= Solution
\b[A node-based name selects a common ancestor from included reference taxa; a branch-based name selects a lineage by including one reference and excluding another.] Both designate a <clade>, so both include every descendant of the selected ancestor. The distinction concerns the rule locating that ancestor, not whether descendants are included. Neither requires its members to share a particular modern appearance.<A new phylogenetic data standard for computable clade definitions: the Phyloreference Exchange Format (Phyx) by Gaurav Vaidya and others>[Fig. 1 and Introduction; minimum- and maximum-clade definitions and internal/external specifiers]{ref}
For a <node-based clade definition>, choose internal <phylogenetic specifiers> $A$ and $B$. Let $m(A,B)$ be their <last common ancestor>, and let $D(v)$ include ancestor $v$ and all its descendants. Then the named group is
$$
N(A,B)=D\bigl(m(A,B)\bigr).
$$
It is the smallest <clade> containing both references. For a <branch-based clade definition>, choose an internal reference $A$ and an external reference $Z$. The named group is the largest <clade> containing $A$ but excluding $Z$: organisms sharing a more recent common ancestor with $A$ than with $Z$. On a rooted <phylogenetic tree>, this selects the $A$-side lineage after its separation from the lineage containing $Z$. These are also called <minimum-clade definitions> and <maximum-clade definitions>. The names describe inclusion constraints, not distances measured from branch lengths.<A new phylogenetic data standard for computable clade definitions: the Phyloreference Exchange Format (Phyx) by Gaurav Vaidya and others>[Fig. 1 and Introduction; minimum- and maximum-clade definitions and internal/external specifiers]{ref}
An informative avian node example is \b[crown <Aves>], here anchored to living <ostrich> and <sparrow> lineages. Their <last common ancestor> is the ancestor of living <Palaeognathae> and <Neognathae>; the name includes that ancestor and all descendants, including extinct descendants within either branch. An informative branch example is \b[<Panaves>], the avian <total group>: the largest <clade> including living <birds> but excluding living <crocodilians>. With standard <archosaur> relationships it includes <Aves>, extinct avian stem relatives, nonavian <dinosaurs> and <pterosaurs>. The external reference is decisive: the definition asks which side of the <bird>–<crocodilian> split an organism occupies, not whether it flies. These crown and total usages were distinguished explicitly in the avian nomenclatural analysis by <Jacques A. Gauthier> and <Kevin de Queiroz>.<Feathered dinosaurs, flying dinosaurs, crown dinosaurs, and the name “Aves” by Jacques A. Gauthier and Kevin de Queiroz>[pp. 9–11 and 24–28; classes of definitions, crown versus total groups, Aves and Panaves]{ref}
Consider a simplified <cladogram> in which the <crocodilian> lineage separates first, followed on the avian side by <pterosaurs>, successive nonavian <dinosaur> branches, <Archaeopteryx>, other extinct avian branches and finally the living-bird crown divergence. <Archaeopteryx> belongs to <Panaves> but lies outside crown <Aves>. A <fossil> on the <palaeognath> branch after the <palaeognath>–<neognath> divergence belongs to both. A <crocodilian> belongs to neither. Finding a still earlier bird-line <fossil> would extend the known <fossil> history of <Panaves> without automatically changing the age or known membership of crown <Aves>. This example is schematic: it illustrates how definitions operate and is not a claim that any sampled <fossil> is the direct ancestor of another.
Two distinctions prevent mistakes. First, a <node-based clade definition> need not define a <crown group>: internal references can be extinct, as in a deliberately broader Archaeopteryx-inclusive node definition. Likewise, a <branch-based clade definition> need not define an entire <total group>; using a nonavian <theropod dinosaur> as the excluded reference selects a much narrower avian-lineage branch than excluding <crocodilians>. Second, a <stem group> is not synonymous with the branch-defined <total group>. The total includes the crown; the stem alone excludes it and normally forms a succession of extinct branches.
The definition must therefore accompany an ambiguous name. Historical uses of <Aves> have included the living-bird crown and more inclusive <fossil> assemblages; <Avialae> has also received differing definitions. Discovery of <feathers> in a nonavian <theropod dinosaur> changes the inferred distribution of a <phylogenetic character>, but does not by itself place the animal inside crown <Aves>. Conversely, loss of flight does not remove a crown descendant from its <clade>. \b[A name supplies an ancestry rule; anatomical and molecular evidence supply the tree on which that rule is applied.] Uncertain <fossil> placement produces uncertain membership even when the definition is precise.
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