How is steelhead carrying capacity even defined? Is there a mathematical equation? Does it vary with the volume of water per time times the time of the run? I've seen hundreds of fish stacked like cordwood moving up river. I've also seen so many salmon in the river they look like they are gasping for oxygen.

The number of returns equals the hatchery escapement plus the number of native and hatchery mixed fish spawning in redds. There's x number of smolts leaving the hatchery plus y number of fry leaving the beds. Maybe some of each die of starvation for competition over food in the river and the salt. There's predication of both hatchery and native. Birds and other fish have to eat. The hatchery fish provide a food source that reduces the number of native fish consumed.

Then there is the mortality caused by pollution, environmental and climate factors or disease in the ocean. Then there is take. There can be obstructions like culverts and dams that prevent the fish from returning.

Then there is the genetics which could affect survivability.

Is there a bio here that has a math degree?