Subsplits

Subsplits are a concept used mainly in phylogenetics to describe how a split on a set of taxa restricts to a subset of those taxa. A split on a finite set X of taxa is a bipartition of X into two nonempty parts, often written as {A, X\A}. A subsplit arises when this split is restricted to a subset Y of X.

Formally, for a split {A, X\A} and a subset Y ⊆ X, the restricted partition is {A ∩ Y, (X\A) ∩ Y}. This is a subsplit of Y provided that both intersections are nonempty. If Y ∩ A is empty or Y ∩ (X\A) is empty, the restriction is trivial and usually not counted as a subsplit.

Subsplits appear in contexts where data or sampling is partial, such as when a phylogenetic tree is only partially observed or certain taxa are missing from a study. They allow researchers to reason about the relationships among the taxa that are present, without requiring full information for all taxa in X. Subsplits also play a role in the analysis of compatibility and in the construction of consensus or supertree methods, where subsplits from different datasets or subtrees are compared or combined.

Example: let X = {a, b, c, d} and consider the split {a, b} | {c, d}. Restricting to Y = {a, c, d} yields the subsplit {a} | {c, d}.

See also: split, phylogenetic tree, partial taxon sampling, supertree.