Classical Morphology of Plants as an Elementary Instance of Classical Invariant Theory

It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT). Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential “accurate morphological method”. However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers). We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the “theory of axilar bud” is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent

Ancestral State Reconstruction Reveals Rampant Homoplasy of Diagnostic Morphological Characters in Urticaceae, Conflicting with Current Classification Schemes

Urticaceae is a family with more than 2000 species, which contains remarkable morphological diversity. It has undergone many taxonomic reorganizations, and is currently the subject of further systematic studies. To gain more resolution in systematic studies and to better understand the general patterns of character evolution in Urticaceae, based on our previous phylogeny including 169 accessions comprising 122 species across 47 Urticaceae genera, we examined 19 diagnostic characters, and analysed these employing both maximum-parsimony and maximum-likelihood approaches. Our results revealed that 16 characters exhibited multiple state changes within the family, with ten exhibiting >eight changes and three exhibiting between 28 and 40. Morphological synapomorphies were identified for many clades, but the diagnostic value of these was often limited due to reversals within the clade and/or homoplasies elsewhere. Recognition of the four clades comprising the family at subfamily level can be supported by a small number carefully chosen defining traits for each. Several non-monophyletic genera appear to be defined only by characters that are plesiomorphic within their clades, and more detailed work would be valuable to find defining traits for monophyletic clades within these. Some character evolution may be attributed to adaptive evolution in Urticaceae due to shifts in habitat or vegetation type. This study demonstrated the value of using phylogeny to trace character evolution, and determine the relative importance of morphological traits for classification