treeness

Definitions

noun nonce word The essence of what it means to be a tree; the qualities that make a tree what it is.
noun genetics The suitability of an evolutionary tree for representing the structure of a population; the degree to which a population structure can be accurately described as a tree of descent, with different branches evolving independently after they split.
noun graph theory The condition of being a tree; acyclicity and connectedness.

tree +‎ -ness

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We have only to uncover and know our own "treeness".

Kay Goldstein: Our Healing Nature 2008
He painted the "treeness" of the tree, as a modern critic has admirably expressed it.

Concerning the Spiritual in Art Wassily Kandinsky 1905
Dan Keathley fields calls from commercial growers who, by dumb luck, find themselves with the Platonic ideal of Christmas-treeness: a Douglas fir or Scotch pine with a straight trunk, thick needles that can hold ornaments, limbs slanted up at a perfect 45-degree angle, an ideal conical shape and strength.

Science Of The Season 2008
I believe some said a seedling has treeness in it.

WBUR and NPR - On Point with Tom Ashbrook 2009
It isn't that Libow worships the tree for its grand treeness.

North Coast Journal Comments 2009
The pigs, pursuing their pigness like an acorn inevitably pursues its oak treeness, end up becomingly unwitting workers on Saletin's farm: they turn the compost pile that is the floor of Saletin's cattle barn.

Bitch | Lab 2008