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 ¼. The branches of this tree of trees suggest new categories of tree-thinkers that could have been overlooked by historians or systematists.

Categorizing ideas about trees: a tree of trees.

The aim of this study is to explore whether matrices and MP trees used to produce systematic categories of organisms could be useful to produce categories of ideas in history of science. We study the history of the use of trees in systematics to represent the diversity of life from 1766 to 1991. We apply to those ideas a method inspired from coding homologous parts of organisms. We discretize conceptual parts of ideas, writings and drawings about trees contained in 41 main writings; we detect shared parts among authors and code them into a 91-characters matrix and use a tree representation to show who shares what with whom. In other words, we propose a hierarchical representation of the shared ideas about trees among authors: this produces a "tree of trees." Then, we categorize schools of tree-representations. Classical schools like "cladists" and "pheneticists" are recovered but others are not: "gradists" are separated into two blocks, one of them being called here "grade theoreticians." We propose new interesting categories like the "buffonian school," the "metaphoricians," and those using "strictly genealogical classifications." We consider that networks are not useful to represent shared ideas at the present step of the study. A cladogram is made for showing who is sharing what with whom, but also heterobathmy and homoplasy of characters. The present cladogram is not modelling processes of transmission of ideas about trees, and here it is mostly used to test for proximity of ideas of the same age and for categorization.