Thanks for the question, Littlek. Good to get specific
I was searching for words in using "whole organismic" --for a meaning that included activities and benefits to trees-as-entire organisms. Benefits not mainly associated with leaves and potentially extending into the environment--such as shading the ground below to keep roots cooler and presumably damper.
People have brought up some fine examples in response to my question. I'm grateful for the mind-opening and connecting of "known" fragments--respiration, shade, etc. (I don't think self-mulching would support the tree much nutritionally, since it already took energy to make the leaves and whatever came back from the tree's own leaves would not support it without imported matter. Lucky leaves blow in from afar.
I am still wondering where sap gets stored and how stored sap gets used precisely. I've been told and read it's store in roots and "other" places. I doubt my grandkids would find this topic as interesting as I do at the moment.
The "fact" that sap contains sugar--useful for other purposes than our pancakes seemed to me to get undertold. So are weeds and flowers out there making sugar too? It seems sugar is the product of photosynthesis and trees making it so furiously and storing it allows them to survive winter when marigolds go down and instead make seed in fall.
So life forms need sugar to burn and bind into their needed fluids and parts, along with certain gases in the air. This would extend into my idea of whole-organismic. Whatever side chemicals get made with sap or sugars.
I found one site on the web that contained less information than I hoped within a plethora of words and evaluations. But it may have been stabbing at part of what interested me in this subject. I may edit that page into an unimbellished few paragraphs and see what it yields. It did have some info, but there was room for more of what you folks brought up and also room for follow-through in a systems and ecological sense. Personally, I didn't care for the fluff.