It depends on how much you look into the forest floor. Many trees in a mature forest actively poison the soil to reduce competition for nutrients. Look at a pacific coastal rain forest (or Star Wars' Endor) and you see big trees and an open forest floor. The big trees do not allow smaller/medium trees to get going.(Some of this is lack of sunlight, but also soil PH.) So a salmon-dependent tree could adapt to prevent other plants from getting ahold of salmon nutrients.

Similar to the nitrogen from salmon on the coasts, I have read about plants getting calcium from deer/elk/moose antlers. You would think it wasn't much but then you realize how depleted a forest can be of calcium. It can put a halt on plant growth. Migrating deer then become a significant source of calcium movement.