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Unrooted trees discovered independently in philology and phylogenetics: a remarkable case of methodological convergence

We report on the only known case of independent discovery of unrooted trees in a historical science outside of biological systematics. The method of textual criticism (ecdotics, i.e., the building of text-version genealogies) created by French philologist Henri Quentin (1872–1935) proposes the use of a type of branching scheme equivalent to unrooted trees in phylogenetics. Because Quentin's method has never become the prevailing paradigm in philology, his insight into unrooted trees has not been noticed in previous studies comparing philology and phylogenetics. In fact, the modern use of unrooted trees in philology is seen as imported from phylogenetics. Quentin's procedure starts by building an unrooted tree (‘chain’) expressing the network of text versions (taxa) based on ‘variants’ (equivalent to unpolarized character states). Such undirected scheme is then rooted on the basis of extrinsic temporal information, thus resulting in a complete (rooted) hypothesis of relationships. Quentin asserts that the building of an unrooted tree precedes the determination of its orientation (rooting) and that the two procedures reflect distinct levels of structural organization, relying on different assumptions. Henri Quentin fully grasped the implications of time-reversible properties of unrooted trees and associated characters, in striking prescience of the same concepts developed in phylogenetics some 45 years later. The two versions of unrooted trees were developed entirely independently of each other and such convergence is testimony to the formal efficiency of approaching historical reconstruction in unrooted and rooted dimensions.