nourishing bass growth as one pound of fish food, but on the other hand BG reproduce in large numbers & utilize natural resources in addition to man made.

What are your thoughts in a pond environment? Does it depend on the carrying capacity?

Your questions are a complex topic to discuss. There are lots of factors involved. Other members can also provide what they have learned on this topic as the thread continues. Here are a few of my initial thoughts.
1. Lots of experience has taught me to first begin with pellet trained fish. Although I have done it both ways of training pond fish to eat pellets while also buying pellet raised fish. The 2nd way is easier and quicker producing the fastest results when someone else pellet trains the stocker fish. Training fish to eat pellets takes time and it is helpful to use the correct training methods which helps a lot for success. Correct methods to train fish to eat pellets is a complete article by itself.

2. If you want some pellet trained fish in a all natural food pond, I suggest that you remove any number of "wild" fish and replace them in equal numbers with pellet trained fish. This relates to carrying capacity. Adding pellet eating fish helps speed the conversion toward a pellet eating fishery. IMPORTANT - The older a pellet raised stocker fish is when purchased,,,,,, the more likely it will remain eating pellets after it is stocked into your pond.

3.. If you are looking to best enhance the whole fish community IMO it is best to feed all the fish species and sizes. This quickly benefits the whole fish community. Usually this means using various sizes of pellet feed for the various sizes of fish. For my small fisheries I use basically one size pellet 1/4". I grind pellets to various sizes for minnows and soften pellets for 3"+ fish. I have learned to soften the pellets so 3" and 16" fish can eat the same soft squeezable pellet. This eliminates buying several sizes of pellets. All my fish seem to grow very well.

4. As far as "What are your thoughts in a pond environment?" Pellet feeding esp using high quality pellets grows more fish pounds and bigger fish faster. This concept is basically the same as raising most all animals for food or your other use. Animal husbandry.

5. There are numerous advantages and disadvantages to a natural fed fishery and a supplemental pellet fed fishery.

6. For best results of a natural and pellet fishery carrying capacity requirements need to be followed for getting or achieving the best results for ones GOALS. Goals have to be realistic based on Mother Nature's Laws.