Apomorphy and synapomorphyIn phylogenetics, an apomorphy (or derived trait) is a novel character or character state that has evolved from its ancestral form (or plesiomorphy). A synapomorphy is an apomorphy shared by two or more taxa and is therefore hypothesized to have evolved in their most recent common ancestor. In cladistics, synapomorphy implies homology. Examples of apomorphy are the presence of erect gait, fur, the evolution of three middle ear bones, and mammary glands in mammals but not in other vertebrate animals such as amphibians or reptiles, which have retained their ancestral traits of a sprawling gait and lack of fur.
Holomorphic vector bundleIn mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle. By Serre's GAGA, the category of holomorphic vector bundles on a smooth complex projective variety X (viewed as a complex manifold) is equivalent to the category of algebraic vector bundles (i.
SpiraliaThe Spiralia are a morphologically diverse clade of protostome animals, including within their number the molluscs, annelids, platyhelminths and other taxa. The term Spiralia is applied to those phyla that exhibit canonical spiral cleavage, a pattern of early development found in most (but not all) members of the Lophotrochozoa. Members of the molluscs, annelids, platyhelminths and nemerteans have all been shown to exhibit spiral cleavage in its classical form.
Plesiomorphy and symplesiomorphyIn phylogenetics, a plesiomorphy ("near form") and symplesiomorphy are synonyms for an ancestral character shared by all members of a clade, which does not distinguish the clade from other clades. Plesiomorphy, symplesiomorphy, apomorphy, and synapomorphy, all mean a trait shared between species because they share an ancestral species. Apomorphic and synapomorphic characteristics convey much information about evolutionary clades and can be used to define taxa. However, plesiomorphic and symplesiomorphic characteristics cannot.
