treeness

From tree +‎ -ness.

• enPR: trēʹnĭs, IPA^(key): /ˈtɹiːnɪs/
• Rhymes: -iːnəs

treeness (uncountable)

1. (nonce word) The essence of what it means to be a tree; the qualities that make a tree what it is.
   • 1912, D. S. MacColl, "A Year of 'Post-Impressionism'", in The Living Age, volume CCLXXIII, The Living Age Company, page 163:

     A tree may, for the imagination, present forcibly one of its qualities at a time; it may be a green dome of shade on a hot day, a ladder of retreat for a man from the attentions of a mad bull, a peg on which an apple hangs, a screen for an assassin, a choir for birds; and its own business of spreading out its million pores to the air and propagating its kind, which comes nearest to being its “treeness,” may be what occupies the artist least and bores him most.

   • 1999 April 18, Sans Will, “Re: DCC and Logic add a bit of philosophy and voila!..”, in soc.culture.vietnamese‎ (Usenet):

     A word represents the entity but not THE entity itself. "tree" is not a tree, you can call it "ca^y" or whatever but the conceptual meaning of treeness stays the same.

   • 2012, Arthur C. Danto, “Replies to Essays”, in Mark Rollins, editor, Danto and His Critics, 2nd edition, Wiley-Blackwell, →ISBN, page 290:

     Let us say that the pigeons learned to recognize treeness, in the sense that they quickly enough learned to differentiate whatever exemplified treeness from whatever did not.

2. (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.
   • 1974, L. L. Cavalli-Sforza, A. Piazza, “Analysis of Evolution: Evolutionary Rates, Independence and Treeness”, in Theoretical Population Biology, volume 8, page 159:

     If factors that contribute to a tree-like pattern of the variance–covariance matrix dominate the evolutionary picture over those that tend to destroy it, one can expect treeness to be reasonably high. Only if this is true, reconstruction of the evolutionary process by tree analysis and a tree representation for descriptive purposes can be useful.

   • 1999, Alan R. Templeton, “Human Races: A Genetic and Evolutionary Perspective”, in American Anthropologist, volume 100, pages 638–639:

     The computer programs used to generate “trees” from genetic distance data will do so regardless of what evolutionary factors generated the distances. It is therefore the obligation of the users of such programs to ensure that the genetic distance data have the properties of treeness before representing their data as a tree.

   • 2007, Gísli Pálsson, Anthropology and the New Genetics, Cambridge University Press,, →ISBN, page 184:

     Failing to statistically test for treeness, they reify the evolutionary trajectories assumed at the outset.

3. (graph theory) The condition of being a tree; acyclicity and connectedness.
   • 1998, Joseph O'Rourke, Computational Geometry in C, 2nd edition, Cambridge University Press, →ISBN, page 174:

     …such a tree can be built up incrementally by adding the shortest edge not yet explored, which also maintains treeness (acyclicity).

   • 2010, Massimo Buscema, Pier L. Sacco, “Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG)”, in Vittorio Capecchi et al., editors, Applications of Mathematics in Models, Artificial Neural Networks and Arts, Springer, →ISBN, page 265:

     …every link that gives rise to a cycle into the graph (viz., that destroys the graph’s “treeness”) is eliminated….

   • 2011, Matthias Irmer, Bridging Inferences, De Gruyter,, →ISBN, page 139:

     To save the treeness of discourse structure – and with that the supplied computational advantages – Egg and Redeker (2008) argue that many apparent crossed dependencies reflect anaphoric relations on the level of discourse cohesion…. They opt for a pure tree structure for discourse relations, keeping anaphoric relations apart.

• serenest, sneerest