A laid-back trip through the Hennigian Forests

Abstract

BackgroundThis paper is a comment on the idea of matrix-free Cladistics. Demonstration of this idea’s efficiency is a major goal of the study. Within the proposed framework, the ordinary (phenetic) matrix is necessary only as “source” of Hennigian trees, not as a primary subject of the analysis. Switching from the matrix-based thinking to the matrix-free Cladistic approach clearly reveals that optimizations of the character-state changes are related not to the real processes, but to the form of the data representation.MethodsWe focused our study on the binary data. We wrote the simple ruby-based script FORESTER version 1.0 that helps represent a binary matrix as an array of the rooted trees (as a “Hennigian forest”). The binary representations of the genomic (DNA) data have been made by script 1001. The Average Consensus method as well as the standard Maximum Parsimony (MP) approach has been used to analyze the data.Principle findingsThe binary matrix may be easily re-written as a set of rooted trees (maximal relationships). The latter might be analyzed by the Average Consensus method. Paradoxically, this method, if applied to the Hennigian forests, in principle can help to identify clades despite the absence of the direct evidence from the primary data. Our approach may handle the clock- or non clock-like matrices, as well as the hypothetical, molecular or morphological data.DiscussionOur proposal clearly differs from the numerous phenetic alignment-free techniques of the construction of the phylogenetic trees. Dealing with the relations, not with the actual “data” also distinguishes our approach from all optimization-based methods, if the optimization is defined as a way to reconstruct the sequences of the character-state changes on a tree, either the standard alignment-based techniques or the “direct” alignment-free procedure. We are not viewing our recent framework as an alternative to the three-taxon statement analysis (3TA), but there are two major differences between our recent proposal and the 3TA, as originally designed and implemented: (1) the 3TA deals with the three-taxon statements or minimal relationships. According to the logic of 3TA, the set of the minimal trees must be established as a binary matrix and used as an input for the parsimony program. In this paper, we operate directly with maximal relationships written just as trees, not as binary matrices, while also using the Average Consensus method instead of the MP analysis. The solely ‘reversal’-based groups can always be found by our method without the separate scoring of the putative reversals before analyses.

Temporal area approach for distributional data in biogeography

“…The hypothetical example (Tables 1-3) was formatted in atemporal, fixed temporal and temporal matrix forms. For each matrix, three analytical approaches were used to analyse the data: (i) the standard maximum parsimony (MP) approach (Farris, 1983; reviewed by Kitching et al, 1998), (ii) the three-taxon statement analysis (3TA; Nelson and Platnick, 1991; reviewed by Kitching et al 1998;Williams and Ebach, 2008) and (iii) the average consensus method (Lapointe and Cucumel, 1997;Lapointe and Levasseur, 2004) as used by Mavrodiev et al (2017). All MP analyses (including bootstrap resampling) were conducted in PAUP* 4.0a (Swofford, 2002) as described by Mavrodiev and Madorsky (2012) and Mavrodiev et al (2017).…”

“…Next, the arrays of the rooted trees were imported to Clann version 4.1.5 (Creevey, 2004;Creevey and McInerney, 2009) to calculate the average consensus tables. All average consensus analyses were performed in PAUP* 4.0a (Swofford, 2002) as described by Mavrodiev et al (2017). In all cases, the optimality criterion of the best tree is defined as 'Balance Minimal Evolution' (BME) (Desper and Gascuel, 2002;Swofford, 2002).…”

“…All MP analyses (including bootstrap resampling) were conducted in PAUP* 4.0a (Swofford, ) as described by Mavrodiev and Madorsky () and Mavrodiev et al. ().…”

“…Conventional binary matrices were converted into fractionally weighted three‐taxon statements (reviewed by Kitching et al., ; Williams and Ebach, ) using the program TAXODIUM version 1.2 (Mavrodiev and Madorsky, ) (command: inputfilename –ib –ob –og –fw –nex ). The binary matrix was then reformatted as a parenthetical matrix using FORESTER version 1.0 (Mavrodiev et al., ) (command: ruby trees.rb infilename ). A parenthetical matrix retains a hierarchical structure, thereby rooting all characters as individual trees (see Mavrodiev et al., ).…”

“…The binary matrix was then reformatted as a parenthetical matrix using FORESTER version 1.0 (Mavrodiev et al., ) (command: ruby trees.rb infilename ). A parenthetical matrix retains a hierarchical structure, thereby rooting all characters as individual trees (see Mavrodiev et al., ). Next, the arrays of the rooted trees were imported to Clann version 4.1.5 (Creevey, ; Creevey and McInerney, ) to calculate the average consensus tables.…”