The possibility of undertaking matrix/optimization-free cladistic analysis is one of the most interesting ideas to emerge in the last few decades from within the field of systematics, particularly in the development of cladistics. The purpose of this paper is to design further opportunities and prospects made possible by eliminating the matrix as the primary source of data representation. The main focus of this paper is to outline a supertree approach that, if combined with the methodology of three-taxon statement analysis (3TA), may be seen as a powerful heuristic alternative to the application of conventional matrix/optimization-based methods used for the analysis of systematic data, and which currently forms the mainstream of contemporary phylogenetics. Using the average consensus technique as an example, we demonstrate explicitly that methods of construction of supertrees may be applied to the array of three-taxon statements (3TS), especially if the latter are represented initially as minimal trees, not as binary matrices, as was originally proposed. The 3TA-average consensus procedure recognizes solely ‘reversal’-based clades and is also free from the potential issues of 3TA, such as the data distortion due to inability to handle putative reversals. Thus the main benefit of this new approach over the traditional one is its accuracy and advantages when implementing the Hennigian views on the cladistic analysis that states that all characters must be a priori polarized before the best fitting tree is found. We also found that the average consensus technique (as well as other median supertree calculation techniques) is purely typological and we stressed that this simple point had never been mentioned before. We proposed that the average consensus of 3TSs (as well as any median consensus of 3TSs) may be viewed as a median type and the extended procedure of the traditional 3TA may be treated as a typology of the relations. The connection between median type and phylogeny may be established only indirectly. The heuristic scientific typology may be derived within a completely metaphysics-free context. Goethe’s idea of “Urphenomenon” and Max Weber’s “Ideal Types” are mentioned as examples of heuristic metaphysical-free typological frameworks.

中文翻译：

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关系的类型学

进行矩阵/无优化的克拉德分析的可能性是最近几十年来从系统学领域，特别是在克拉德开发中出现的最有趣的想法之一。本文的目的是通过消除矩阵作为数据表示的主要来源来设计更多的机会和前景。本文的主要重点是概述一种超级树方法，如果将其与三分类子语句分析（3TA）方法相结合，则可以被视为替代传统的基于矩阵/优化的方法的强大启发式替代方法。对系统数据的分析，目前已成为当代系统发育学的主流。以平均共识技术为例，原来作为最小的树，而不是最初提出的二进制矩阵。3TA平均共识程序仅识别基于“反转”的进化枝，并且没有3TA的潜在问题，例如由于无法处理假定的反转而导致的数据失真。因此，这种新方法相对于传统方法的主要好处是，在对分类分析执行Hennigian视图时，它的准确性和优势在于，在发现最佳拟合树之前，必须对所有字符进行先验极化。我们还发现，平均共识技术（以及其他中位数超树计算技术）纯属类型学，并且我们强调，这一简单点之前从未提到过。我们建议将3TS的平均共识（以及3TS的任何中位数共识）视为传统3TA的中位类型和扩展程序可以被视为这种关系的类型学。中位类型和系统发育之间的联系只能间接建立。启发式科学类型学可以在完全无形而上学的背景下得出。提到歌德的“ Urphenomenon”思想和Max Weber的“理想类型”作为启发式无形而上学类型学框架的例子。