The treeness of the tree of historical trees of life.

This paper compares and categorizes historical ideas about trees showing relationships among biological entities. The hierarchical structure of a tree is used to test the global consistency of similarities among these ideas; in other words we assess the "treeness" of the tree of historical trees. The collected data are figures and ideas about trees showing relationships among biological entities published or drawn by naturalists from 1555 to 2012. They are coded into a matrix of 235 historical trees and 141 descriptive attributes. From the most parsimonious "tree" of historical trees, treeness is measured by consistency index, retention index and homoplasy excess ratio. This tree is used to create sets or categories of trees, or to study the circulation of ideas. From an unrooted network of historical trees, treeness is measured by the delta-score. This unrooted network is used to measure and visualize treeness. The two approaches show a rather good treeness of the data, with respectively a retention idex of 0.83 and homoplasy excess ratio of 0.74, on one hand, and a delta-score of 0.26 on the other hand. It is interpreted as due to vertical transmission, i.e. an inheritance of shared ideas about biological trees among authors. This tree of trees is then used to test categories previously made. For instance, cladists and gradists are « paraphyletic ». The branches of this tree of trees suggest new categories of tree-thinkers that could have been overlooked by historians or systematists.